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BOOK II

EXCURSIVE AND CRITICAL

Cum rerum natura nusquam magis quam in minimis tota sit.

Pliny the Elder.

Nowhere is the nature of things more intimately revealed than in the calculus of infinitesimals.

CHAPTER I

MARGINS AND THEIR DIAGRAMMATIC REPRESENTATION

Summary.—This chapter is devoted to a fuller examination of the principle of declining marginal significances. It is always the provocatives, opportunities, or supports of desired experiences or vents of impulse, and never those experiences themselves, that this law illustrates; but within that area it seems to be universal. It may appear, at first sight, that the claims of duty, of faith, or of humanity are not (or at least should not be) subject to any declining urgency as they are more fully met; and also that some satisfactions are habitually indulged in down to the point of satiety, whereas, according to our theory, the last and least significant increments of the things that minister to them should be less valued than increments of other things that would minister to still unsatisfied wants. But a careful examination will shew that these objections either rest on some misapprehension or are due to the fact that, under any given set of conditions, there is always a "minimum sensibile" below which conscious estimates cannot be carried. Another set of difficulties arises from a confusion between the positive and negative sign of increments of satisfaction and a positive or negative state of satisfaction. The attempt to dispel this confusion, in connection with the diagrammatic method, leads us to an examination of the reactions of various kinds of indulgence upon the organism itself and its future capacities for enjoyment. This again leads to the discovery of interesting relations between a hedonistic calculus and current moral judgments. Our method, however, does not imply a hedonistic theory of conduct. The chapter closes with some notes on the dangers and limitations of the diagrammatic method it has introduced.

The whole structure raised in the First Book of this treatise rests upon the principle of declining marginal significance as supplies increase; and though we have established and illustrated it with sufficient firmness and accuracy for the immediate purposes of that Book, yet a number of problems to which no precise answers have been given may well present themselves to the reflective reader; and the extreme importance of the principle itself makes it desirable that it should be investigated and tested, not only in its immediate applications to economic problems, but in its fuller scope. Any misgiving as to its general validity might throw a taint of suspicion on its special applications. Moreover, we shall find that the closer investigation upon which we are now to enter will throw much light upon the connection between the narrower problems of Economics and the broader problems of Sociology; or perhaps we might say, between commercial Economics and the true Political Economy, in the sense of the economy of the polis, or regulation of the resources of the community.

Let us begin by noting that in speaking of declining significance we are never dealing with the ultimately desired experiences themselves, but always with something that we value as likely to produce such experiences. Thus, we spoke of concerts which a man wishes to attend because he thinks he will derive enjoyment from them; and we saw that, other things being equal, he would value a fifth concert per week less than a fourth. We did not say that a fifth "unit of enjoyment of music" would be less valuable to him than a fourth, for our only conception of a unit of enjoyment must be a quantity of enjoyment which equals some standard amount; so that each unit, being equal to the standard, would be equal to every other unit, and to say that the fifth unit was of less value than the fourth would be to say that two amounts were equal to the same but not equal to each other. Indeed it would obviously be nonsense to say that equally desired experiences have a declining significance, for if their significance declines they are not equally desired. In the same way, if we declare that opportunities of study have a declining value to a man, we may mean that if he has twelve hours a day clear for study he will attach less value to a thirteenth hour than he would to a fifth hour if he had only four; but we can hardly mean that successive acquisitions of a unit of information have a declining value, for we can hardly define a unit of information; and we cannot mean that successive increments of the pleasure or advantage he derives from the results of his study have declining value, for our only conception of equal increments of satisfaction must be increments that have the same value. And so throughout. So we are never speaking, in this connection, of units of experience, which (if we can form any conception of them at all) must be regarded as equal, but of units objectively measurable, roughly or accurately—whether by time, space, weight, number, or otherwise,—which are valued for the sake of the states of consciousness they are expected to produce or the vent they afford to impulses.

What we assert, then, is that after a certain point successive increments of external stimulants, or opportunities, produce successively declining increments of the desired internal experiences. And this principle applies not only to things provocative of delight to the senses, but to means of artistic and literary enjoyment, and even to opportunities for securing the satisfactions, or obeying the impulses, of friendship or affection. But it is sometimes asked, "Is not the case different when questions of duty are concerned? Does not duty always remain paramount, however much of your powers and resources you have already devoted to its demands? And are not the claims of compassion always superior to those of selfishness, however much you may have indulged the former and starved the latter? Is it possible for a well-regulated mind to bring about a marginal coincidence of value between the means of satisfying desires which are on essentially different ethical levels? Can such qualitative distinctions be reduced to questions of quantity?" That they are so reduced, it will be admitted, is a fact (whether lamentable or not), and in dealing with ordinary humanity we might be safe enough in assuming that such a reduction would take place; but when we find that the martyr who has borne the rack is ready to be burnt to death sooner than depart a hair's breadth from the formula of his confession, we seem to have reached a region to which this law of diminishing significance does not apply. However much the martyr has given to his faith and however little he has kept for his comfort, it would appear that the escape from no quantity of physical anguish, however great, will weigh against any concession in the matter of faith, however small.

Such questions may seem to take us very far from our proper subject, and so indeed they do, and it is for this reason that they have been excluded from consideration at an earlier period. But I have maintained from first to last that the laws of Economics are the laws of life, and consequently if a law declares itself to be paramount on the economic field, it proclaims itself by implication as a general law of life and conduct. It may therefore be legitimately challenged on any field, and if it cannot hold its own everywhere it must at least lie under suspicion in its economic applications. In any case, a closer inspection of our general principle, in other applications, is almost certain to throw light upon the special applications in which we are most interested. To begin with, then, it is not only consistent with our theory of "prices," but is actually involved in it, that to any man, at any given time, there may be some alternative so horrible that sooner than accept it he would endure all the physical and mental torment that can possibly be inflicted on him. This does not necessarily mean that he does not feel the torture, though even that might be the case, but it means that the whole sum of torture which he is capable of enduring before his frame cracks will not be enough to overcome his shrinking from the only alternative open. Something must give way first, and if his resolve, or his aversion, is stronger than his physical vitality, the tissues of his frame will be disintegrated or his vital functions unhinged before his choice is reversed.

History shews that these conditions have from time to time arisen; and we contemplate with awe the heroes who have supplied the demonstration. We probably think that few people could rise to this pitch of heroism in any cause; but, on the other hand, it is no more than we have a right to expect of every normal human being, living a normal life, that there should be certain things which he would not do for any amount of money, however large; perhaps because he regards the actions as detestable or dishonourable, perhaps only because he regards them as intensely disagreeable. This only means that to him the total difference between the command of things in the circle of exchange that he already enjoys, and an indefinite or unlimited command of them, does not weigh as heavy in his mind as the dishonour or the discomfort of the specific thing that he is required to do. It does not mean that his objection is "infinite." It merely means that it is larger than his estimate of all the satisfaction that he could derive from unlimited command of articles in the circle of exchange, and this is a strictly, perhaps narrowly, limited quantity.

These considerations, it is true, do not completely satisfy us; for they would seem to imply that although the offer of money may not be enough to make an honourable man do a dishonourable action, yet if he is in want of money at all the offer must tend in the direction of making him do it, so that raising the bribe would strengthen the temptation. If it is true, as we have said, that every force tells for all that it is worth whatever other forces are already on the field, would it not follow that if a man is in want of money the offer of money must tell for what it is worth, whatever other motives actuate him? And if so, must he not be nearer to doing the dishonourable action (though he does not do it) than he would have been had the bribe not been offered to him? And if the bribe is raised (so long as he would still value the increased sum), must not the tendency to make him do the dishonourable thing become more marked? Or in the case of the martyr, if he shrinks from pain at all, must not the infliction of greater and greater degrees of pain tend to make him renounce his faith, though the inducement is not high enough actually to bring about the renunciation? It is true that there is nothing in these conclusions that greatly shocks our general experience or observation. We hear men say, "I confess I was almost tempted by the prospect, for a moment," or "It required all my resolution to hold out, I can assure you," when they are speaking of actions the commission of which would have filled them afterwards with shame and self-contempt. But nevertheless we can by no means admit that every man can be at any rate tempted, though not seduced, by a bribe, or shaken, though not broken, in his resolution by torture. We are certain that this is not even approximately true as to the bribe, and we cannot believe that it is completely and universally true as to torture.

On this we may note, in the first place, that the very offer of the bribe or application of the torture may wake resisting forces which were dormant before.1 I might be considering whether or not an action was really dishonourable before the bribe was offered, and as soon as a bribe is proposed I may have a conclusive reason for associating it with dishonour. Or again, if a man offers me half a crown for doing or saying something I may be contemptuously amused, but if he offers me £1000 I may be deeply insulted. For I might take the first proposal as a naive attempt to overcome my inertia, but the second as revealing a serious intention of finding out the price at which I would sell my honour. Thus the increased inducement might itself touch the spring of increased resistance. If the briber can contrive to associate his material offer not with dishonour but with some appearance of honour, and can make his insult take the semblance of a tribute of respect, it will perhaps be found that £1000 does indeed weigh more than 2s. 6d. in the scale. But even here a finer perception might detect the finer insult, and might resent it the more deeply for its deliberate subtlety.

But there is something deeper even than this, and its examination will lead us back to our economic and commercial investigations. Just as it is very easy to suppose that a man could tell the difference between a half-pound and a quarter-pound weight by trying them in his hand, but very difficult to suppose that he could tell the difference between 14 stone and 14 stone plus a quarter of a pound by lifting them in a basket, so it is very easy to imagine a man's refusing to give 1s. for a thing that he would be glad to have for 6d., but very difficult to imagine him willing to give £1000 for some object but refusing to give £1000:0:6 for it. That is to say, 6d. is appreciable when the whole matter at issue is only 1s., but inappreciable when the matter at issue is £1000. It is a case of proportion. When the stake is of any given magnitude there is a certain minimum sensibile or minutest quantity that can be felt or appreciated in connection with it; and this minimum sensibile will vary with the magnitude of the thing at issue. The same principle applies in the moral world. When my feelings are deeply moved and I am vividly realising any one of the main issues of life, things to which I should give careful attention on other occasions do not affect me in the least. The mind does not readily adapt itself at one and the same time to the higher and the lower end of the scale. When it is experiencing great things it is not sensitive to small ones. When some grave disturbance of equilibrium has occurred or is threatened, or some vast issue is at stake, small things are not felt. Only if the great things were secure and had not recently been disturbed would the small things be able to assert themselves as significant. If I hear of the sudden and unexpected death of a dear relative and immediately begin to speculate about his will, why am I ashamed of myself? Because I had imagined that my affection for him was so great that immediately on the news of his death the significance of a few hundred or thousand pounds would have sunk below the minimum sensibile. And when I find that it is not so, I perceive that I have given myself credit for a higher appreciation of the things that are not in the circle of exchange, relatively to those that are, than I really possess. It is a startled sense of my own sordidness that brings my shame. It is not that I believe I ought not to care whether I have or have not the sum of money, but that I should have supposed that at that moment there would have been no room in my mind for such a thought, any more than for the fit of my trousers, or any other subject of consideration in itself perfectly proper but not sufficiently important to claim a share of my attention at the moment. I might experience the same kind of shock if, in catching up a child wounded by a passing dog-cart or motor-car, I found myself annoyed because my cuffs were stained or my clothes damaged by his blood. And the proof that this correctly represents the psychology of the case is that if the question of the legacy or of the stained cuff merely presented itself to me externally but failed to touch the springs of interest or emotion, if it were a mere shadowy presence with no weight or "tactile value," I should note it as something strange, but should not feel it as anything shameful. The same analysis applies to occasions on which some great happiness comes to a friend accompanied by a slight incidental inconvenience or disappointment to oneself. The examination of such cases reveals the possibility of any given consideration sinking beneath the minimum sensibile, but it also reveals the fact that in an enormous number of such instances the feeling or the motive that we neglect without one moment's hesitation is nevertheless actually felt. It is negligible, but if we look for it, it is there. It does weigh something, but it does not for a moment threaten to turn the scale.

Returning now to the martyr or the "incorruptible," we see that it is perfectly possible for the extremest pressure that can be brought to bear upon either to be quite negligible, so that it would no more be recognised as a reason (even an inadequate one) for doing the abominable thing than fear of staining my cuffs would be recognised as a reason against helping a wounded child. And it may be that it is not only negligible and practically unrecognized, but absolutely imperceptible even when we look for it. There is ample room for these facts within the limits of our theory.

Another point suggests itself for consideration in connection with moral questions. There is much confusion and ambiguity in our use of the word "duty." I may say that no personal or private considerations however urgent ought to affect the performance of my duty, even in the minutest point; but I shall not allow that I ought to leave a burglar despatching his business in my house rather than be a minute late at the office. "Of course not," it will be said, "because it is your obvious duty to protect your family, to say nothing of your property." Apparently, then, it is my "duty" to attend to whatever I conscientiously consider the most important matter at stake; and to say that nothing should interfere with duty simply means that I ought to do the thing, whatever it is, which a high-minded man would regard as most important. Certain family claims which are not "duty" in a general way become so when they reach a certain point of urgency; and when satisfied down to a certain point they will again cease to be duty. In this sense "duty" is not a label which is attached to certain classes of action and not to others, giving precedence to the smallest volume of that to which it is attached over the largest volume of everything else. It is a name we give to the resultant course of action when every consideration has been given its due weight and no more, and nothing that is irrelevant has been allowed to weigh at all. And we shall generally find, on analysing any dilemma, that the dictum "Duty before all things" is only maintained by giving the name of "duty" to whatever, under the circumstances, properly comes first; and that our determination on this point is influenced both by the terms on which the alternatives are offered to us and by the extent to which we have already paid tribute to the one or the other claim. The label can only be attached after the conclusion is reached, and cannot indicate any short cut by which to reach it. If I insist on allowing no weight to any considerations that cannot be labelled "duty" in advance, I shall generally find that I must include in my "duties" not only my duty to my family and to my friends, but also that trump-card of the casuist, my "duty to myself." And I shall find myself speaking of a "conflict of duties," thereby implying that duty itself is a quantitative conception. It is of course true that if we are to allow no more than its due weight to a certain consideration we shall often allow it no weight at all, because it is irrelevant. If I am asked, for instance, to arrange a number of candidates in order of merit, I shall probably regard it as absolutely irrelevant to the matter in hand that a widowed mother is dependent on the success of one candidate, while another is a man of property himself and has no one dependent upon him, or that I am attached to one and am repelled by the moral character of another, or that I believe that success will react prejudicially on the character of one and favourably on that of another. And if I take this view, then undoubtedly it is my duty not to give any weight to considerations that ought not to weigh, and it may or may not require some heroism on my part to act up to my convictions; that is to say, the temptation may tempt or it may not, as in the cases already noted. Or I may find that the real temptation is to incline to the verdict counter to my wishes, in order that I may escape the reproach of having been influenced by them. We may note that it is usual to protect examiners, as far as possible, from all knowledge of facts that are to be regarded as irrelevant; and this shews that the difficulty of ignoring them, if known, is generally recognised.

On the other hand, if I am making an appointment I may think that some or all of these considerations are relevant, and in that case it may be my duty carefully to appraise them all and weigh them against each other. When we have admitted that considerations of extreme strength in their personal appeal may be wholly irrelevant, and ought not to be realised as motives at all, even if they are felt, we shall have done full justice to the absolute conception of duty; but it is interesting to note how very many cases there are in which we are inclined at first to regard a consideration as irrelevant in principle, but find on close examination that a mere quantitative change in the things considered, if sufficiently pronounced, appears to us to raise the irrelevant into relevancy. In any case, our theory only asserts that when a consideration that "ought" not to weigh at all does as a matter of fact weigh—that is to say, is felt as a temptation—it may be felt more or less according to the magnitude and urgency of the issues at stake.

It is highly instructive to turn from the objection to the doctrine of declining significance which we have just examined to another which is quite as frequently urged. It is said that the whole theory of distributing our resources so as to gratify our wants pari passu and keep the marginal wants balanced, is false to fact and experience. The truth is, it is said, that there are certain things that we "must have," and we get "as much as we want" of them before we begin to consider less urgent requirements at all. For instance, we all eat as much as we want several times a day, and do not stop short of satisfaction because our desire for literature or travel is unsatisfied. Now to begin with, this is obviously an argument of the well-to-do. It is flagrantly untrue of the very poor that they get as much food as they want before they begin to trouble about keeping up their supply of clothes.2 We have already spoken of the thousands of young people, well above the line of actual want, who in managing their own slender resources consciously and constantly bring their meal to a conclusion at a penn'orth or two penn'orth short of satisfaction in order to advance some other margin. In its crude form the whole contention that we are examining is palpably false. Where do we or can we find in civilized society the man who gets as much food as he wants "before" he gets any clothes or any shelter? All that can be seriously maintained is that if a man's resources are sufficient to provide him with a certain amount of the things he needs most urgently, including food, he will soon come to points in every other branch of his expenditure at which he will be content to rest until he has completely satisfied his desire for food as far as mere quantity, apart from quality, goes.

In the contention so formulated there is a great deal of truth, but it need not disturb our confidence in our general theory. Any one who has tried saving pence out of his meals by restricting them in quantity, not quality, will know that the significance of these pence rises very rapidly as they are successively withdrawn. A halfpenny-worth of bread (two thick slices of a half-quartern loaf) may carry a man from a sharp sense of hunger to a sense of satiety. To save 3d. a week on bread might involve a very considerable volume of unpleasant experiences, and therefore, unless the 3d. would minister (as in Cobbett's case) to very keenly felt wants in other directions, it would be bad husbandry to save it. "Yes," it may be said, "but by your theory to save 1½d. a week would involve less than half the sacrifice of saving 3d. a week, and its expenditure on something else would secure more than half the gratification of three pennyworth; and since by hypothesis the expenditure on bread is taken down to a point at which it ceases to have any significance at all, there must be some small quantity3 of the resources expended upon it that could be profitably turned elsewhere." This is theoretically true as far as it goes; but theory also tells us that this adjustment would be an exceedingly delicate matter, and that it might demand an amount of attention and exercise of will that could be more profitably employed somewhere else where it would have a higher marginal significance.4

We have now examined two attempts to invalidate the general principle on which, as I have maintained, we administer our resources. It has been contended both that the sense of duty ought to be completely satisfied down to the last and minutest demand, and that the appetite for food actually is so satisfied, before anything else is attended to at all. The collocation of these two contentions is amusing; and before we leave them we may note that the sense of duty and the desire for food may become direct rivals. In that case I may perhaps cheerfully go without a meal at the call of "duty"; but presently I shall find that it has become my imperative "duty" to suspend the direct performance of my "duty" for a short time in order that I may eat something to enable me to perform my "duty" more strenuously (or to perform it at all) afterwards; and the graduated formulæ of "it is an imperative duty," "I almost think it is a duty," "I really think that without any dereliction of duty I may allow myself," etc., ease the (in this case) difficilis descensus from the pretentious heights of absolutism to the avernus (shall we call it?) of practical relativity.

Another and closely related aspect of the question of declining significances is suggested by charitable appeals. For instance, there is a famine in India, and I subscribe a guinea. That would appear at first sight to mean that I consider the want of food in India more urgent than any other wants of my own or any one else's to which the guinea would have ministered. But if so, why not give a second guinea? Has the want in India been sensibly reduced by my subscription? In bulk, yes. But in intensity? Even if I could suppose that my guinea had met the most urgent case, would there be any perceptible decline of urgency in the next case waiting to be met? It is exactly the question of the increments of tea over again. We saw that there was no perceptible decrease in the significance of tea as we passed from one quarter-ounce to the next at the margin of 4 lbs., though there was a perceptible satisfaction in the consumption of either.5 So I must suppose that a perceptible relief of suffering has been effected by my guinea, but I can hardly believe that a second guinea would relieve suffering perceptibly less intense than that relieved by the first. The marginal significance of a guinea, then, in relieving distress in India, appears to remain the same. Why do I not pay a second guinea and a third, and so on? The answer is twofold. In the first place, in the majority of cases it is not really the famine in India but my own conscience that I am appeasing, and my own conscience becomes perceptibly less clamorous after the first guinea has been paid. It may still grumble, and dispute the ground with other applications, but it may no longer dispute it successfully. My conscience may be right or wrong in insisting that I should take a share in the burden, and in being appeased when I tell it I have done so; but that is not the question. The point is that the demand I am meeting is, as a matter of fact, perceptibly reduced by what I have done to meet it. It is otherwise, however, if I really am directly appraising the urgency of the want that my guinea relieves when given to the famine fund, and the wants it can supply in other applications. In this case it is true that the want in India does not perceptibly decline as I give guinea after guinea, but it is also true that the wants that I neglect in order to meet it perceptibly rise as guinea after guinea is subtracted from the supply of them, until at last they rise to the level at which they balance my sense of the urgency of the need in India. This point may not be reached till I have reduced myself and all those dependent upon me to the level of misery of those that I am relieving; and some moralists are courageous enough to hold this up as an ideal. Our theory of marginal significance is elastic enough to adapt itself to their creed; for all that we assert is that, whatever the grounds on which we form estimates of the relative significance of rival applications of resources, we can so administer those resources as to bring their marginal significance in each application to equality. The urgency of the Indian claim is no doubt gradually declining if the administration of the fund is even approximately sound; but within the limits of the influence of my fortune it does not decline perceptibly. The balance is therefore found when all other expenditures are curtailed to the point at which their rising marginal significance equals that of the Indian claim.

Curious light is thrown on this class of problems by the added joy and relief which is not unfrequently felt by the recipient of a present that comes with the condition that it is to be spent on a holiday or on some personal indulgence. Presumably the recipient, if free, would have spent the sum as he wished. Why is he pleased at being forbidden to do what he would have wished? Because it is the sense of his duty to do the thing, not his sense of the importance of the thing's being done, that would have successfully contested the first place; and his "sense of duty" is entirely extinguished by the prohibition. The demand that would have had to be appeased before the other could be indulged is withdrawn from the lists, and the indulgence can be secured without a drop of gall. A goad has been blunted, and the hedonistic gain is obvious. In cases where this analysis would be untrue and where the wish to do something else with the money is really inspired by the eagerness of direct sympathy, the restriction would be actually felt, and perhaps resented, as a reduction in the value of the gift. Perhaps by the painful associations it waked it would altogether annul it or leave a balance to the bad.

We have now concluded our examination of the class of objections to the law of diminishing psychic returns which is based on the absolutism of ethical or social conceptions; but in the course of these investigations we have been incidentally led to contrast a demand or craving that has to be appeased with an enjoyment that may be secured. This opens in its entirety the important subject of positive and negative satisfactions, their relations to each other, and the proper notation to be employed in their calculus; and to this subject we must now turn.

If we regard pain as negative pleasure, and discomfort as negative satisfaction, then a supply of anything that gradually relieves me from acute suffering leaves me in a state of (decreasing) negative satisfaction throughout the process. But the reduction in the volume of this negative satisfaction, which is taking place all the time, is a movement in the positive, not the negative sense. It is an addition, not a subtraction, of desired effects; for it is a subtraction of undesired experiences. The acquisition, therefore, is a positive quantity, and must be noted by a plus, not a minus sign. Here we may introduce the familiar notation of curves. On Fig. 1 we measure the supply of any commodity per unit of time along the line OX, or the axis of X; and on OY, or the axis of Y, we measure rates of satisfaction. Thus the curve pp₁x₂ would represent that the initial increment of the commodity per unit of time satisfies some kind of desire at the rate of Op per unit of commodity; that by the time the supply is increased to Ox₁ the rate at which it is satisfying desire has risen to x₁p₁ or Oy₁, and that when the supply reaches Ox₂ per unit of time, the desire is completely satisfied. The quantities measured along OX, which are called abscissas, indicate the breadth of the supply per unit of time, or the breadth of the stream of supply. Quantities measured along OY, which are called ordinates, indicate the marginal values investigated on pages 47-71 of Book I.,6 and areas such as Opp₁x₁ sums of satisfaction per unit of time, secured by the consumption per unit of time of the quantity of the commodity indicated by the corresponding abscissa. Generally speaking, such an area must (as we have here supposed) itself be taken as representing a rate of total enjoyment per unit of time, rather than a sum of total enjoyment;7 but sometimes it will be convenient to take the whole figure as representing not a rate of consumption, but a single act. And in such cases we shall take x₁p₁ as representing the marginal value, and the area Opp₁x₁ as representing the "value in use" or total significance of the definite quantity Ox₁. For instance, the figure might roughly represent the experiences of a single meal, during which for a time "the appetite comes as we eat" and we are conscious of increasing enjoyment, whereas after that point our hunger is gradually appeased to the point of satiety.

Now this diagrammatic method is useful as an instrument of research, as a means of demonstration and exposition, and, most of all, as a vivid and comprehensive form of statement. But it is very dangerous, and if not used with due caution and precision it may lead to grave confusion and may encourage loose and irresponsible thought. In the next chapter, accordingly, we shall examine the construction of one particular curve in great detail; and whenever we make use of curves we must try to bear in mind the necessity of giving an exact account of what they mean, so that the results obtained may not be in any way equivocal. The necessity for caution in this matter is illustrated on the very threshold, for (apart from the difficulty of determining how we are to measure a unit of satisfaction8 ) we have to note at once that this first curve which we have introduced is ambiguous in relation to the very matter we are now discussing, viz., the relation between assuaging a craving and securing a positive enjoyment, or, more generally, between removing negative and securing positive objects of desire. We have seen that the removal of a pain must have the positive sign, and it must therefore be represented by a positive area, so that if we begin in pain and the supply of a commodity gradually removes that pain, the result must be represented as positive—comparable with, and to be weighed against, a gain of positive satisfaction. Our figure, therefore, will not tell us whether we begin in a state of positive satisfaction, a state of indifference, or a state of negative satisfaction, or pain. It will only tell us that if we command the quantity of the commodity represented by Ox₂ our state will be the better, by the whole area Opp₁x₂, than it would have been had we had no supply at all. If we only command Ox₁ our state will be the better by the area Opp₁x₁. The area x₁p₁x₂ will then represent either an unassuaged pain or an unrealised pleasure, but in either case the area Opp₁x₁ must have the positive sign. It is a gain, not a loss. The existence of the possibilities represented by the figure may in itself constitute a misfortune or a privilege; but granted their existence, the command of Ox₁ of the commodity, whether it means plus a pleasure or minus a pain, is a gain (in the estimation of the subject), and must be regarded as positive.

If we draw Fig. 2, it will represent the effects of the supply of a commodity which ceases to act in a positive sense when it exceeds Ox₁ in quantity. Thus at a given temperature the consumption of fuel might begin by being extremely acceptable, and when it had reached the rate of Ox₁ per hour it might cease to be acceptable at all, and might, if raised still higher, become positively undesirable, or negatively desirable. Now one man may be so constituted that whereas he does not feel any positive distress by sitting without a fire, he may be conscious of a distinct pleasure if a fire is lighted; and another may be consciously miserable without a fire, and as the warmth increases may be conscious only of more or less adequate relief from discomfort till the quantity Ox₁ is exceeded, after which another kind of discomfort ensues from excessive heat. Yet another may at first be conscious of relief from suffering; then, before the quantity Ox₁ is reached, may feel that all his discomfort is gone and a positive enjoyment of the cosy warmth has succeeded to it; until, as the quantity Ox₁ is exceeded, he feels that although the room is still positively pleasant it would be pleasanter yet if the fire were kept a little lower. To all these men alike the supply of the commodity up to the quantity Ox₁ will produce a result that should have a positive sign and should be represented by a positive area, though to one it is minus pain, to another plus pleasure, and to the third at first minus pain and then plus pleasure; and to all of them the further increments represented by the line x₁x₂ produce a result that should carry the negative sign and should be represented by a negative area, though to one it is plus pain and to another minus pleasure. All of them are in a state more to be desired as the supply grows from zero to Ox₁, and in a state less to be desired as it grows from Ox₁ to Ox₂.

It follows from this example that an area below the axis of X, which represents negative satisfaction, may mean a subtraction from pleasure that leaves a positive balance, just as well as an addition of pain. Fig. 3 would represent a supply, or an experience, that, whether it detracts from the happiness of a happy state or makes a neutral one positively painful, or a painful one more painful yet, in any case produces a negative result, of increasing intensity per unit, as one increment follows another. If we are speaking in terms of positive satisfaction we shall still say that these increments have a declining (positive) significance, though if we were speaking in terms of negative satisfaction, or pain, we should say that they had a rising (negative) significance. Thus the fact that things which cause discomfort normally act with increasing intensity as unit is added to unit does not affect the generality of our proposition that additional increments, after a certain point, produce decreasing (positive) results.

It sometimes happens that a positive quantity (in the technical and ambiguous sense in which it includes the subtraction off a negative quantity) is only to be had in association with a negative quantity. In that case probably the positive ordinates of the first will decline, and the negative ordinates of the second will increase, the movement in both cases being technically in the sense of positive decline. Thus a man who has bitten his tongue or has bitten a piece half out of his cheek may be in need of food, and yet eating may cause him acute annoyance. As his hunger or sense of faintness gradually yields, and his demand for food becomes less urgent, the increasing painfulness of the terms upon which alone he can assuage the declining urgency of his want will soon balance it, and his meal will come to what would else have been a premature conclusion. This might be represented either analytically by Fig. 4, or synthetically by Fig. 5. Both figures alike represent the fact that up to Ox an advance from the origin is accompanied by a balance of advantage, and that after that point the reverse is the case. And both figures agree in the magnitude of the advantage or disadvantage in either case.

Where there is no indication to the contrary a curve must be taken to indicate not a history but an anticipation, and an anticipation that has discounted (not necessarily for what they are worth) all conflicting elements, risks, and reactions as far as they come within the ken of the person who makes the estimate. It will be a synthetic and resultant estimate of the balance of advantage to be anticipated from the acquisition of each successive unit of the commodity, of the type of Fig. 5.

We have noted that positive and negative quantities may be balanced against each other, and also that mathematically positive and negative quantities may both alike be ambiguous psychologically; for just as a subtraction from pain and an addition to pleasure are alike positive, so a subtraction from pleasure and an addition to pain are alike negative. Thus Fig. 2 (page 417), where the increments of the same commodity at first have a positive and then a negative effect, is explicit as to the positive or negative sense of the process in question, and as to declining (positive) significance of all increments after a certain point; but it is equivocal as to the positive or negative state of the person affected. He might be either in a state of suffering or a state of enjoyment throughout the process, or he might pass from suffering to enjoyment at any point on the line Ox₁, or from enjoyment to suffering at any point on the line x₁x₂; but in any case he has either more enjoyment or less suffering as he passes from O to x₁, and either less enjoyment or more suffering as he passes from x₁ onward.

Now, although the relief from a pain and the securing of a pleasure, or the deduction from a pleasure and the addition of a pain, have respectively the same signs, and may be taken as equivalents, yet they are in themselves very different things. Given my constitution and circumstances, a certain relief from pain must be regarded as equivalent to a certain positive pleasure, a certain deduction of pleasure to a certain access of pain; and certain pleasures and pains taken together, or certain relinquishments of pleasure and escapes from pain taken together, must be regarded as balancing or neutralising each other; but it makes all the difference in life whether my constitution and circumstances are such that my energies have to be given chiefly to escaping or minimising undesired things or are mostly free for securing or developing desired ones, and whether I can often or only seldom get a pleasure without a concomitant pain or escape a pain without a concomitant loss of pleasure. And it is just here that our immediate choices react upon our future possibilities.

This subject of the reaction of our enjoyments, privations, and endurances upon our future capacities for enjoyment has already been touched upon in Book I.,9 but the investigation we have just completed will now enable us to enter upon it more fully. We have to make constant adjustments between the immediate gratification of desires and the building up of capacities. A great part of wise conduct obviously consists in forgoing a present gratification, or incurring present pain, or making irksome effort, in order to acquire a capacity for future enjoyment, or power ultimately to secure or promote desired ends. Wise administration of vital resources must therefore take constant note of this reaction of the present upon the future.

Every wise man must desire to build up for himself such habits of mind and body from within, as well as to surround himself with such outward circumstances, as will make life as little as possible an escape from wretchedness and as much as possible an experience of well-being and an achievement of desired ends. We must therefore cultivate the power to endure such undesired experiences as are inevitable, and to forgo such desired experiences as are unattainable, with the minimum of suffering, and to derive the maximum of satisfaction from the realisation of things desired. An example may make this clear. Two men are on a tour together in a beautiful and sparsely inhabited country. They find themselves out of their reckoning, and when dinner-time comes they are far from any opportunities of dinner. The spirits of one of the companions begin to sink, his temper becomes unstable, he cannot enjoy the scenery through which he is passing, the exhilaration of mountain air or of the battle with the waves is a thing he knows not, the suggestion to turn aside and spend half an hour in ascending a rock or exploring a cave is fiercely resented, and, in fact, the man's whole moral, æsthetical, and physical being is swept up into one hideous craving for food. At last the friends (if they still deserve the name) reach hospitable quarters. Their hostess wishes to do justice to her reputation and keeps them waiting for an hour in order to set a noble repast before them. But when it comes it is too late. The poor wretch can now eat nothing, and goes sick and miserable to bed. His companion (so far as his sympathetic heart allowed) has meanwhile been drawing in delight at every pore, keenly enjoying the tussle with the waves or the stride across the heather, with an eye that (like Wordsworth's) finds no hairbreadth of earth, sea, or sky from which it does not gather delight, ready at any moment to turn aside and delay the end of the journey in order to increase the enjoyment of its progress, conscious indeed of keen hunger, but conscious of it rather as a prospect of future pleasure than as a present experience of pain; and when at last he finds himself opposite his victuals, a harmony is established between the organism and the environment which almost rises to the dignity of a spiritual experience. The less fortunate of these travellers derives the maximum of suffering and the minimum of enjoyment, the other the minimum of suffering and the maximum of enjoyment, from the necessity of taking food. The one is the victim of a craving; the other has a capacity for enjoyment. To the one it is agony to be thwarted, and only a negative satisfaction to be humoured; to the other privation is no pain, but a supply "adds sunshine to daylight."

The wise or happily constituted man has a mind so regulated that many of his desires only become rampant as the prospect of satisfaction approaches. Till then they are dormant potentialities of enjoyment. Thus the man who on coming in sight of a public-house declared that he "had a thirst on him for which he would not take £5" was perhaps to be congratulated if he had been thoroughly happy before he saw it; but if he had been miserable himself and a cause of misery to his companions for the last hour or two because there was not a public-house in sight, he was an unenviable person as well as an undesirable companion.

What, in the instances we have given, may be regarded at any rate primarily as a difference of physical constitution has all manner of analogies in acquired habits of mind and body; and every wise man would desire for himself and others such habits and impulses as would conform to the happier type. Now, though all means or opportunities of gratification seem to have this in common, that the immediate effect of successive increments is (after a certain point) of declining positive value, yet different kinds of gratification differ enormously in their after-effects upon the organism itself. Is our present enjoyment building up an increased capacity for future enjoyment? Is it leaving us permanently unmodified, so that after a time we shall return to exactly the same state in which we were before? Is it undermining our power of future enjoyment, so that after every act of indulgence we return not to the same, but to a lower power of enjoyment than we had before? Or is it substituting a craving for a capacity for enjoyment?

The characteristic of ruinous enjoyment is that it not only tends to satisfy us at the time (as do all enjoyments), but that it also tends to undermine our capacity for future enjoyment. The most pronounced forms of ruinous enjoyment are probably those which are popularly regarded as vicious, such as intemperance. The characteristic of a vice, from a hedonistic point of view, is that it tends to replace a capacity for enjoyment by a craving. Intoxication may be extremely delightful, but the more habitually a man drinks, the less pleasure it gives him to be drunk and the more pain it gives him to be sober. He begins, perhaps, by hitting on a means of heightening enjoyment; but he ends by being in a state of chronic misery, from which he gains occasional respite in an intoxication which no longer gives him any positive pleasure. His whole conscious being has been swallowed up in the vortex of one frightful and incessant craving. This is a typical case of ruinous enjoyment. I am not here concerned with any attempt to analyse the ultimate grounds of the reprobation implied in the terms "vicious" and "vice," but it is interesting to note that the popular moral judgment stands in intelligible relation with the results of a hedonistic calculus. And note that our diagrammatic method gives us no notice of this change from a source of pleasure to a craving. Diagrammatically the appeasing of a craving is indistinguishable from the securing of a satisfaction; and if the acquired craving is more imperious than the natural desire for pleasure originally was, we should have to represent the change by an increased height of the curve indistinguishable from the representation of an increased capacity for enjoyment.

But there are many enjoyments which, so far from producing a vicious craving, rather tend to beget a sense of satiety, or even disgust, unless kept within very moderate limits. The danger here is not of converting a possible source of enjoyment into a craving, but simply of deadening by indulgence the susceptibilities from which the enjoyment springs. For example, most people enjoy a little salmon occasionally, and are inclined to regard it as something of a treat; but it is pretty generally known that, if used as a staple food, salmon very soon loses its charm. The provision long customary in the indentures of apprentices, that they must not be required to eat salmon more than so many times a week, is the historical record of this fact. Salmon therefore could not well take the place of the Englishman's traditional rasher of bacon as the breakfast dish for all the year round. It seems to be a fairly general experience (though of course by no means universal) that you may eat fried bacon for breakfast whenever you are inclined to do so, and may continue to be so inclined day after day and year after year; whereas if you were to eat salmon whenever you were inclined to do so, you would very soon cease to be inclined to eat it at all. The appetite for bacon, then, when extinguished for the moment, rapidly recovers its pristine vigour; whereas the appetite for salmon, unless it is allowed a long period of recovery, becomes permanently lowered or deadened. If a man, though eating salmon as often as he feels inclined, does not eat as much at a time as he is inclined to do, the effect may be deferred. But even so, salmon will soon cease to be much of a treat.

Again, a man is not likely to eat oatmeal porridge for the pleasure of the palate when the appetite (as an index of an organic demand of the system) is assuaged; whereas the skilled cook, "by successive intensifications of his diabolical art," may tempt a man from excess to excess by appeals to his palate, even when his appetite has long been sated. Now healthy and vigorous persons who are accustomed to simple and frugal ways are perhaps conscious, or subconscious, on most days that they would enjoy a rather more elaborate diet than they are accustomed to. But every one who has had experience of the two ways of living will tell us that those who live with severe simplicity get more enjoyment out of their meals than those who have an elaborate dinner every day. It is very easy to see why. The man who tries to extract the maximum of sensuous satisfaction out of every meal is securing trifling increments of satisfaction at the margin to-day, and is thereby deadening his capacity for enjoying the more significant increments nearer the origin10 to-morrow. He is not indeed substituting a craving for a source of satisfaction, but he is lowering his possibilities of satisfaction. Thus, if a man has a moderate supply of any such luxuries as we have been discussing, his enjoyment may be represented by Fig. 6. He stops at x₁, and there are still unexhausted possibilities of enjoyment. But if he habitually goes on to x₂, though at first he secures the additional area of enjoyment x₁p₁p₂x₂, yet he gradually lowers the significance of the initial increments, and ultimately only enjoys the smaller area bounded by the dotted line above Ox₂ instead of the larger area Opp₁x₁. Again, the man who eats or drinks as soon as he is inclined to do so, often falls into the habit of eating and drinking as soon as he is able to do so; and, as he never recovers a state of healthy hunger, he too always remains at the low level of enjoyment.

Let us take another illustration. Some moderate smokers will declare that a pipe two or three times a day gives them great satisfaction, but that they do not miss it, in the sense of feeling any positive discomfort, if for any reason they are deprived of it. For the time being a single pipe completely exhausts the possibility of enjoyment, so that they would find no pleasure in further smoking. Let Fig. 7 represent the total pleasure, declining from the initial point of intensity to the point of complete satisfaction.

It is obvious that after a pipe has extinguished the present possibility of further enjoyment a certain time must elapse before it is recovered; and it will not be recovered suddenly. Let us suppose that after an hour the area of possible enjoyment x₄p₄x₅ has been recovered; that is to say, the man is in the condition in which he was when he had smoked four-fifths of his pipe. He may now enjoy a cigarette that contains one-fifth of a pipeful of tobacco as much as he enjoyed the last fifth of his pipe; and if he repeats this every hour he enjoys five times the area x₄p₄x₅ in the course of five hours. Whereas if he had not smoked for five hours he would then be just where he was before he smoked his last pipe and could enjoy the whole area Opx₅ again.

We have seen that our diagrams do not distinguish between the assuaging of a craving and the conferring of a positive satisfaction, and that in many cases the earlier increments of a commodity may perform the first function, and the later increments the second; and, moreover, that the two may overlap. In the case of smoking it is possible, though not usual, for a man who enjoys it to be able to abstain completely from it without positive suffering. In the case of food or drink this is impossible. Thus, if a man had a suitable allowance of food and drink, he might divide it up into a number of rapidly succeeding nibbles and sips (like cigarettes), or he might take larger portions at longer intervals. It would seem that in such cases the man who does not allow his organism time to recover its full sensitiveness to pleasure before he endeavours to extract renewed enjoyment out of it, and the man who pushes abstinence to the point of positive pain and craving before he assuages it, supposing them both to eat the same amount, would be alike wasteful in their administration. The man who lets his organism recover its power of yielding enjoyment without inflicting positive suffering on it (or, if the two states overlap, goes back to the point at which the pain incurred and the pleasure secured just balance) is administering his resources to the best advantage.

Note here again the extreme care that must be taken in the use of diagrams. If our curve in Fig. 7 represented the value of successive increments of any commodity per month (as in the case of tea in Book I. Chap. II.), or per year, or per day, it would take no note of the different effects of the same rate of supply differently distributed within the period in question, which is the problem we have now been discussing. Some system as to this internal distribution is tacitly assumed (as it was in our former tea problem) as constant during the whole inquiry, or as modified according to some consistent system as the supply contracts or expands. This is as it should be, for whatever particular condition we are examining and are supposing to be subject to variations, it must always be assumed that the other conditions are constant.

To return to our main inquiry. We have seen that certain kinds of enjoyment, and certain habits of consumption, while apparently innocent in themselves, are eminently wasteful from the hedonistic point of view, either because they more or less permanently deaden the keener powers of enjoyment, or because they never give those powers the opportunity of recovering themselves. And yet deliberately to stop eating salmon when you would like more, in order that you may be able to get more pleasure out of a help of salmon this day week, is a piece of self-conscious sybaritism from which the healthy mind revolts. Even the man who will not eat when he is hungry and has suitable food before him, for fear of "spoiling his appetite" for a more sumptuous repast which he expects in a couple of hours, fails to excite our admiration. We seem then to be in the presence of a kind of waste against which it is impossible to provide without unworthy attention to appetites that are only wholesome so long as they are unreflective. And so indeed we are. But our analysis has resulted in a triumphant vindication of certain instincts which we may henceforth trust more completely, and which, if we follow them, will effect the desired saving and give zest and vigour to life, without any habitual self-consciousness. Luxurious living has always lain under suspicion as hostile to a vigorous life, as something which, if not absolutely culpable, deserves a certain disapproval, and moreover as self-defeating even on its own chosen ground of physical enjoyment. Self-indulgent habits which, on the face of it, only seem to open up innocent sources of enjoyment are nevertheless regarded with a certain contemptuous impatience by healthy and vigorous minds. The man accused of self-indulgence retorts on his critic with a charge of asceticism; and his mentor, while repudiating the charge, often finds it difficult to defend by logic the position to which he is guided by an obscure instinct. But that obscure instinct, we now see, is perfectly sound, and it warns us against forms of enjoyment which, if not viciously ruinous, are yet wasteful.

We seem now to have got at something like the philosophy of it. The self-indulgent person is perpetually nibbling and never giving himself the chance of a hearty meal. The ascetic is always cutting back to the point at which the potentiality of a satisfaction passes into the realisation of a pain. And both alike debilitate their frames, and unduly concentrate their minds upon material sources of satisfaction. For, be it observed, persons who have practised genuine asceticism (as distinct from persons who by nature or training have become indifferent to what most men enjoy) will generally tell you that they were never so greedy in their lives as when they fasted severely; and perhaps that they have never quite recovered from the effect of the practice. A sufficient effort of will, or a strong enough preoccupation, may extinguish or indefinitely suspend a craving, but to maintain a want at the stage of craving, without extinguishing it, is to fix the mind upon it. Hence many curious parallels in the moral effects of luxurious and ascetic living; and hence the justification of the instinct for a robust and simple life that shuns both.

We can now fully understand the recognised failure of all elaborate attempts to make life enjoyable by luxuries. A rich man trying really to enjoy himself in the midst of his wealth often suggests a man attempting to bathe in his Sunday clothes. He cannot feel the sweep of wind and water over his limbs. Hence the genuine but futile wail of persons surrounded by luxury, hence their craving for the "simple life," and their restless longing to break away from their surroundings and to put themselves into circumstances where money positively will not command any but the simplest supports of life. Only so can they get into contact with the initial satisfactions which are reserved for those whose nerves have not been deadened and blunted by being called upon to respond to fresh supplies before they have recovered from the last, or to seize a little more excitement at the margin to the detriment of their tone at the origin. There can be little doubt that those who constantly go without things, not because they do not want them, but because they cannot get them, and who have an unfailingly abundant supply of nothing but a few simple things, selected by experience for their staying qualities, get more physical enjoyment out of life, and a larger amount of physical delight out of their contact with things, than all the devices of luxury can secure. And, very happily, this mode of ordering life, with all its invaluable reactions, may be maintained, when once deliberately embraced, not by thinking but by not thinking about it. The man who cares most for other things will act with the greatest wisdom in these matters; and he will instinctively form habits, or, if you like, contract prejudices, which without self-consciousness will secure the best fruits of reflection.

This question of self-consciousness enters closely into another problem, which has to be faced in all housekeeping above the lines of poverty and below the lines of luxury. We have seen that "second helps are never so good as first," and it would seem to follow that there is a prima facie gain (under the reserves indicated on pages 82 sq.) in having no second help to-day, but another first help to-morrow or this day week. That is to say, if green peas or new potatoes (in themselves, let us take it, of the "staying," not the "cloying" order of commodity) are a treat which cannot be indulged freely, it would seem to be better to have a little often than a great deal seldom. And many housewives follow this line. But it is by no means above challenge. Children who are habitually stopped at the first help when they keenly desire more will almost certainly become greedy, if the reason given for stopping is that they may have the rest to-morrow; whereas if they had sometimes had as much as they wanted; and none at other times, they might have remained healthily animal. And so we are back again at the point which we encountered early in our inquiries.11 We may pay too heavily for securing the best possible administration of certain defined resources in their application to their immediate purposes. On the whole, may we not say that the popular instinct regards as the most desirable life one which is simple to the verge of severity, but which allows a certain amount of variety, and prefers long or even complete and permanent abstinence to stinted and watched indulgence? Bread and water, Epicurus declared, were good enough for him; but for all that he would like a bit of cheese, so that he could have a blow out when the fancy took him. We may be sure that when he did have cheese he liked to have plenty. I once heard of a servant girl who every year bought and cooked for her single self a peck of green peas. She said she liked to "have her fill o' peas" once a year, and when that was accomplished she was in a state of equilibrium for the rest of the season. She was a true Epicurean.

As far as material indulgences are concerned, then, the instincts of popular moral judgment condemn the most ruinous forms of enjoyment as vicious, regard less ruinous but still wasteful forms as undesirable, if not exactly culpable, and look askance at too scrupulous attempts to economise and maximise enjoyment, as savouring of self-conscious materialism and wanting in directness and robustness. The man who so orders his life that, with small or great variety, he periodically pursues his enjoyments down the slope of diminishing returns to a point determined by his general resources and the claims upon them, but never dulls his capacity for periodical renewal of them, escapes the censure of the most rigid moralist. He is "living the simple life."

But there is another kind of satisfaction, the indulgence of which positively increases the capacity for future enjoyment. The man who enjoys himself in such ways as neither to reverse nor to destroy nor merely to maintain, but to increase his hedonistic capacity, gets a curious kind of credit for his conduct. Intellectual, literary, and artistic enjoyments (to those who really enjoy them) belong to this class. Most of them demand at some period or other a certain more or less painful effort and discipline. Probably no one can get the highest and most sustained form of enjoyment out of literature without a considerable amount of drudgery of one kind or another; and the same is true of art, and at least equally so of science. Even exercises or studies which are in the main enjoyable must often be pursued all down the scale of diminishing returns of satisfaction until they cease to give any pleasure at all and become in various degrees painful, if we are really to make anything of our studies. Some wise man (is it Ruskin?) has said that if we wish to do our best we must never work against the grain, but if we wish to do better than our best we must often go on when the work is irksome. We shall spoil it, but next time we shall do better than our former best.

Now this kind of gratification, sometimes merely pursued past the point of enjoyment, sometimes associated with painful training or irksome preparation, but always tending to create an increasing fund of possibilities of enjoyment, is regarded by the popular instinct as "superior." We speak of people who cultivate such sources of satisfaction as having "superior tastes." The slight half-veiled contempt for the "superior" person that we can often trace is apparently due, partly to a doubt whether he really does enjoy his superior pursuits, and partly to a suspicion that he may be starved into them by the lack of a wholesome and vigorous appetite for the robuster enjoyments of his neighbours. Lady Jane Grey appeared to prefer reading Plato to hunting and hawking; but did she really prefer it, or did she only wish to prefer it, or wish to be thought (by herself and others) to prefer it? And if she did prefer it, was it because she got more out of Plato or because she got less out of hunting and hawking than the others did? Was it the presence of a faculty they had not, or the absence of a faculty they had, that made her choice differ from theirs? Our respect for "superior" tastes when they are genuine is shewn by our extreme desire that the "working-man" should contract them, by our distress if more fiction than history and science is taken out of our public libraries, and our willingness to bear a part of the expenses of lectures on "superior" subjects—for others to attend.

Roughly speaking, these more fruitful enjoyments seem as a rule to be less exclusively and often less directly connected with the senses than the neutral or ruinous enjoyments are. It is true that the eye and ear are directly concerned in the enjoyment of music or of art, but the element of intellectual analysis and judgment, and, far more, the element of imaginative and emotional association, play a preponderating part in them. In the enjoyment of literature or of scientific investigation the place of the senses is still more subordinate. Now it is generally regarded as an axiom that mental and spiritual enjoyment is of a higher order than the enjoyment of the senses, and it is interesting alike for those who are, and for those who are not, prepared to receive such a judgment as axiomatic, to note that at any rate it finds itself, like the other moral judgments we have examined, in easily traceable relations with the hedonistic calculus.

But the coincidence is not quite complete. For capacities that can be developed and rendered fruitful, perhaps at the expense of initial pain, sometimes yield material, not spiritual or intellectual satisfactions. They are then on a level with "superior" satisfactions hedonistically. But the moral judgment declines to consider them "superior." The process of learning to smoke wakes no moral enthusiasm even if it results in a power of enjoyment free from any vicious or wasteful craving. Having the ears pierced for earrings, in the old days, was only regarded as really praiseworthy by those who thought it a woman's first "duty" to make herself attractive. No one gets moral credit for what has been called "the long and painful apprenticeship to the art of liking olives." We have got some light, I trust, in this chapter on the relations of instinctive moral judgments and the results yielded by a hedonistic calculus; but it is far from my own belief that the one can be completely resolved into the other. This last set of instances may serve as a warning against any such belief.

The tendency, not fully accounted for by hedonistic considerations, to attach a note of intrinsic inferiority to pleasures of the sense is curiously illustrated by the case of connoisseurship in wines. If an interest in wines and a delicate judgment of them is combined with strict moderation it presents many of the qualities of an artistic enjoyment; and the old-fashioned elaborate conversation about wine presented a curious analogy to the discussion of the merits, say, of pictures. Yet to have given such close and earnest attention to things of sense suggested a more or less material view of life. Hence a somewhat confused feeling. Connoisseurship in wines seemed in itself to belong to a "superior" order of enjoyments, but by its associations and suggestions, to an "inferior" order; and accordingly it often provoked in the mind of the impartial outsider curiously mingled and conflicting feelings, now bordering on contempt, and now rising to something very like respect or even envy.

It will hardly have escaped the reader's notice that our examination of the reactions of different enjoyments upon the organism, and especially the section on the wastefulness of enjoyments of the intrinsically cloying order, or enjoyments carried to the cloying point, has been a running commentary on the dangers of civilisation and of increased command of material comforts. If wisdom does not grow with power, our latter state, even from the material point of view, may well be worse than our former, as material wealth increases; and the action of the economic forces, unguided and unchecked, naturally favours the growth not only of a class of ministers to vice, but of a class of persons who live by enabling people to get another drop out of the squeezed orange of to-day's capacity for enjoyment, reckless of its reactions upon to-morrow. And further, it will be seen that the "simple life" comes, if at all, rather incidentally as a natural result of caring for worthy things than as an object self-consciously aimed at for its own sake. The remarks on pages 186-189 may be re-read in the light thrown on them by this chapter.

Nothing that has been said in this chapter must be taken as committing the author to a hedonistic theory of ethics. Suppose a man deliberately desires to cultivate impulses, and to train himself to a sense of values which he does not expect to give him the maximum of personal happiness. Suppose there are things that he really does care for more than his own happiness, or impersonal objects that he wishes he did care for, and hopes he one day will care for, more than for his personal enjoyments. Such a man would endure suffering, sacrifice pleasure, and fight against many of his impulses, in order to secure a permanent set or habit of will and a firmly established scale of values which could only be justified by reference to some social or religious test. These purposes would have secured his loyalty, but not on the ground that they promised to secure his happiness. But the formation of such habits and the cultivation of such affections would, in this case, be the man's active desire, for whatever reason; and he would sacrifice the gratification of other desires in pursuing it. His self-discipline and his renunciations would be, from our point of view, of the same order as those of the man who undergoes irksome discipline for the sake of acquiring a hedonistically valuable taste, though he would not be moved by hedonistic considerations. It is not my purpose, however, to discuss ethical theories, but merely to shew that the general principles on which our investigations are based, while throwing light on the hedonistic calculus, do not presuppose a hedonistic theory, but are equally applicable to any other.

I will conclude this chapter with a few additional notes on the nature and limitations of the diagrammatic representations we have used. They may be best regarded as attaching themselves to the examination of roused and dormant desires on pages 422, 423. A large number of personal curves probably rise for some time before the ordinates reach their maximum and begin to decline. The matter is a little difficult to decide, for it is not easy to keep it clear from the considerations, entered upon above, of changes in the ethos of the individual during any considerable period. But it may well be that the same man with the same tastes and capacities would be willing to pay a larger sum for, say, a second chance in the month of hearing good music than he would for the first, possibly more for a third chance than for a second (and then less for a fourth and fifth, and so on), not because his musical taste is improved, but because his musical appetite is roused. In any case, when a dormant capacity or desire is roused, or a mild one stimulated, an abrupt or early cessation of the means of satisfying it may leave us in a balked or aching state, which constitutes a pain in excess of the original sense of want or privation (hunger, or what not) which is as yet imperfectly relieved. It is possible that, starting with any given condition, and regarding relief from discomfort and positive pleasure alike as positive, the sudden arresting of satisfaction might leave a legacy of actual pain which would not be represented on our diagram; because the supply of the commodity has a positive value as long as it lasts, and would continue to have a positive value if it proceeded. Fig. 8 might give some kind of representation of such a case. It might mean that the man started from a state of indifference, but pursued some occupation or enjoyment with growing keenness, and derived a pure access of satisfaction as the appetite was at once roused and gratified. Up to the amount Ox₁ he has secured the area of satisfaction Op₁x₁, and there remains an unexhausted possibility of satisfaction represented by the area x₁p₁x₂. But if the supply is now broken off, the unsatisfied desire continues and the satisfaction ceases. The result is a pain represented by the negative area below x₁t. It is only after a lapse of time represented by x₁t that the pain wears itself out and the man returns to his initial state, having experienced both a positive and a negative satisfaction, the latter of which might in some cases be the greater. In such cases we say we had rather have had none of a thing at all than the tantalising amount we secured, even though we thoroughly enjoyed that little while it lasted. Fig. 8, however, is a monstrosity; for progress along the axis of X means increments of commodity up to x₁, and for the positive area above, up to x₂; whereas for the negative area it means the passage of time from x₁ to t. It is really two figures, and the units of area alone are common to the two.12

Returning to the phenomenon itself, we note that it may occur in every case of gratification arrested short of complete satisfaction. As a rule we may suppose that the lower the point to which we have reduced the ordinate the smaller will be this offset of dissatisfaction. And in a well-filled life it will often be absolutely eliminated; for although the lowest increment of satisfaction has not been squeezed out of some indulgence, and a theoretical sense of want might supervene if the next occupation or experience of the man were inherently neutral, yet if there is some other pleasant or desired occupation to which to turn, the anticipation of it substitutes eagerness for something else in the place of a languid desire to continue the present experience on the declining slope. Perhaps the best theoretical defence of smoking that has yet been discovered by the numerous and able advocates engaged in the cause is the assertion that it prevents listless and self-indulgent persons from over-eating, because when the keen demands of appetite have been satisfied but there is still enough left to dally with, the seductive prospect of a smoke turns the mind into another direction and offers a greater satisfaction from the arrest of the process of eating than can be gained from its continuance.

It is a fact pointed out and abundantly illustrated by the psychologists, that the very same present sensations may be pleasant or painful, according to the anticipations of the immediate future with which they are associated. The hunger that is a conscious pain, if the prospect of a meal is at all remote, may be a source of keen pleasure to the man who actually has his victuals before him, even before he has eaten the first mouthful. And in the same way the man who is accustomed to associate self-control with vigour, enjoyment of life, sense of command, and self-respect, may derive positive and immediate satisfaction from the absence, at the end of every meal, of that "sense of repletion" which in itself, according to Alexander Bain, is "massive and serene."

The conclusion of the whole matter, so far as our diagrams are concerned, is that it is generally an abuse of the diagrammatic method to attempt to make a curve represent, with any closeness, an isolated and concrete experience. A curve must represent the estimate formed by the consumer of the value to him of the successive increments of the commodity, and that estimate will be formed in view of all the immediate effects and remoter reactions and implications which he is capable of appreciating. All these considerations therefore will tell on the height of the ordinates, which must be regarded as registering the resultant estimate. The anticipations on which they rest will perhaps never be perfectly justified; but as anticipations they have already made all the necessary discounts, and they need no kind of supplementing or correction. Declining ordinates mean that the consumer, taking at his own valuation all the considerations that can influence him, desires successive increments of the commodity with declining eagerness; and his estimates are based upon anticipations which are constantly being checked and modified by experience.

CHAPTER II

ON THE DIAGRAMMATIC METHOD OF REPRESENTING AREAS OF SATISFACTION AND MARGINAL SIGNIFICANCES13

Summary.—The method of representing economic phenomena by curves demands closer examination than we have yet given it, and turns out on inspection to present many problems both of interpretation and construction. The measurements on the axis of Y indicate limiting rates of marginal significance, and, while expressed in an objective rate-unit, they must ultimately rest on estimates based on psychic experience. Hence difficulties arise as to the relation between objective and psychic units, the possibility of keeping that relation stable, the meaning we are to attach to accuracy of estimate and the conditions which limit that accuracy. If we express the data of Book I. Chapter II. as to the significance of tea in the form of a tea curve we are led to examine (a) the implications of the special formula to which our data conformed, and (b) the possibility of any simple mathematical formula approximately representing the facts. An attempt accurately to interpret the curve further leads us to distinguish between a curve of total satisfaction and marginal significance on the one hand, and a curve of price-and-quantity-purchased on the other hand. We find that these curves can, at best, only coincide approximately, and that an individual curve purporting to represent both series of phenomena can theoretically only be a "temperamental" compromise.

In the preceding chapter I have represented satisfactions by areas bounded by curves, though with the express reservation that this procedure raised questions and required explanations upon which it was not convenient to enter at the time. We will now proceed to a more careful examination of this method. We shall frequently employ it hereafter.

The representation of a given satisfaction by an area of any kind, whether rectilinear or curvilinear, involves by implication the conception of a unit to which different satisfactions can be reduced, and in which they can be expressed for diagrammatic comparison with each other. And though this idea is far from familiar and presents great difficulties when first expressly suggested to the mind, we have nevertheless seen that it is directly implied in all our practical dealings and deliberations; and it underlies all the investigations upon which we have hitherto been engaged. For to say that two things are of equal value to us, and that another thing is just as valuable to us as both of them put together, is to say that the latter is worth twice as much to us as either one of the former, or that we anticipate a satisfaction twice as great from the one as from either of the others. If we say that a thing is just worth a penny, we are thereby equating the satisfaction we expect it to yield with all the other satisfactions which we believe a penny would secure at the margins of other branches of expenditure, and if we went on to say that something else was worth exactly three shillings and not a penny more, we should be saying that we expect it to yield as large a satisfaction as any thirty-six things we could get for a penny each, or a satisfaction thirty-six times as large as that which any one thing just worth a penny is expected to yield. Now it is quite true that such estimates are often vague, and almost casual, and that they are subject to every kind of fluctuation and inconsistency; but every deliberate act of choice, or of administration of resources, is an attempt to make them more precise and consistent; and even an impulsive choice is a declaration that at any rate one thing is more valued by us than another, and this involves an act of quantitative comparison. Such as they are, these choices, impulsive or deliberate, are verdicts as to comparative volumes of satisfaction, considered as magnitudes, and they often express themselves in units of pence and shillings.

Now all commodities, services, or opportunities that enter into the circle of exchange are ultimately estimated not as physical or objectively measurable magnitudes, but as sources of anticipated satisfaction; and we frequently estimate things that are not in the circle of exchange in terms of things that are, and constantly choose between things that are and things that are not in this circle, weighing them against each other. Thus it is clear that for each one of us, at any given moment, the ordinary conduct of life unmistakably implies and involves the conception of satisfactions as magnitudes, and therefore as expressible ideally in units, which may be represented diagrammatically by unit lines, or areas, or otherwise, as suits our convenience. And just as, in measuring and comparing lengths with a view to determining their relative magnitudes, it does not matter whether our unit is an inch, a metre, or a mile (the difference being only in the numerical expression of the results obtained, not in the results themselves), so it is of no consequence whether we take our unit of satisfaction as that represented by 1d. or that represented by £1. But in comparing different satisfactions, expressed as areas, we must always remember that to be comparable as magnitudes the satisfactions must be estimated by the same person. With these reservations we may now proceed to the diagrammatic representation of the estimates dealt with in the second chapter of Book I. and generally to the interpretation of curves of total and marginal satisfaction.

We may take (arbitrarily) a small square on the ruled paper of Fig. 9 to represent one-quarter of the satisfaction anticipated from the expenditure of a farthing. Then four squares will represent the satisfaction corresponding to a farthing, sixteen squares that corresponding to a penny, and 12 × 16 = 192 that corresponding to a shilling. Any rectangular or curvilinear area, irrespective of its shape, if equal to 192 small squares would then represent this shilling volume of satisfaction. It might, for instance, be a rectangle with a base of 1 and an altitude of 192, or one with a base of 16 and an altitude of 12.

Taking a side of a small square as our linear unit, let us now agree that the unit length (not area) measured along any base line shall represent a periodic (monthly or as otherwise defined) supply of one ounce of tea, and a base of 16 such units a supply of one pound. We can now represent diagrammatically any of the data as to tea which we assumed in Book I. Chapter II. For instance, the fourth pound was expected to yield a satisfaction equal to the significance of 8s. in any other application. This would be represented by an area of 8 × 192; and as we have agreed that a basis of 16 shall represent a pound, a rectangle of base 16 and altitude 8 × 12 (=96) will be the proper representation of the satisfaction anticipated from the consumption of the fourth pound per month (Fig. 9 (a)). But of this fourth pound we saw that the first half was estimated at 4s. 5¼d. and the second at 3s. 6¾d. These values would be represented respectively by rectangular areas containing 852 and 684 small squares, and since the basis of each would, by our convention, be 8 (corresponding to ½ lb.), their altitudes would be respectively 106½ and 85½ (Fig. 9 (b)). We can now interpret units of altitude. They will not signify positive quantities, as the units of the base do, but penny rates of satisfaction per pound of the commodity, or halfpenny rates of satisfaction per half-pound, and so forth.

Now, taking ad in Fig. 9 (b) at an altitude of 96 as in Fig. 9 (a), it is obvious that the rectangle ab, which is added to the original rectangle at the left, is equal to cd subtracted from it at the right, since the total area of the two differentiated rectangles is to be exactly equal to that of the integral rectangle that represents the satisfaction yielded by the whole pound; and we may suppose that this differentiation between half-pounds, quarter-pounds (or any other fractions, for it is not necessary to proceed by bisection of a pound rather than trisection, for instance), may be carried as far as we choose. The area of any succession of differentiated rectangles will always remain equal to that of the integral areas that present them collectively as a single magnitude. In Fig. 10 let us carry out this process to different degrees of advancement for the different pounds; and let us draw a curve such that in the case of the small and the large rectangles alike it always adds on an area to the left equal to that which it cuts off to the right, so that for any base the area bounded above by the curve shall be exactly equal to the rectangle standing on the same base. Such a curve may be regarded as integrating any number of contiguous rectangles which we choose to take in succession. That is to say, the area intercepted by the curve above any line measured along OX will be exactly identical with the area contained in the whole series of rectangles standing upon the same base.

This is a curve of total satisfaction, and its meaning is now obvious. We have seen that ideally, and in the limit, the significance of any commodity is a magnitude continuously changing as we recede from the origin, so that, however small the increment we are considering, the change cannot be regarded as suspended during the progress of its consumption. The whole process, then, ideally considered, is properly represented not by a series of steps or discrete areas, however small, but by a curve-bounded space. Such a curve, could we obtain it, would give us at a single view the whole infinity of facts to be registered. If we take any portion of the weekly, monthly, or other periodic supply of a given commodity (whatever our conventional units may be), e.g. the third unit, or the quarter of a unit between 7 1/3 and 7 7/12, or generally the portion represented by the line ab on the axis of X (Fig. 11), then the curve is constructed so as to bound an area, ap₁p₂b, exactly representing the satisfaction anticipated from the consumption of the portion of the commodity represented by ab. And note that whereas in Book I. Chapter II. we directly assumed data as to pounds and binal fractions of pounds only, a curve assumes that we have all conceivable data, and can begin and end anywhere we like.

This continuity and entire accuracy of data is, of course, purely ideal. We may conceive approximations to it, but to imagine that any one could distinguish between the rate at which tea was ministering to his satisfaction at the beginning and at the close of his consumption, say, of the 7.9432th pound, and could express this difference in fractions of a shilling-per-pound rate, is an absurdity. Indeed the reader who has some tincture of mathematical culture will perceive that even an underlying assumption of commensurability between the satisfactions accruing from successive conventional units of the commodity and those represented by the conventional units of the currency is inconsistent with ideal accuracy. These reflections reveal at once the great convenience and the ingrained artificiality of the method of representing economic quantities by curves. The very nature of a curve is incompatible with the nature of the phenomena we are investigating; but it is of high value as an ideal simplification, and as a means of mentally arresting phenomena, which in their actual existence are unmanageably complex and fluctuating. If we professed in our diagrams to present possible or actual facts, we should have to undertake the hopeless task of determining in each case what degree of accuracy might reasonably be assumed; whereas by frankly presenting the unattainable limit in every case we declare at once the ideal nature of our hypothesis and of our representation of it.

This being understood, the reader will have no difficulty (if he turns back to our investigations as to "limiting rates" on pages 60 sqq.) in recognising the height ap₁ of the curve above any point a as the graphic representation of the limiting rate of significance (in whatever unit measured) of increments or decrements of the commodity taken from the point a. For on considering the errors (p₃fp₁ and p₁gp₂ respectively) that would be involved in treating the areas above ab and ac as equal to each other and to the rectangle on base ab (or ac) and with altitude ap₁, we shall find that they become smaller not only absolutely but proportionally to the areas themselves as we make the increments ab and ac smaller; and this without limit. For if we halve the lengths ab and ac and erect perpendiculars on them and then compare the rectangles on these bases, and with altitude ap₁, with the areas above the bases bounded by the curve, we shall see that the error involved in treating them as equal is in each case less than half of the corresponding error for the wider basis. The proportion of error, therefore, decreases, without limit, as smaller bases are taken. Thus the height ap₁ represents a rate of satisfaction per unit to which no increment or decrement taken from the point a ever conforms, as a whole, but which always lies between the rates proper to any given increment and to the corresponding equal decrement, and to which those rates approximate without limit as they decrease in magnitude. The units on OY, therefore, measure limiting rates of the significance of units of the commodity (per unit of time) as the increments are taken smaller. Or, in abbreviated terminology, the ordinates represent the marginal significance of the commodity for any given supply. So, too, in Fig. 10 the areas p₁cd and p₂ed respectively will be not only smaller, but smaller in proportion to the rectangles da and db as c or e approaches d.

We have now a provisional conception of what a curve of marginal significance would mean if we had it, and we may go on to the examination of the bearing upon the determination of the form of such a curve of any data we may suppose ourselves actually to command. Let us rule our paper, as in Fig. 10, so as to mark rectangles of base 16 and altitude 12. Returning to our example of tea, we may retain the significance of all our units, and for convenience may register successive pounds (each pound being 16 ounce-units) of supply along OX, and successive shilling-per-pound rates of significance (each being 12 times a penny-per-pound rate) along OY. Each large rectangle, containing 192 small squares, will indicate, as before, the area of satisfaction represented by a shilling.

It is obvious, to begin with, that any datum we may be able to obtain will give us some information as to the course of the curve. If we know, for instance, that the fourth pound of tea yields an area of satisfaction valued at 8s., we shall know that the curve must be such that the area ap₁p₂b equals the area ac, and the area p₁df equals the area fcp₂. (We shall express compliance with this condition by saying that the curve "satisfies the datum" of the area ac.) But there is an infinite number of curves that would fulfil this condition. Some of them might bisect dc, and others might cut it at points indefinitely near to d or c, and they might intersect the verticals from a and b at any variety of points. But if we have the additional data that the first half of the fourth pound corresponds to the area ag, and the second to the area bh, many of these possibilities will be excluded, for the area which the curve adds to ag must equal the area it cuts off from it; and the same must hold for bh. The course of the curve, therefore, will be more closely determined by the two rectangles ag and bh than by the one rectangle ac, which is equal to their sum. In our original hypothesis we supposed the estimates of successive pounds of tea to reveal an easily detected law which enabled us at once to calculate any smaller areas we liked to choose. This formula would absolutely determine the form of the curve, and tracing it would only be a matter of calculation. But if we assume no such property, and imagine each datum to stand alone and not to involve any derivative data (assuming only the general property of continuous decline, after a certain point, which we may take as fixed by the nature of our inquiry), then it is clear that the minuter the increments for which we can obtain estimates, the more closely can we determine the course of the curve. For instance, we have set out on Fig. 10 (page 444) a series of data as to pounds, half-pounds, etc., and we see that, so far as they shew (that is to say, apart from our knowledge that our formula would enable us to split up the larger rectangles as finely as we choose), there would be room to suppose that the curve undulated with considerable violence over the portion corresponding to the increment from 4 lbs. to 7 lbs., but that our data enable us to assert a more regular course for the portion corresponding to the increment from 2 lbs. 12 oz. to 3 lbs. 4 oz. Seeing then that if we have given any two contiguous rectangles of satisfaction, akgm and mhnb, the curve must always pass between the points g and h, it follows that if we could determine the areas corresponding to indefinitely small increments we could determine the position of the curve at any part of its course within indefinitely narrow limits; for just as we determine a point absolutely if we can determine any position we choose of points, that approach each other without limit, between which it lies,14 so we can determine a curve absolutely if we can determine, as closely as we like, two mutually approximating points between which the value of y, corresponding to any given value of x, lies.

But here it will be well, for our security, to establish the fact that whereas (as we have just seen) a curve may satisfy the datum of a certain area, but may fail to satisfy the data of two smaller areas into which it can be broken up, it is not possible for it to satisfy the data of two adjacent areas, severally, without also satisfying the data of the total area which is their sum. The general proof of this proposition, to which we will now proceed, applies to all the different forms of curve shewn in Fig. 13.

We start with the two rectangles ah and ks and construct a curve, enofpg, such that it adds and subtracts equally from each of the two rectangles. The equal areas we mark by oblique or horizontal lines respectively. There are, of course, an indefinite number of such curves; but if we construct an integrating rectangle, ac, by drawing a line, bc, that makes the rectangles bh and rc equal, the area which the curve enofpg cuts off from the rectangle ac will be equal to that which it adds to it—that is to say, the area ebf will equal the area gcf. Since we have emn = nho we may substitute the latter for the former, and we shall have ebf = bmhof. Again, since we have bh = rc, we can obtain by substitution bmhof = scfor. And since we have rop = psg, we can again obtain by substitution scfor = gcf. Therefore we shall have ebf = gcf. Q.E.D.15

Thus, if we have any series of rectangles arranged as in Fig. 10, on bases measured continuously along OX, a curve which adds to and cuts off equally from any contiguous pair of these rectangles, severally, will have the same property with respect to the integrating rectangle that is equal to their sum. The rectangle so obtained may then be substituted for the two rectangles of which it is the sum, and we may again integrate it with another rectangle, still relying on the same result, so that the curve will always add and subtract equally from the area of the integrating rectangle that sums any number of contiguous areas with the data of which the curve complies severally.

It is evident, therefore, that since we can always rely on the curve's retaining its fundamental property when we add together the data on which we build it, but never when we subdivide them, the accuracy with which we can determine it will depend on the accuracy and the fineness of the data on which we can construct it.

To what degree of approximation, then, can we hope actually to determine such a curve? Or, rather (since the question so put hardly admits of a definite answer), what are the principles which will determine the degree of approximation to an ideal curve that may be realised in any particular case? In the first place, let us consider the question of accuracy. In the case of the tea curve, for instance, we have to ask what will determine or influence the limits within which we can reasonably suppose our housekeeper's estimates to be exact. But on the very threshold of this inquiry we are met by a grave difficulty. What do we mean by accuracy of estimate? If we are speaking of the estimate a man forms of the length of a stick, for example, or the height of a top-hat, we are speaking of something which can be tested by actual measurement. Thus if we say that a man can be trusted to judge a yard to within a quarter of an inch, we mean that if he declares such and such a thing to be exactly a yard long, or undertakes to measure with his eye a yard length from any given point, we shall find on testing it by standard measure that what he pronounces to be a yard will not be less than 35¾ inches, nor more than 36¼ inches. But what could we mean by saying, for instance, that you could rely on a housekeeper's estimates of the significance to her of such and such an amount of tea, under such and such circumstances, to a farthing? She is making an estimate, and if that is her estimate, what is the meaning of calling it accurate or inaccurate? Even if you try to bring it to the test of experience, and ask her afterwards whether her estimate is justified by the result, she can only tell you that it has or has not procured a satisfaction equal to what she now supposes she could have got by the sum she mentioned, if she had applied it otherwise; and this is itself an estimate. Though her estimates, therefore, are based on experience, and are checked and modified by it, yet no objective standard of experience can be kept for reference, or can be applied objectively as a check, like the standard yard.

Apparently, therefore, what we should mean, in the first instance, by saying that a housewife's estimates, under certain conditions, will be reliable to a farthing, would be something like this:—If we are dealing with estimates, as such (and not with the experiences which might or might not correspond to them if the experiment were made), we shall find that they may be made in various ways. We might ask a housekeeper to say how much another half-pound of tea would be worth to her if she already had 2½ pounds, and then some time afterwards, when she had not that question and answer in her mind, we might ask her what half-a-pound would be worth if she had 3 pounds. Then again we might divide the amount into other fractions of a pound, thirds or fifths, and begin at some other base than 2½ pounds, but include the former area in our new inquiries. And finally, we might ask how much a whole pound would be worth if she already had 2½ pounds. Now if she answered all these questions independently, giving every answer on the strength of a direct estimate, without mental reference to previous answers, and if the answers when compared never revealed inconsistencies of more than a farthing in the pound, and if similar tests produced similar results wherever applied, we could say with confidence that her estimates were not mere guesses or random selections of prices or quantities on which her mind was accustomed to rest, but were direct and genuine quantitative estimates, accurate as estimates, and therefore consistent, to within a farthing a pound. Another test would be to present the same question at different times in such different lights or connections as to suggest different answers, and see whether such suggestions or associations influenced the answer.

This must be the primary meaning of accuracy and reliability of estimates as such. But behind this we may think of the correctness of the estimates as attempts to realise hypothetical experiences. We may have a clear and consistent idea of the value we should attach to such and such a supply of a commodity if we already commanded just so much of it and no more, and it may be impossible to shake that estimate by the most skilful cross-examination; but yet if the experience comes we may find that we had formed a very erroneous conception of it, and our estimates may be very different now from what they were when the experience was only hypothetical. Thus remoteness of the supposed case from experience may either affect the precision of our estimate as such, or it may make our estimate now (whether precise or vague) unreliable as a forecast of what our estimate would really be under other circumstances. These two things must always be distinguished in our minds, though it may not always be necessary to insist on the distinction in any particular context.

But yet again. It is impossible to banish the idea that as well as more or less imperfect estimates there are certain definite and ultimate facts to be estimated, and that faults or errors of estimate do not affect these ultimate facts. How can we get at precise conceptions in this matter? Clearly we are still dealing with subjective experiences and not with external magnitudes. But just as we know that many impressions are received by the eye but not consciously registered by the mind, so there may be many sensations and experiences that actually go to making us happy or strong or the reverse, but of which we are not conscious as causes, or which are in themselves so slight that we have not learned to pay attention to them. An ideally perfect estimate would identify every cause and register every effect, and would actually assign to all experiences the values they would have for us if we distinctly realised them. We can reach no conception more nearly approaching objectivity than this.

Returning now to our actual estimates as such, we may go on to examine some of the influences which make a greater or lesser degree of accuracy, in the sense of precision and consistency, possible in any given case. But it will be well at this point to develop a distinction that has already been made, though not emphasised.16 Accuracy is not the only valuable quality in our data, for we have seen that the curve which satisfies the minuter will always satisfy the broader data, and the minuter data determine the curve more closely than the broader. Minuter data of a certain relative inaccuracy might therefore determine the course of the curve more closely than the broader data of relatively greater accuracy. In Fig. 10, for example, we might suppose that the area of satisfaction corresponding to the sixth pound was given with great accuracy, but if we had no minuter data the curve might, for anything we should know, undulate in an indefinite number of ways, within wide limits, over that portion of its course. We should have one accurate datum, but the course of the curve would be indeterminate; whereas we might suppose a considerably higher degree of proportional inaccuracy in our data at and about the end of the third pound, and yet be more certain that we had determined the course of the curve about that point within narrow limits. The relatively inaccurate data, because narrower, would exclude many possibilities which a more accurate datum, if broader, might admit. And, as we shall see, it may very well happen that the broader data are, as a matter of fact, proportionally more accurate than the narrower. In such a case the narrower data may be of service to us in determining the general course of the curve within the limits of the broader data, but owing to their relative inaccuracy in detail their summation might give results incompatible with the broader data, and in such cases we should be guided by them only in such a general way as is consistent with compliance with the less determinate but at the same time more accurate conditions implied in the broader data.

With this proviso we will proceed with our examination of the conditions favourable to precision and consistency of estimate. Some general remarks on precision in estimating objectively measurable magnitudes may precede our examination of the more evasive estimate of satisfactions as magnitudes.

We must not blink the difficulty and complication of this problem, or the fact that any general principles we can lay down will be subject to every kind of disturbance from the personal idiosyncrasies or the special experiences of the individual who makes the estimates. It will, however, be admitted that in estimating quantities of any kind, a given individual will have a range, or theoretically a point, of maximum accuracy. Take an observer whose experience, professional or other, gives him no particular guidance in the matter, and present him successively with two pieces of wire, one an inch and the other an inch and a half long; then, successively, with diagrams shewing spaces of 1/32 in. and 3/64 in. respectively, intercepted between fine lines. Then take him to a place from which he has a variety of views, and under conditions identical as to distance, angle of observation, and so forth, ask him to notice the distance between the trunk of a tree and a boulder (known by you to be 1000 yards), and subsequently the distance between the edge of a tarn and the edge of a snow patch (which is 1500 yards). In each case ask him what proportion the first length in each pair bears to the second. You will probably expect a more accurate proportional estimate in the case of the inch and the inch and a half than in either of the other cases. Perhaps there will be some other length which he will be able to estimate more accurately still, but there will be some point, between the thirty-second of an inch and 1000 yards, in the neighbourhood of which his estimate will reach the maximum of accuracy. And as he recedes from this in either direction his estimate will become less reliable. It does not follow, however, in individual cases, that this departure from accuracy will be regular and continuous. There may be certain definite magnitudes which, for one reason or another, the individual has been accustomed to measure with unusual accuracy, and these may be irregularly distributed. Thus, if we take a carpenter who is also a professional cricketer, and who, when a boy, sometimes ran along a mile of road keeping pace with a stage-coach, and if we submit to him pairs of lengths which are really the same fractions of each other in every case, and not very remote from equality (say that one is nine-tenths of the other), probably if their mean is a foot he will estimate them with greater proportional accuracy than if their mean is 9 yards. But again he will measure them with greater accuracy if their mean is the 22 yards of a cricket pitch than if their mean is 9 yards; with less accuracy if their mean is 1000 yards than if their mean is 22 yards; but with greater accuracy again if their mean is a mile than if their mean is 1000 yards. Thus, the general principle that there is a certain magnitude in the neighbourhood of which estimates reach a maximum of accuracy from which they depart in either direction, may be qualified by any vivid experience or frequent practice which may have cultivated particularly accurate observations of certain lengths. And whatever the points of maximum accuracy may be the man will attempt to reduce his problems, when possible, to terms of the lengths he can best judge. Thus if a length is unmanageable he will try to divide it into halves, thirds, or quarters, or to multiply it by two or one and a half, and see whether these fractions give him lengths that he can judge immediately with some confidence and from which he can then calculate the others. The boy who, when asked how he would estimate the distance of the sun from the earth, answered, "Guess a quarter and multiply by four," had a confused sense of a sound method in his mind, though he was not fortunate in his application of it.

Now in the case of our tea curve all these complications are present, and certain others as well. The ultimate quantities to be estimated and compared, here as elsewhere in the administration of resources, are not tea-leaves and pence, but quantities of satisfaction; and yet the housewife is never accustomed to think of these as quantities at all. She thinks in pounds and ounces of tea, and in shillings and pence of money, but the half-unconscious and wholly unanalysed processes which emerge into conscious deliberations under these denominations of ounces and pence really concern lots of satisfaction. Hence a divergence between the points on which her deliberations crystallise themselves in her own consciousness and those on which they actually depend.

It is not difficult to see why this is so. In order to estimate tea with reference to other commodities we must express its value in terms of money, as the common measure between all the commodities in question; and we shall estimate it in the quantities in which we are accustomed to buy it. But our direct experience of its value is based on much smaller units, for while we pay for tea by the pound we consume it by the cupful. If a man drinks two cups of tea of a certain average strength every day for breakfast, his estimate of the value of a pound of tea must be arrived at by considering it as supplying, say, sixty-four breakfasts, and the marginal value of a quarter-pound by considering the significance of substituting a cup and a half for two cups at these sixty-four breakfasts. The enjoyment of tea at one breakfast is the quantity of satisfaction he really estimates, but in order to bring it into correspondence with his problems of expenditure he must reduce it to the terms in which he actually deals in it. If we express our estimate of one sixty-fourth of a pound of tea in terms of money we fall into manifest absurdity. For money is an instrument of practical exchange, and since we cannot give effect to these minute estimates of a fraction of a farthing in any actual transaction, this method of expression loses all its value. Hence the sense of intolerable unreality in our previous working out of the tea problem (pages 44-63). As we narrowed the areas of our estimates and so brought ourselves nearer to the actual basis of realisable experience we continued to express those estimates under a denomination that was becoming more and more hopelessly inappropriate and unconvincing.

Thus the point at which we deliberate as to alternative expenditures of money is likely to be remote from that at which our experience gives us the most direct and vivid sense of the immediate value of a commodity. In a word, to compare one expenditure with another we have to recede indefinitely from the points at which we can best compare one experience with another. Commodities are not practically exchanged with each other, or obtainable as alternatives, in the quantities in which the experiences they provoke are most directly comparable with each other. And as we are more accustomed to deliberate consciously as to expenditure than as to satisfaction (though our whole expenditure is ultimately regulated with a view to satisfaction), a difficulty inevitably arises. The careful administrator does occasionally revert consciously to the primary and ultimate basis. She may from time to time calculate, for instance, how many rice puddings can be made out of a pound of rice, or how many breakfasts a pound of tea will provide, in order to establish a kind of bridge along which she may pass either way from the quantities in which she buys commodities to the quantities in which she experiences their services. She sometimes travels from her expenditure per pound or per annum to her satisfaction per quarter-ounce or per diem, in order to base herself upon experience, and she sometimes calculates how much a saving too minute to be estimated in coin of the realm day by day would amount to in a month or a year, in order that she may bring one set of experiences into terms under which it may be compared with another and alternative set.

As we are now to deal with the ultimate limits of accuracy in the construction of a curve, it is obvious that we are concerned not directly with shillings and pence per pound, but with the estimates of satisfactions per cup, and so forth, as quantities. Obviously it is with these that the housewife must ultimately wrestle. For instance, if an economy is to be effected she may have tea at fewer meals, never supplying it at certain times of day unless it is expressly asked for, or in the last resort saying that it cannot be had; or instead of this she may make it weaker, or she may practically limit the amount of the infusion at each meal while not limiting the amount of hot water that passes through the pot, or she may look for a cheaper tea, or (horresco referens) one that will not be so popular in her household. She may or may not be subject to such more or less unsympathetic pressure from her family as is implied in some of the foregoing suppositions, but in any case she is dealing with certain alternatives, and in considering them she is estimating and comparing volumes or areas of satisfaction, and it is a reference to these that underlies her estimates in money of the marginal value of an ounce of tea, and determines at what point of pressure she will buy more or less of any given quality at any given price.

It is therefore here that we must apply the principle of the magnitude that is estimated with greatest proportional accuracy; for there may be some one or more of the satisfactions she habitually considers which, as magnitudes, are realised with especial distinctness and vividness, and to which others are consciously or unconsciously referred as to a kind of standard. Suppose, for example, there is one member of the household whose wants, for any reason, good or bad, the housekeeper considers it specially important to satisfy, and whom she occasionally disappoints, as to quality or quantity, in the matter of tea. The significance of this occasional contretemps may well constitute the actual unit of greatest proportional accuracy of estimate, and it may be by unconscious reference to it that the housewife can determine most accurately the relative values of all the alternative refusals, indulgences, evasions, devices, and pecuniary expenditures, with which she is concerned in the matter. Here, as in the case of the carpenter, there may be other points impressed by other experiences that give an exceptional degree of firmness to estimates of certain other quantities; but, neglecting this consideration, we may follow up the special clue we have grasped.

Note that our housekeeper will probably never deliberately incur or inflict the specific privation we are considering, merely in order to economise the tea needed to avert it. It will occur through some inadvertency or miscalculation, and it will be the delay, or trouble, or want of courtesy to a guest, or incidental (as distinct from primary) waste, that would be involved in correcting the error that will determine her to accept the result. But when the housekeeper is asked to make a number of hypothetical estimates as to what successive increments of the supply would be worth to her, and comes to think of a contraction of supply great enough to make this specific privation normal and permanent instead of occasional and accidental, she finds she has a very clear conception of that particular "lot" of satisfaction, that she has been accustomed to translate it into a great variety of equivalents, and that she has from time to time defined it pretty closely as worth just so much of certain other things, but not even a little more. She can now translate it, by a deliberate calculation, into so much tea per month, and can estimate it with some precision at its money value. This may form a kind of standard unit of reference, and may be the magnitude she is capable of estimating with the highest degree of proportional accuracy and precision. The area thus determined will be that of the elements out of which our curve can be constructed with greatest accuracy. For in considering the value of other increments nearer to the margin or further from it, our housewife (we are supposing) will find it easiest to make accurate estimates of areas of satisfaction of this particular magnitude; and she will find, of course, that if she has to think of herself as compelled by the further contractions of her supply to cut deeper back into the satisfactions of her household than she has ever actually done, she will realise that a smaller amount of tea, at the higher significance so reached, would yield the standard unit of satisfaction, and that in like manner at a more advanced point it would require a correspondingly larger amount to secure it. Geometrically the standard area will stand on a narrower basis as we approach the origin, and on a broader one as we recede from it.

Thus, subject to all the qualifications hinted at or developed, we may suppose that the ultimate elements out of which data for the curve would be obtained with the greatest proportional accuracy would consist in estimated satisfactions of a magnitude about equivalent to that of the satisfaction relinquished on the occasions of disappointment that have impressed themselves most vividly on the housewife's mind. They would be represented on our diagram (when reduced to the terms of a month's supply, and expressed in shilling and penny rates per pound) by a series of rectangles of uniform area standing on progressively larger bases as we recede from the origin.

Now seeing that every day the housekeeper deals with the whole supply for the day, and has the opportunity of experiencing or observing the actual service rendered by every increment from the initial to the final one, we might be tempted to think that she could base her whole conjectural construction of the curve from the origin to the margin upon direct experience. But this is not so. We have seen that recurrently satisfied wants never take us back to the real initial significance of the things that satisfy them.17 If our supplies were very much contracted (even apart from any reaction upon the organism that might ultimately take place) we should gain experience of significances that had evaded us before; for the want which to-day's first increment supplies is a different want according to the point up to which our want was satisfied yesterday. And as soon as we begin to contract or increase our supply at all this process sets in, though its effect at first may be hardly perceptible, and it may only become pronounced as we recede considerably from our present margin. Thus an additional element of uncertainty enters into all estimates far behind or far in advance of the present margin, and our ideal equal areas will become correspondingly more speculative. This speculative element may reveal itself consciously in a refusal to make equally precise estimates, or unconsciously in an inability to make equally consistent ones, as we recede from the actual margin. Past experiences, vividly remembered, may establish at irregular intervals other bases of comparatively direct and immediate estimates; or critical points may so appeal to the imagination as to give a firm but illusory precision to speculative estimates; or some changed unit of maximum accuracy may assert itself in certain regions of the curve; and throughout we must distinguish between precision and consistency in the sense explained above, and approximation to the estimates which would be formed under the pressure of immediate experience should it ever be realised.

When formed, our curve, such as it is, will be an estimate, or a register, more or less reliable, both of the total significance to be derived from the consumption of any given quantity of the commodity, and of its marginal significance at any point.18

Before leaving this branch of the subject we may note that if we asked for estimates of the significance of a series of objectively equal increments of the commodity we should have a series of rectangles, not of equal area but on equal bases, from which to construct our curve; and we may ask what conditions would influence the delicacy and accuracy of our estimates of the difference of area between them. Two considerations are relevant here. In the first place, the same magnitude is less easily perceived and estimated as part of a larger than as part of a smaller whole. The difference of an inch is more conspicuous in the length of two men's noses than in their heights. Small differences will therefore be less delicately noted when the areas are large than when they are small, and therefore a given difference between two contiguous rectangles might escape detection near the origin but might be distinctly felt farther from it. But in the second place, our whole investigation has shewn us that the significance of successive increments of the commodity changes more rapidly in some regions than in others. Between two successive rectangles on equal bases, therefore, we shall sometimes have greater differences and sometimes have keener powers of observation. The first condition is indicated by a rapidly falling curve, and the second by a higher positive altitude of the curve. In our example of the tea, and in Fig. 14, a, these two conditions tend to counteract each other; for as the differences themselves decrease, our power of perceiving them increases. But in Fig. 14, b, they reinforce each other. As the differences themselves become greater our power of observing them also becomes more acute.

Enough has now been said to shew in the first place how extremely precarious any actual evaluation of a curve of total significance of any commodity must necessarily be, but also, in the second place, that this value, which it is so difficult to estimate, is actually a definite and a highly significant quantity.

The area bounded by the curve represents what the older economists called the "value in use" of the commodity, that is to say, the total satisfaction or advantage derived from its enjoyment; and the height of the curve above any point on the abscissa represents its marginal significance, which, in the case of exchangeable things, will always tend to be brought into coincidence with its "value in exchange." And note that if our expenditure is wise a decline in marginal significance due to an increased supply will always coincide with an increased volume of satisfaction. A reduction in the "exchange value" of any commodity, taken in itself, should always result in its increased "value in use" to us.19

We have now sufficiently examined the general meaning of a curve of total significance or satisfaction, and we have seen the very precarious nature of the data upon which any attempt actually to evaluate the total significance of a commodity must depend. But we have still to take note of certain points, a neglect of which might lead to erroneous or inaccurate thought.

It will be understood that a curve proves nothing whatever as to the facts from which we start. It is merely an idealised picture of facts and their implications. It may therefore enable us to understand the full meaning of any set of supposed facts, but it cannot establish them. At most it can only shew us the relations in which certain facts, if they exist, stand to each other. But by doing this it may bring out implications involved in our data that we had not fully realised, and this may throw back light on the validity of the data themselves. For instance, a glance at the tea curve at once suggests that it will not decline any further after the point to which we have carried it; and as there is no reason why the law of declining significance should become invalid after seven pounds, we begin to suspect our data of being in some way self-contradictory or impossible. And this is really the case. We supposed our original data as to the values of successive pounds of tea to conform to a perfectly rigid and easily discernible algebraical law. But this is strictly impossible. In the first place, it is impossible that the estimates should be mathematically accurate at all. That is to say, it is impossible that an infinitesimal change in the quantity of the commodity could be actually and directly appreciated, and its significance registered in terms of money. But if we are dealing only with approximations it may possibly happen that the more or less loose estimates given may conform loosely to some simple algebraic formula. Since, however, an immense number of heterogeneous factors would enter into the composition of every region of the curve, some of them changing as it proceeds, we may be very sure that no simple algebraical formula would be able to represent them all even approximately, though it might approximately fit a certain portion of the curve. So if we had assumed this precise algebraical law as determining the whole curve, we should have assumed in the first place an impossible precision, and in the second place a highly improbable (and, as it turns out, impossible) simplicity and regularity. As a matter of fact it will be found that our original data themselves assumed that after the sixth pound the law of the curve would change; for the series 23s., 17s., 12s., 8s., 5s., 3s. would give as its next term 2s., and we have constructed the curve on this estimate. But this contradicts our original data, for we started with the supposition that at 2s. a pound the purchaser would take 7 lbs.; and the figure makes it very clear that if the whole seventh pound is only worth 2s., then the first half-pound is worth more than a shilling, and the second half-pound worth less. The second half-pound therefore would not, on this supposition, be bought at all. Our curve would give about 6.42 lbs. as the ideal point at which the purchase would stop. So if we are to suppose that 7 lbs. would be bought at 2s. we must suppose the character of the curve to change after 6 lbs. It might take some such course as that indicated by the dotted line.

In very many cases a curve that approximated to a similar formula during a part of its course might reasonably be expected to change its character as it approached the origin; for we have seen that at first a commodity may have increasing significance, and may only enter upon the period of declining significance "after a certain point."20 In the case of tea, however, there is nothing palpably absurd in supposing our curve to follow approximately the formula we have assumed, at any rate up to a very close proximity to the origin. It is easy to imagine that as tea (or coffee) became dearer and dearer a careful housekeeper, whose family still retained a taste that they were less and less able to indulge, might limit the purchases more and more till at last it was only on occasions of special festivity that the precious infusion was consumed. When the price of £1:6:4d. a pound was reached, a quarter of a pound, or two ounces, might be bought for Christmas Day, and none at all at any other time. This consumption (four or two ounces a year) would be at the rate of one-third or one-sixth of an ounce per month, and would be represented on our figure by a point only one-third or one-sixth of the side of a small square from the origin. And if we had lowered the whole curve by, say, two of the large units on Y so that it intercepted the axis of X at a little under 6 lbs. 7 oz., the whole series of marginal values from the initial increment to the one that completed the full satisfaction of the desire might, without palpable absurdity, have been supposed to be represented by this particular curve. As it is, it is clear that our original data involve the supposition that the law indicated by the successive steps in declining value from 1 lb. to 2 lbs., etc., up to 6 lbs., would not continue to hold for the decline from 6 lbs. to 7 lbs.

Even if we do not assume an algebraical formula for a curve, we can seldom use this diagrammatic method without expressing more and expressing it more precisely than we desire, and this constitutes a grave disadvantage in the use of curves for popular demonstrations. If, for example, we say that successive increments of a commodity will decline in significance after a certain point the statement remains general. But if we illustrate it by a curve, the "point after which" will be determined and the rate of decline at every point will be determined, and a general conception of the modes of variation will be suggested. And so the incautious student may be misled by the characteristics of the individual curve selected, and may fail to distinguish between them and those characteristics really involved in the data. The utmost caution is needed to prevent a curve from surreptitiously insinuating into our minds suppositions which are not included or involved in our data, but which we nevertheless receive into our conclusions. Nor is it beginners only that have fallen into this trap.21 But this by the way.

We might now suppose that in such a diagram as Fig. 15, if properly constructed, we should have an ideal presentation of the amount of the commodity Ox that would be purchased by a certain individual at any given market price Oy; of the total satisfaction Oy₀px that its consumption would afford; of the volume of other satisfactions Op sacrificed in the total sum paid for it; and of the surplus of satisfaction yy₀p which is secured over and above what is sacrificed. If this were so, then this last-named area would represent the advantage which the consumer derived from the existence of this particular market, and the volume of satisfaction of which he would be deprived if it closed or became inaccessible to him, all other things remaining equal.

These conclusions, however, are still subject to sundry modifications and qualifications which we must now examine.

In constructing our curve, we have used denominations of shillings and pence simply as measures of certain definite satisfactions, and we have tried to shew how, ideally, the area of total satisfaction corresponding to any given supply Ox of the commodity could be actually evaluated in these denominations. But on closer inspection we become aware of a disturbing instability and ambiguity in our unit when regarded as a psychological magnitude. We have often noted that 1s. has a different psychological significance to two different men, and also to the same man if his income rises or falls. Theoretically, then, the marginal significance of a shilling will be affected by the sum the man has already paid to secure a certain satisfaction. We supposed, in our example of the tea, that the housekeeper gave us the outside value of the first pound of tea to her, and then supposing herself to have paid that sum for it went on to give us the outside value of a second pound, and so forth. If our Fig. 15 has been constructed on this system, then x₁p₁ will represent the marginal value of a commodity to a man, on the supposition that he has actually paid the money represented by the area Oy₀p₁x₁ for the quantity Ox₁. But will Ox₁ represent the amount he would actually buy if the market price were Oy₁? Not unless the sum of money represented by the whole area Oy₀p₁x₁ is so insignificant a part of the man's total expenditure that it makes no perceptible difference to the marginal significance of a penny whether the area Oy₀p₁x₁ or only the area Op₁ has been spent upon tea. If this is not so, then the fact that he can actually get Ox₁ for the expenditure of Op₁ will leave him better off than on our first supposition by the area y₁y₀p₁; and this being an appreciable sum it will enable him to get a little more of everything or anything (including the commodity under direct consideration) than he would have been able to do had he spent y₁y₀p₁ (as well as Op₁) on the supply Ox₁. A little more than Ox₁ may therefore be purchased. And again, since all the man's wants will be satisfied down to a lower point of urgency, the significance of what a penny will buy at this advanced margin is lowered. Thus the psychological significance of our unit will be smaller if the whole supply is purchased at the lower price than if the full sum represented by the mixtilinear area had been given for it. As we imagine Ox to advance or recede, the changing values of the total or the rectangular areas will react upon the psychological significance of the unit, and the difference between them will prevent the abscissa from accurately representing the amount that would be consumed at the price represented by the ordinate.

This is not a mere fanciful speculation. If a careful housekeeper were giving any such estimates as we have supposed, when she came to think of herself as paying 50s. or 60s. a month for tea instead of something like 14s., she might be perfectly conscious of the constraint she would feel in all branches of her household expenditure, and might realise that she was estimating the increments of tea in a unit of higher significance than that by which her actual expenditure is regulated.

The curve as constructed, therefore, does not represent the relation of price to quantity purchased with any theoretical accuracy at all, and it represents the psychological value of the satisfaction secured in a fluctuating unit.

We will begin with the latter difficulty. How can we maintain the stability of our psychological unit throughout a series of estimates? What we really want is to fix in our own minds or the mind of our informant the actual psychological magnitude represented by the objective unit at the margin of our current expenditure; and then to estimate in that unit the significance of small increments of the commodity at various margins. We should then have, for any given quantity consumed, what we set out to obtain, viz. an evaluation in a stable unit of the total estimated satisfaction enjoyed, as distinct from the sum paid. These estimates, however, are such as we could only imagine experts trained in a psychological laboratory attempting to make. The naïve, however careful and acute, answers we could expect from practical administrators would never be based on so subtle a conception as that of the psychological unit. We should have to assist our informant by putting our questions in some such form as this: "If when you had bought your tea for the month and paid for it at market prices, you lost half, three-quarters, nine-tenths, or all of your stock, what in each case would you pay for a first small increment, sooner than go without it?" The smallness of the increment estimated would reduce to a vanishing point the reaction of the sum to be paid upon the psychologic value of the money unit, and the fact that in every case the full amount that is actually paid for the commodity, and no more, is already written off, would keep that psychological value uniform. The ingenious reader may still think of disturbing influences, the shock of the loss, the changed significance of other enjoyments caused by the reduction in the supply of tea and so forth; and he may imagine any system of discounts that pleases him. It is clear that in any case absolute fixity of the psychological unit is only an ideal conception, and that actual estimates in money will never be more than approximately consistent in their psychological significance. The essential point is that the total psychic value of the satisfaction derived from the consumption of a given amount of a commodity is a finite quantity, capable of ideal evaluation in a fixed unit, and that over a vast field of our current expenditure it exceeds, in our own estimate, the value of the alternatives we relinquish for it.22 This total area of satisfaction may, in theory, be represented accurately by a figure which sets forth the marginal significance of every successive increment of the commodity; but if we have taken as our psychic unit the satisfaction which the money unit commands at the actual margin of our expenditure under existing conditions, then any hypothesis which sensibly changes those conditions (as by increasing or diminishing the amount actually spent on our commodity) will change the significance of the unit; and therefore, if we measure penny or shilling rates on the axis of Y, it follows that the same figure cannot represent, with theoretical accuracy, the meaning of a number of different hypotheses, regarded as co-existing. Given any price and the actual administration of resources that corresponds to it, we can ideally construct a curve of total satisfaction, the unit of which corresponds to the marginal satisfaction now secured by a penny or a shilling; but if the price changes we cannot preserve the same figure and get an accurate result by simply changing the point on OX at which we erect a perpendicular to cut the curve; for under the changed conditions the satisfaction secured by a penny or a shilling will have changed.

I have been careful to speak of the Figure as giving, ideally, a representation of the total satisfaction derived from the consumption of Ox, in the mixtilinear area above it. I have not said that the surplus of satisfaction over payment would be accurately represented by the area yy₀p. For this again would only be an approximation. In evaluating the price actually paid at Op our Figure implies that if the market for the commodity in question were closed, or if the commodity ceased to exist, the purchaser, while losing the total area above Ox, would gain the released area of the rectangle Op. This means that the whole of the money now spent on this commodity could be expended on other commodities at a marginal significance represented by xp or Oy. But theoretically this is not true, for if the supplies of other commodities were increased, it would of course be at a declining significance, and consequently, when the whole sum Op had been distributed amongst them, their marginal values would have declined to some extent, however small, from the height xp. Some portion of them, therefore, would have less value than if their marginal significance had remained at xp; and in the sum they will not equal Op. And here again, as we recede from the actual point of departure towards the origin, there will be another source of disturbance in the psychic significance of the money unit, independent of the advancing margin, viz. the change in the whole significance of remaining sources of satisfaction as the one to which the Figure refers dries up. Here again, therefore, all attempts to guard against and discount sources of disturbance in the psychic value of our objective unit must be at once subtle and clumsy. The only ideal method is to conceive of a mind trained to hold a psychic magnitude firmly and apply it consistently as a unit. That magnitude would be the satisfaction represented by the money unit under existing conditions, but it would be applied to hypothetically changed conditions directly, and not through the convenient but treacherous intervention of a money unit which might be perpetually changing its significance.

If we traced our original curve with a stable psychic unit, based on the satisfaction secured by a penny or a shilling at present margins, and if we then allowed for the decreasing values of other commodities as the margins advanced, represented by a decline in the height of the ordinates as we pass from xp to Oy, we should have a consistent representation of total satisfaction, and of surplus of satisfaction over the sacrifice represented by the price, corresponding to the actual state of things. It would shew how much satisfaction I get and how much I pay for it, measured in a stable unit. But it would not give us accurate information as to any other than the actual state of things.

If, on the other hand, we were to ask, not "how much would you give for an ounce of tea under such and such circumstances?" but "how much tea would you buy if it were such and such a price?" we should get a curve with just the opposite characteristics. It would give us information about a number of different hypothetical conditions, but its different parts would have no consistent significance. Thus, by asking "how high would the price of tea have to rise before you would stop buying it altogether?" we might find a point on the axis of Y, and then, by asking how much would be bought at the several prices descending from that to zero, we might obtain points on a curve which would accurately represent the relation between price and quantity purchased for every hypothesis at once. But on each hypothesis the psychological significance of the unit would be different, and as it would always make a (theoretical) difference whether the whole sum represented by the mixtilinear area above any abscissa, or only that represented by the rectangle, were paid, the area would never represent accurately either the total sum that the consumer would pay for the amount Ox, or its psychological evaluation in any fixed unit.

A curve, therefore, which professes to give, for every price, (1) the quantity that would be purchased at that price, (2) either the pecuniary or the psychic evaluation of the total satisfaction it would yield, can only be a compromise, for it endeavours to comply with two incompatible sets of conditions. Its construction would illustrate the principle of "temperament" by which a note on the piano which is neither D sharp nor E flat, but a compromise between them, is made to do duty for both alike. This is only possible if the interval between them is small. In our case the errors involved in confounding the two curves become negligible in proportion as the total expenditure on the commodity in question is a negligible part of the man's whole income.

The psychological curve always remains the ultimate and basal fact, and though we can never rely on its precise evaluations it is essential that we should form a precise conception of its nature and should realise that it has a definite value. The price-and-quantity-purchased curve is the most accessible and is the one with which we shall usually work; but unless the contrary is expressly stated we shall assume that our curves have a "temperament" which allows us to read them either way.23

CHAPTER III

ON THE NATURE OF CURVES OF TOTAL SATISFACTION

Summary.—Curves of total satisfaction are purely abstract; that is to say, they represent the subjective value attached by a consumer to each increment of the commodity, or the amount he would purchase at any given price, apart from any consideration of the causes that might be supposed in actual experience to limit his supply or raise the price of the commodity, and apart from all reactions upon the price of other commodities. They are also isolated; that is to say, we cannot conceive of a system of such curves being so constructed as to be valid simultaneously. Nor can we sum their areas, taken successively, without omitting some values and counting others more than once. Nor can we read on them the effect of a rise or fall in the consumer's income. Nevertheless their general form has a high theoretical significance. Communal curves of price-and-quantity-saleable cannot be interpreted psychically, though they rest on a psychic basis. A system of such curves cannot possess simultaneous validity.

The refinements dwelt upon in the preceding chapter are usually ignored. A curve of price-and-quantity-that-would-be-purchased is supposed to be constructed by a direct process of estimates; and its area is taken to represent the total satisfaction accruing from the consumption of any given amount of the commodity, while the rectangle of price-multiplied-by-quantity is taken to represent the value of the sacrificed alternatives, the surplus satisfaction being secured without corresponding sacrifice or payment. But, independently of the difficulties thus ignored, the legitimacy of the whole conception has been seriously challenged. Probably this is due to the fact that a personal curve of total utility, though its formation is in itself entirely legitimate, is nevertheless of such an ideal and isolated character, that it cannot be regarded as co-existing with other curves of the like nature, for the same individual, nor can it, and its analogues for other individuals, be made, as they stand, the basis for the calculation, by summation, of a communal curve of the one commodity. And therefore when we try to bring a curve of this nature into relation with any practically realisable hypothesis as to the conditions of markets, it assumes an elusory and evasive character which has tempted the bewildered and impatient student to fling it aside as a mere illusion. All this must now be explained.

We shall best avoid the confusions in which the controversy has often been entangled, and shall at the same time best vindicate the fundamental value and significance of the method itself, by examining more closely the meaning of the condition that "other things must remain unchanged" while we are obtaining our successive data as to how much of the commodity the consumer would purchase at such and such prices. To begin with, amongst the other conditions that are to remain unchanged, we must include the power of purchasing substitutes at the prices now current. For example, when our housekeeper is considering how much tea she would buy if it were 6s. a pound, she will probably think of herself as increasing her purchases of coffee or cocoa as she contracts her purchases of tea; and she will suppose that she will still be able to buy coffee and cocoa at the present prices. Now this shews us at once the isolated nature of our hypothetical tea curve. For suppose we had constructed a coffee curve, as well as a tea curve, on the same principles. We should then find that the conditions we supposed to be stable when we were drawing up our tea curve included the possibility of getting more coffee at the present price; and, in like manner, the conditions we supposed to be stable when we were drawing up our coffee curve will have included the possibility of buying tea, as required, at the present market price. Thus, as soon as we suppose the price of tea to rise, we are violating one of the conditions on which the validity of our coffee curve depends; and, in like manner, if we supposed the price of coffee to change, we should thereby be violating one of the conditions on which the validity of our tea curve depends; for it is sufficiently obvious that the amount of coffee which a housekeeper would buy at any given price might be affected by a change in the price of tea; and vice versa. It seems impossible, then, even ideally to draw up a system of curves which shall be valid simultaneously; for any curve purports to represent a number of simultaneous possibilities, indicating what quantities would be purchased at any given price; but a change in the price of any one of the commodities will, or may, affect the quantity of other commodities that would be taken at any given price. That is to say, if we change our supposition as to the price of any one commodity, that very supposition will change the form of the curves of other commodities, throughout their course. This perhaps needs some further elaboration and explanation.

Let us start on the assumption that the consumer's income is as a matter of fact distributed in a certain way. He buys Oa of commodity A at the price aa, Ob of commodity B at the price bb, Oc of commodity C at the price cg, etc. We construct the curves severally as in Fig. 16, on the principles already illustrated, in every case starting from the same initial hypothesis. Each commodity is measured on the axis of X in its own conventional unit, but the unit on the axis of Y is uniform. We can now suppose any one of the curves (say the curve of B) to set forth (as a first approximation, subject to the secondary inaccuracies and inconsistencies dwelt on in the last chapter) the marginal significance of B at any point of supply, the quantity that would be purchased at any given price, and the surplus of satisfaction over enjoyment attendant on the consumption of any quantity, provided always that A, C, etc., can be obtained in any quantities desired at the prices aa, cg, etc. But the moment we suppose the price of B to rise and the consumption to contract we may find the consumer taking more of A or C as a substitute, and in that case Oa would no longer represent the amount of A that would be consumed at the price of aa. Nor would the curve as it stands (unless by accident) represent the relation between price and quantity at any other point either. The curves of A and C therefore may change their form for every value of bb and are drawn up on the supposition that it is constant, whereas the curve of B is drawn up expressly to illustrate the significance of changes in that value, regarded as causes or effects of a change in the magnitude of Ob.

In constructing the curve of B we must be supposed to register the value of bb for any value of Ob, or vice versa, as the resultants of all the complex readjustments of expenditure caused by a change of supply, or a change of price, in B, the prices of A, C, etc., remaining constant. And if we start in every case from the actual prices aa, bb, cg, etc., we may thus trace the curves of A, B, C, etc., severally and independently, and any one of them will then be valid as long as all the others are cancelled and the original data (aa, etc.) treated as constant; but no two of them will represent a system of relations between changing quantities and marginal values which holds contemporaneously for both of them.

We have now sufficiently developed the fact that we can only regard such a curve as we have been discussing as valid in isolation. But it will be instructive to consider a little further the nature of the reaction of a change in the price of one commodity upon the demand for another. A glance at any of the figures will shew that a rise in the price of a commodity (A), while it will always cause a contraction of the quantity purchased, will sometimes increase and sometimes diminish the amount of money spent on it. And in either case it may cause an increased expenditure on the readiest substitute (B). Thus a rise in the price of A, whether causing an increased expenditure on A or not, may easily cause an increased expenditure on A and B between them. This may extend to other commodities also; but since the man's total resources are not increased by the rise in the price of A, economies must be effected somewhere. Thus a rise in the price of A may cause an increased consumption of B but a diminished consumption of C.

In some cases this result might be the direct, not the indirect, effect of the rise in the price of A; for there are commodities which are complementary to each other as well as commodities which are substitutes. Thus a man may have a taste for café au lait but not for café noir, so that if the price of coffee rose it might check his purchases of milk. If the total expenditure on the two commodities were reduced, then some other expenditure would be increased.

Thus every modification in the price of any one commodity reacts on the demand curves, or curves of total estimated value, of some other, ideally of all other, commodities, services, and opportunities. A system of such curves purporting to represent the whole range of any man's scale of preferences would be mutually destructive, for each one only represents the possibilities of a sliding scale of purchases and prices on the supposition that there is no movement in any of the others. Any one curve represents a track, movement along which incidentally modifies some one or more of the other tracks, and which is itself modified by a movement along any one of them. This is the meaning of the principle so constantly insisted on by Pareto, that the marginal significance of any commodity is a function not only of the quantity we possess of that particular commodity but also of the quantity we possess (including zero as a quantity) of other, ideally of all other, commodities. The quantities of all desired things, services, and opportunities which we command, and the marginal significances we attach to them, are therefore a system of magnitudes which mutually determine each other within the limits imposed by our total command of resources.

Well, then, taking these curves as indicating, severally, the consumer's own estimate of the addition to his total satisfaction which the existence of each market confers upon him, his resources and alternative opportunities being what they are, can we say that as the market in A does under existing circumstances yield the net additional satisfaction corresponding to the mixtilinear area shewn by the curve of A, and the market in B the corresponding area shewn by the curve of B, the two areas added together will indicate the total additional satisfaction yielded by the two markets?

Manifestly not. Let A and B be tea and coffee. Now there are (or may be) services that can be rendered either by tea or coffee indifferently. If the rise in the price of tea, while making the consumer buy less tea, makes him buy more coffee, this is manifestly the case. The curve of A, therefore, shews the value not of the whole service which is actually rendered by the tea the man consumes, but that part of the services only which could not be rendered by coffee. And in like manner the curve of B represents that part of the services rendered by coffee which could not be rendered by tea. Thus, if we first take the advantage we derive from the tea market on the supposition that the coffee market is open as an alternative, and then the advantage we derive from the coffee market on the supposition that the tea market is open as an alternative, and then add the two together, we shall have arrived at something very different from the total advantage which the two markets together confer upon us; for that range of wants which can be indifferently satisfied by tea or by coffee will have evaded our estimate altogether. When we estimate tea it escapes and is transferred to coffee, and when we estimate coffee it escapes and is transferred to tea.

If we suppose the effect of the closing of the markets to be cumulative, then if we take tea first this common service will escape to coffee, changing the form of its curve and increasing the mixtilinear area for any given abscissa. If we then close the coffee market too, the value of the common service will be apprehended and registered under the head of coffee; whereas if we had taken coffee first it would have been the tea curve that would have been modified, and the common service would have been evaluated there; but in neither case would the sum of the areas shown by the original curves, drawn out severally on the basis of existing alternatives, give us any evaluation of the service that can be rendered indifferently by either of the commodities.

And again, the service which can be rendered by tea or coffee indifferently, but not by anything else, does not exhaust the whole service that they do now severally render. If when the tea and coffee markets are closed the cocoa market remains open, the alternatives still available may enable a considerable portion of the services now rendered by tea and coffee still to be performed. Perhaps, indeed, an important part of the services which they render is discharged by the hot water and not by the infusions or solutions it contains. So that we shall not capture the whole of the significance of the service actually rendered by tea till we have closed all access to hot water—nor then either, for the most important of all its services could be rendered by cold water.

But when commodities are complementary to each other, the several curves, instead of not counting certain values at all, will count them twice (or many times) over. To enjoy tea we require fuel and a kettle, and we value a teapot and cup, and the value we attach to tea depends upon our command of these things. Or there might be a man who found cream with his tea essential to high enjoyment. If such a man declared that he would go up to £1 for two ounces of tea sooner than give up his Christmas Day treat, the estimate might be made on the supposition that he could command an adequate supply of cream for a few pence. If he were asked about cream he might say that he would give £1 for a small jugful once a year sooner than give up his Christmas celebration, but that would be on the supposition that the tea would cost him a few pence. If we added the two estimates together we should have counted nearly all the enjoyment of tea-with-cream twice.

These sources of confusion have, as a matter of fact, puzzled many a student of marginal and total significance, and obscured many an exposition of them. For example, we are told that a man gets a loaf of bread for a few pence, for which he would give his whole fortune sooner than go without it. Nay, by a still deeper confusion we are told that the value of an initial supply of bread is "infinite." And it has been suggested that a wheat curve should stand at an infinite height at the origin—that is to say, should be what mathematicians call asymptotal to the axis of Y. This at once prompts the question, "How about water?" Should the curve of water be asymptotal to the axis of Y too? If it were so, we should have an extreme case of repeated counting of the same value; for a man dying of thirst would certainly not attach an "infinite" value to a crumb of bread. He would not give a drop of water for it. But of course the truth is that price cannot be "infinite." If a millionaire paid his whole fortune for the smallest crumb of bread he could see, the price would be high but not "infinite." Moreover, even if we substitute more accurate language for talk about "infinities," and say that if a man had plenty of water he would give all the rest of his possessions for a certain supply of bread, or if he had plenty of bread he would give them all for a certain supply of water, it remains true that if he is without either bread or water he can but offer all the fortune he has for both, and we cannot take the two previous suppositions as applicable concurrently.

Nor must we raise the initial value of bread by crediting it with relieving us from all the agony we should endure if we had water but nothing to eat, and credit water with relieving us from all the agony we should endure if we had bread to eat but nothing to drink, and then put down the sum to their joint credit; for to be without both food and drink would not involve suffering equal to this sum.

The outcome of all this inquiry is a more enlightened perception that the importance to us of increased supplies of any one commodity depends not only on the degree to which we are supplied with that commodity, but also on the degree to which we are supplied with all other alternative or complementary commodities. And since our general state of vitality and sensitiveness may be regarded as complementary to every desired experience, we may venture on the generalisation that theoretically the marginal significance of any commodity depends primarily on our supply of that commodity, secondarily on our supply of the most obvious substitutes and complements, and remotely on our supply of all things, whether in the circle of exchange or not, which in any way affect our vitality.

Hitherto we have been trying to evaluate the loss of desired experiences which the closing of a market would involve to a given individual, on the supposition that he could still obtain the same total amounts of all other commodities that he would be able now to obtain, should he choose (from change of taste or convictions or for any other reason) entirely to give up purchasing the commodity in question. We may express this by saying that his total resources or income are to remain the same, but that this particular market is to be closed to him. We are neglecting the lowered marginal significance of other commodities which would follow his increased purchases.24 Now let us suppose the reverse case, that while his income remains the same some new possibility is opened to him: bicycles or motor-cars are invented, or new fruits are imported, or opportunities of study or of hearing good music or of travel are organised, and he finds that by contracting his expenditure on other articles to the total amount of Ox (Fig. 17), and expending the sum thus saved on the freshly opened alternative represented on the figure, by the sacrifice of an area equivalent to yx he will gain the total area contained between the axes, the line xp, and the curve. This newly opened opportunity then will present him with a total advantage of the mixtilinear area above yp for the expenditure of the same income. Whether this will be for his ultimate good or not is of course quite another question. We have seen ample reasons for declining to assume anything of the kind.25 But at any rate he has now got something for which he would have been willing to sacrifice the whole mixtilinear area, and has only surrendered the area yx for it. Measured by his own immediate desires, then, there is the gain indicated.

But now let us suppose that a man's income increases or diminishes. This will obviously affect the whole system of his scales of preference. Possibly "pop and cockles" may completely fall out of his list of purchases, and "champagne and oysters" may appear on it; but in an ordinary case (especially where the change is not so great as to declass the man), while some modes of expenditure will probably be dropped and some almost certainly introduced, a large number will be extended. He will perhaps increase the scale of his hospitalities, will pay more for houseroom, and so forth. That is to say, on a great number of individual commodities the amount of his purchases will increase, but he will pay for land, railway tickets, concerts, and provisions at the same rate as before, and, as before, will gratify his tastes to the point at which the relative marginal significance of the things he buys is the same to him as it is to his competitors in the market. But the price of things, though the same, will not represent the same sacrifice, for he is better supplied with all the things in the circle of exchange that the price represents. But as for those things that do not enter into the circle of exchange—irksome effort, for example, or the sacrifice of personal tastes or the thwarting of personal affection—he would not now incur the same sacrifice in these things to avoid a slight decrement or to secure a slight increment of any of the things in the circle of exchange that he would have done when his smaller income gave each of these latter a higher psychic significance to him at the margin.

For instance, if one of his children shews signs of ill-health, and by the expenditure of £100 a year he can place him under more favourable conditions, he may not hesitate to sacrifice the alternatives of things in the circle of exchange at the margins of his other expenditures which will be necessary; whereas when his income was narrower he could not have faced the acuter hardships and sacrifices which would have been involved in drawing back these margins. Thus his marginal estimates of the significance of things on which he still expends his money, relatively to other things in the circle of exchange, are the same as they were; but relatively to things not in the circle of exchange they have taken a lower place. Whatever his income he will always bring his expenditure into equilibrium with the market prices; that is to say, the marginal units of the things he buys will always occupy at the margin the same fixed place on the objective scale of things in the circle of exchange, but on the subjective scale they have advanced to a point of lower significance.

It would be useless to attempt to indicate this change diagrammatically, for, as we have seen, every curve is changed by a change in the supplies of other commodities as well as that to which it specially refers. If we were, therefore, to draw up a man's curve of a certain commodity on the supposition that he was poor, and then again on the supposition that he was rich, the only fixed point on which we could rely would be that if he continued to consume the commodity at all, he would consume it down to the same point of objective value as before, but that the objective unit would have a lower psychic significance. Whether he would consume more or less of the commodity, whether his surplus satisfaction would, measured in coin, be greater or smaller, and if greater in coin whether it would be greater psychologically or not, and what its proportional significance to his whole satisfaction would be, we should have no means of determining. The two curves, therefore, would have no significant relation to each other. All we can say is that if the man's expenditure is wise, he enjoys a larger total area of satisfaction as the marginal satisfaction which a shilling will command diminishes; but that it really is so would be a rash assumption.

There is still another source of confusion. We have been attempting to evaluate the surplus satisfaction, over and above the sacrifice involved in the payment, which a consumer actually derives, under existing circumstances, from his normal consumption of a given commodity, and to evaluate it in terms of the actual significance of pounds, shillings, and pence under the actual conditions of his resources and expenditure. Our questions as to what he would give for such and such an increment at such and such a margin, or how much he would buy altogether at such and such a price, have merely been a device for discovering the actual value in use that things have for him; and he will not give us the answers we require unless he treats the hypothesis of an increased price as purely ideal and applying to himself alone. For as soon as he begins to think of any actual circumstances under which the price would rise, it will involve the supposition that causes are at work which affect not only him, but others also. And if he imagines that the supply of tea, for instance, is contracted, and that is why he has to pay a higher price for it, he may assume that other people are in the same position as himself; and if that is so, then obviously the general demand for substitutes such as coffee and cocoa will rise, and the prices will rise correspondingly, and the condition "other things remaining the same" will be violated, for he will not be able to purchase the substitutes at the prices for which he can now obtain them. If he is a commercial man he may instinctively take this into account, and give us estimates of what he would do under given conditions, modified by an instinctive sense of what others would be doing under pressure of the causes which had brought these circumstances about. And even the noncommercial student, as he imagines himself retreating towards the origin in his consumption of some particular commodity, often frames half unconsciously some hypothesis to account for the fact, which reacts upon his suppositions as to the supply of other commodities.

Thus when we imagine a curve that rises rapidly as we recede from the actual rate of supply towards the origin we may very generally detect ourselves arbitrarily and tacitly assuming both a gradual (or sudden) exclusion of all natural substitutes and a continued command not only of the strictly complementary commodities but of all the other things necessary to continued life and sensitiveness. That is to say, we begin by considering how much we give for a loaf of bread, all our other supplies and open alternatives being what they are, and consider what inconvenience we should actually suffer if we happened to be "short of bread" one day; but when our imagination travels back towards the origin we not only cut down our supply of bread, but silently cut ourselves off from increased supplies of potatoes, etc., until at last we find ourselves in a besieged city—but always with a good supply of water. And during this process the significance of money has itself indefinitely changed. Money, as we have seen, represents open alternatives. And in a besieged city a shilling represents less and less of the common objects of desire. Many things it cannot get at all. Of many other things it can get very little. The only things of which it may possibly be able to get more than before are such as have little relevancy to our distressed condition and narrowed opportunities—jewels and works of art, for instance. So the value of the unit in which we estimate our rising want as we approach the origin is itself declining, owing to the changed conditions that affect the whole society in which we live.

Thus an attempt to trace an individual curve back towards the origin is legitimate, and its results are interesting, suggestive, and enlightening, in proportion as the condition "other things remaining the same" is observed. But as in the case of any great and essential article or group of articles of consumption we can scarcely imagine the origin to be approached owing to an actual rise in the price while other things remain equal, such curves must depend for their construction on imaginative estimates of the value we ourselves should under present conditions attach to small increments of the commodity at given margins; not on attempts to reconstruct conditions that might really raise the market price to a high figure.

It may well be asked whether a method that needs so much guarding and explaining is worth adopting at all. The answer is that the principle of declining marginal significances is absolutely fundamental. The doctrine of surplus value in the thing bought over and above the value of the price paid, is an inevitable deduction from it. The awakened mind must, and as a matter of fact does, speculate upon it. It underlay the old distinction between value in use and value in exchange. It underlies modern discussions of the significance of a more even distribution of wealth. It is intimately connected with the relation of Economics to life. A want of a clear understanding of it brings perpetual confusion into our speculations and entangles the student in perplexities and contradictions. And it is therefore of the very first importance that we should try to find out exactly what it is and how far it takes us.

Moreover, though we cannot assume a system of curves of total significance to co-exist and to retain its general validity while modifications take place in one or more of the supplies, yet we may assume that, in spite of all the modifications which are perpetually taking place, all the curves of commodities, some supply of which is still enjoyed, continue to be such that in the neighbourhood of the actual supply an advance would mean an increased, and a retreat a diminished, marginal significance. That is to say, at and about the point of the actual supply, the curve, however fluid we may consider its form, will always preserve the property of declining as we recede from the origin.

What we have regarded as a source of disturbance and confusion in our attempts to construct individual psychic curves would become an essential element for consideration in the construction of a curve representing the collective or communal scale spoken of in Book I. (pages 142 sqq.). That scale, as we saw, is purely objective, and is not susceptible of any consistent psychic interpretation, though it ultimately rests on psychic phenomena. If we take any given commodity, and ask not how much any individual would take of it at a given price, other things being equal, but how much the community would take, other things being equal, the term "other things being equal" has essentially changed its significance. When dealing with the individual, "other things being equal" would mean that all the substitutes were to be had at their present prices. When we are dealing with the community we cannot mean any such thing. For obviously if the price of any one commodity were seriously changed, the consumption of substitutes or complementary commodities would also be changed, and if this were done on the large scale it must alter their prices also. By "other things remaining equal" then, we must now mean "no changes taking place in the conditions on which other commodities may be obtained, except such as are directly involved in the reactions of the supposed change of price in the commodity under direct consideration." Those changes themselves must necessarily be considered, and the estimates as to how much the public will take of any given commodity at such and such prices must be based on the consideration of the actual effect which the price would have on the general expenditure of the public, at the prices which that general expenditure would determine, if no independent causes changed the supply of other commodities. Dealers might be able to form a fairly accurate estimate of the course the curve would take in the near neighbourhood of actual experience, but might have no means of forming a close estimate at points near the origin, for example, or near the point of intersection with the abscissa.26

In such a communal curve of a single commodity, the mixtilinear area above the rectangle of price paid would have no consistent psychic significance. It would be made up of satisfactions corresponding alike to the halfpence of Cobbett and those of the millionaire. The figure would merely represent the objective fact that persons could be found who, under existing circumstances, would pay for so much of the commodity at the rates represented by the successive ordinates; and, therefore, the area in question would represent satisfactions for each of which some one would pay the money unit sooner than go without it, but they would have no psychic parity or equality at all.

If we compare a communal curve with an individual one, the former certainly appears to have a firmer and more defined significance, for it represents the tangible fact that so much of the commodity would be bought at such a price. But it will be noted that this objective fact is merely the resultant of the play of innumerable psychic forces which take causal precedence of it. It is a perfect illustration of the Aristotelian distinction between that which is first relatively to the observer, and that which is first in the order of nature. The observer of the market who has little concern with psychology finds the phenomena of the market directly accessible, and, if he works back towards the psychic phenomena at all, he does so from the basis of the objective facts. But the apparent firmness of these objective facts really rests on what has perhaps appeared to us the quagmire of the psychic data which are first in the causal order of nature.

Finally, we have to note that with the collective, as with the individual curves, it is impossible to construct a system the members of which shall be simultaneously valid; for any change in the selection between the alternative points presented by the form of any one curve reacts upon the forms of all the others. If we start with the existing state of things, we might trace a curve for any one commodity, shewing the prices which would result from a reduction of the supply by one-tenth, two-tenths, etc., on the supposition that the supply of all other commodities remained what it is; and then, returning to the supposition of a normal supply of the first commodity, we might trace a curve with respect to a second, and so forth. But the members of the system thus created would each start from the basis of the present state of things and on the supposition that no change took place in the supply of any commodity but the one under direct treatment. The conditions, therefore, on which they are constructed would mutually cancel each other, and only one could be regarded as valid at a time.

APPENDIX TO CHAPTERS II. AND III.

We have generally assumed that the same curve may represent, with a sufficient approximation to accuracy, both the total excess of satisfaction over payment for a given amount purchased, and also the system of relations between prices and the quantities that would be purchased. But this assumption will not always be justified.

If a man's income rises or falls, he does not increase or diminish his expenditure upon every article of consumption.27 The consumption of bread per capita is likely to be larger, not only relatively but absolutely, in a poor man's household than in a rich one's. Thus a marked diminution in a man's effective income may actually increase his purchases of bread. Now if such a practical diminution is caused by a rise in the prices of articles other than bread, there is nothing surprising in an increased consumption of bread resulting from it. But it may be that it is a rise in the price of bread itself which contracts the man's general resources, and we may then have an apparently anomalous result, for in that case a rise in the price of bread may make him buy more of it; and within certain limits he may therefore take more bread when the price is higher than when it is lower.

This, however, does not affect the principle of declining marginal significance. It still remains true that if the man were deprived of half his stock of bread he would suffer more than twice as much as if he only forfeited a quarter of it.

On the principles finally formulated on page 461, we may construct the curve of marginal significances, shewing the surplus of satisfaction over payment for any given quantity purchased at a given price. But this curve, so far from representing with approximate accuracy the curve of price-and-quantity-purchased, will be of a wholly different character from it. The latter curve will, at this point, be sloping upwards as we recede from the origin. Within certain limits the higher the price the more the quantity purchased; but this will not be because the price is higher, but because the man is poorer. This example is an emphatic warning that no curves which depend for their validity upon the condition "other things remaining equal" can be fruitfully applied to any hypothesis that covers more than a small fraction of the whole area of a man's vital experiences.

Before leaving this illustration we may note that if the rise in the price of bread is caused by a defective harvest, then, the total amount of wheat being reduced, and the consumption of a certain class of the community being increased, it is obvious that there must be a diminution of consumption in other classes of the community sufficient to cover both the deficiency in the crop and the extra consumption; and that means that the poor would outbid the rich for bread to a certain point, as they already completely outbid them for tripe.

If it is true that for a large proportion of the community the curve of price-and-quantity-consumed really has this rising slope in the neighbourhood of the actual supply, it seems possible that the poor may be forced deeper into this disastrous necessity of outbidding the rich as an incidental consequence of "corners" in the wheat-market manœuvred for financial purposes.

There is another case in which portions of a curve of marginal significance will entirely fail to coincide with the curve of price-and-quantity-purchased. We have seen that some curves of marginal significance rise in the region near the origin. Fig. 18 represents such a case. For any price, Oy, the figure suggests that there are two possibilities of purchase, Ox₁ and Ox₂. But a moment's reflection will shew that the earlier portion of the curve cannot be interpreted in this way. To buy Ox₁ would be to sacrifice yx₁ and only to gain Ozp₁x₁. The curve, therefore, only begins to be a curve of price-and-quantity-purchased after the point k, at which the total area of the price would equal the total significance of the commodity.

CHAPTER IV

BUYER AND SELLER. DEMAND AND SUPPLY

Summary.—This chapter deals with the application of the diagrammatic method of curves to the phenomena of the market. Individual curves of price-and-quantity-taken, if properly constructed for the purpose, can be added into a communal curve, on which the price corresponding to any given supply can be read. A disguised method of reaching the same result by means of intersecting curves is frequently employed, but though legitimate in itself it is misleading when used, as it generally is, in conjunction with a distinction between buyers and sellers, which is irrelevant to the issue. The same principle that determines the flow of any given commodity to the various consumers also determines the flow of the factors of production to the different industries. Capacity for productive effort is distributed between economic and non-economic employments, or is reserved and not put forth at all, on the general principles of the distribution of resources or choice between alternatives.

We have seen that the curves of the total significance of different commodities to the same individual cannot be added together, though a joint curve of two or more commodities can be constructed independently. When we pass to the consideration of the summation of curves of different individuals referring to the same commodity, we see at once that so far as we interpret them psychologically there can be no sense in speaking of addition at all, for there is no common psychological unit. But so far as we interpret them as curves of quantity-taken-at-the-price, there seems no reason why they should not be added. If we know the quantity that each individual would take at a given price, we know the quantity that they would take amongst them, and if we know the total supply of the article, we can find the price by determining to what point of relative marginal significance that supply will satisfy all the individuals concurrently.

But here a difficulty presents itself. If the price rises because the supply is reduced, the amount that A will take at this higher price is affected by the terms on which he can get all the available substitutes; but if B is having his stock reduced at the same time as A he will probably run to the same substitutes, and since this will raise their market value A will find that the conditions under which he made his estimates have been violated. We asked him how much he would take at such a price, "all other things remaining equal," and we constructed his curve from his replies; but now we find that (in the normal case) as the price rises all other things do not remain equal, for the price of substitutes rises also; and the modifications which this will introduce into A's estimate of the relative significance (expressed in the objective unit) of the commodity at any given margin cannot be determined simply by analysing his present sense of values, for the terms on which the alternatives will be offered to him will be changed to an extent which he cannot determine and which does not depend on his own estimates of different satisfactions.

It is the dealer's business to forecast the effect which a change in the supply will produce upon the price of the commodity when all these reactions have had their full effect, but he will not individualise the different demands. He will estimate the nature of the sum of all the individual curves, but he will think of it (or at any rate estimate it) as a single thing, not as arrived at by the addition of a number of individual demands. Thus, neither the mind of the dealer nor the minds of the individual consumers contain material out of which we could construct a number of personal curves of price-and-quantity-consumed, which could be added together into a total curve. The dealer's mind contains the material for the (speculative) construction of such a total curve, but not for the construction of the elements out of which it is composed; and the minds of the individual consumers contain the material out of which the first approximation to the individual curves might be made, but not the material for estimating the modifications which will be produced in those individual curves by the reaction of the changing prices of substitutes, which the dealer estimates in the mass.28

Nevertheless, it remains true that these effects, which are only estimated by the dealer in the mass, are actually composed of the sum of the effects on individual demands, and we may therefore conceive ideally of a series of individual curves of price-and-quantity-demanded, in which these reactions have been discounted, and which can therefore be added together.

They will represent for each individual the prices which he would give for each successive increment sooner than go without it, under the modified possibilities as to substitutes which would accompany the contracted supply which caused the rise in price; and the sum of them will constitute a collective scale shewing at what price any given quantity of the commodity could be sold, or what quantity could be sold at any given price, all other supplies remaining constant, though the demand upon those other supplies varies.

In Fig. 19 let (a), (b), (c), etc., represent the curves of one commodity for the individuals A, B, C, etc. On the axis of X the commodity itself is measured in its proper conventional unit, and on the axis of Y the corresponding price or marginal significance is marked. Now take (d) equal to the sum of (a), (b), and (c) read laterally. That is to say, for any ordinate of determined length Oy the abscissa on (d) is to equal the sum of the abscissas on (a), (b), and (c).

Supposing A, B, and C to represent all the potential consumers of the commodity, this would mean that (d) represents its collective or communal scale of significance. If we have the three curves and know the total amount of the commodity at command, we can construct the collective curve (d), measure off the total supply on its abscissa, as Ox, and find the corresponding ordinate Oy. This will be the point of relative significance down to which all the claimants will be satisfied; and we can measure off the several abscissas on (a), (b), and (c) that it will determine. They will shew the amounts of the commodity that A, B, and C will respectively take out of the market. The communal curve will be represented by (d), on which equal areas, though they represent satisfactions that correspond to the same objective unit, have not the same psychological significance.

This addition of curves is given primarily as a graphic device for finding that point on the ordinates of the curves which will make the corresponding abscissas amount, in their sum, to the total supply. This distribution is actually determined by the play of the demands represented by the several curves. If the supply were distributed in any other way, there would be no equilibrium, and the conditions of further exchange would exist. But we have seen that the collective curve directly represents the facts of the market in the form in which the sellers actually endeavour to estimate them. They have more knowledge by experience of the collective scale than they have of the individual scales, and each purchaser may find a price ruling in the market which has been arrived at by a direct attempt on the part of the sellers to construct a portion of this collective scale, without reference to the elements out of which it is composed; and the purchaser will then regulate his purchases in accordance with this price. Thus the graphic process of determining the price by finding the ordinate on the collective scale that corresponds to the total supply, and then determining the share that falls to each individual by ascertaining the abscissas that correspond to the ordinates on the individual curves, closely corresponds to the facts of the market.29

We may now, therefore, pursue our investigations into the constitution of the market by aid of this system of diagrams. Our figures, so far, have given no indication of the amounts of the commodity (if any) which the individuals concerned possessed before the market opened. And we shall find that no suppositions we can make as to this will affect the result so long as the curves and the total quantity of the supply are supposed to remain the same. If neither A, B, nor C possesses any of the commodity when he comes into the market, and the whole of the supply Ox (d) is brought in by sellers who have no reserve price, A will be the purchaser of Oa, B of Ob, etc. If each of the individuals A, B, etc., already possessed the exact amount that we have arrived at as his ultimate portion, no business would be done at all, and the "price" would be virtual, not actual. But now let us suppose A, B, etc., to possess respectively the amounts Oa, Ob, Og, (Oa, ab, bg, on (d)). And let us further suppose that an amount gd, bringing the total to Od (which we will call Ox), is thrown upon the market without reserve. The total Ox remaining unchanged, and the curves remaining the same, the final distribution will also be the same, but A will have sold aa, B will have bought bb, C will have bought gc, and the sellers who are not potential buyers on any terms will have sold gd.

Thus the initial distribution of the stock affects the amount of business done and the movements that bring about equilibrium; but it does not affect the price or the ultimate distribution, which depend solely on the total amount of stock and the curves of the individuals. If we know what the stock is we know where the ideal equilibrium will be, and if we also know how the stock is distributed we know the extent of the disturbance of equilibrium from which we start; but this latter piece of information does not affect the point of equilibrium itself.

The facts of the market, however, are very generally presented in a disguised form, determined by considerations irrelevant to the result, and fostering what I take to be a mistaken conception of the whole matter. If we had a number of curves to deal with, we might suppose them to be divided (on any or no principle) into two groups, and then reduced by addition to two collective curves. We should then be able to escape the cumbrous process of addition as far as these two curves were concerned, and arrive at the resultant price by the graphically simpler method of intersection. In this case too, of course, it would be necessary to know the total amount of the commodity in the market, and unnecessary to know its initial distribution. Thus in Fig. 20 let us add together in (d) all the constituent curves except (c), and instead of adding (c) as before, let us measure Ox (the total amount of the stock) along the axis of X, and taking the point x as the origin of the curve (c) let us reverse that curve. The point of intersection will have the same ordinate which we obtained by addition in Fig. 19. This is easily seen from a study of the dotted line, which is constructed, as before, by adding all the curves together. Thus every mn will equal the corresponding pq. In the figure, p₃q₃ and m₃n₃ coincide. Therefore (Ox being the whole amount of the commodity, and the dotted line being the collective curve) xn₃ is the price that was determined by our former method (Fig. 19). And it coincides with the height of the point of intersection of the sum of (a) + (b) with the reversed (c). Every point on every curve has been taken into equal account in obtaining this result; and it does not matter which curve or curves have been reversed. It is the height of each point that affects the result, not the question whether it has been registered and combined with the others in a curve rising towards the left or one rising towards the right.

What we have now got is an ordinate such that the portions of all the curves which are above it have abscissas that collectively make up the length Ox, representing the total amount of the commodity.

But this method of intersection can only be applied once. It cannot be applied cumulatively, for it confuses the record while registering the result. Thus if we add (a) and (b), and suppose the stock still to be the same, we arrive at xp as the price which would rule between A and B if C were not in the market; and having C's curve we can then arrive at the modification in the price effected by C's entrance into the market either by the method of addition or that of intersection. But suppose we had originally treated (a) and (b) by the method of intersection. We should have arrived at the same result as far as they are concerned (Fig. 21), but we should not now be able to combine it with the data of (c). Thus it will be seen that the method of addition is the only fundamental one. Intersection is a disguised form of addition, and this very disguise obliterates the record. We shall see the importance of this more clearly as we proceed.

The methods of addition and intersection may both be applied in cases where our data are less complete than we have hitherto supposed; for the process of addition may be regarded as beginning at any point of the collective curve which we like to select. Thus, if we knew, for instance, not how much of the commodity A, B, C, etc., possess collectively, but how much more (or less) than would satisfy them down to the urgency represented, say, by 20, and if we knew the course of the curves in the neighbourhood of the 20 point in each case, we should have all the material necessary for determining the equilibrating price that would satisfy all the consumers, and the ultimate distribution of the aforesaid excess amongst them; but we should not know how distant that point might be from the origin either of the collective or of the individual curves.

We shall enter upon the detailed examination of a case of this kind presently, and it will be seen that it is a perfectly natural one. Our present business is to illustrate it diagrammatically. We are not supposed to have complete knowledge of the curves. We do not know where they start or how they arrive (Fig. 22) at the points in (a), (b), and (c), which bring A, B, and C respectively to the margins at which the commodity has a value of 20 for them; nor do we know the total amount of the commodity; but we know how much of it is left when the 20 points in (a), (b), (c) have been reached, and we know the course of the curves for some space about these points. Assuming data consistent with those of Figs. 19, etc., let us say that the supply is 14 in excess of that required to bring all the margins to 20. We simply have to add the curves as before, beginning at this point, and we shall obtain a portion of the identical curve (d) which we had in Figs. 19 and 20, only we shall not know how far off the origin is. We measure off the length 14 from this point, and obtain, as before, 15 as the price. If we preferred the method of intersection we could first add (a) and (b), and then reverse (c), making the space between the highest point of (a) + (b) and the highest point of (c) equal to 14; so that wherever the curves intersect we shall have the collective abscissas of all the curves taken together, above the height of the point of intersection, subtending abscissas to the amount of the stock (Fig. 23).

It would be a great mistake to suppose that in such a case the portions of the curve and the stock about which we have no information are without influence upon the result. It is because the total amount of stock is what it is and because the curves are what they are that the whole amount of the stock, minus fourteen, is capable of satisfying all the demands down to the ordinate 20. There might, of course, be other combinations of data which would yield the same result, but that would be a coincidence. At any rate the result from which we start is determined by definite data, and our final result is as much determined by those data, of which we only possess the registered results, as by those which are represented by the fragments of the curves and the surplus of the supply which are given us in detail. What ultimately determines the price, then, is the whole amount of the commodity and the character of the individual curves.

We may suppose our information to be given in yet another form. Suppose a whole body of curves (no longer the same body we have represented in Figs. 19, etc.) has been reduced to two (Fig. 24), and we have one of these collective curves given us from the origin onwards (a). Concerning the other we are told that the total amount of stock (unspecified), if distributed exclusively amongst the consumers represented by this second curve, would satisfy them to the point with the ordinate 4. The course of this curve upward from the point in question towards the origin is given us for a certain distance (b), but we do not know how far off the origin is. We measure 4 on the ordinate of (a) at the origin, and then reverse (b). The point of intersection will give us the price 17. But this again is only a disguised addition of the partial character that we have just examined. We do not know what the quantity of the commodity is, but we know how much it is in excess of any ordinate on curve (b) which we choose to select, within the limits of our information. Thus we know that it is 63 in excess of the amount required to bring the ordinate of (b) to 40, 39 in excess of that required to bring it to 20, and so forth. The reversed curve (b), therefore, will secure that every point is at such a distance from the origin, or highest point of curve (a), as to comply with the conditions specified in connection with Fig. 23; and the data of the latter figure can be reduced to the form presented in the other with perfect ease. The total amount of the commodity required to bring the ordinate of group (b) from 40 to 4 is 63. We know from curve (a) that 10 would be required to bring group (a) to the same point. Starting then at the points of the two curves with ordinate 40 we have 63 - 10 (=53) as the surplus of the supply; and we can present the two curves from the points of ordinate 40 onwards, with a space of 53 between these two points, and obtain (Fig. 25) the price by intersection precisely as in Fig. 23. But here, as before, the real process is one of addition. We could of course have started at any other point of (b) lower than 40, and the corresponding point of (a), with the same result. In fact our Fig. 25 includes all such alternatives in itself.

We can now understand the exact meaning of the confirmed habit of presenting the phenomena of the market under the form of a curve of "supply" and a curve of "demand," the intersection of which determines the price. It is based in the first place on a division (irrelevant as we have seen) between those persons in the market who have, and those who have not, a certain stock of the commodity in question. The curve of the latter is given in its completeness, or, at any rate, the origin is marked and the portion of the curve which is sketched is made to begin at a defined distance from the origin. This is called the curve of demand. The other curve in then inserted as a reversed curve, and a definite ordinate is assumed either for the point at the origin or for a point at a defined distance from the origin; and this is called the supply curve. Now this curve is a curve of reserve prices, which, as we have seen,30 is merely another name for the demand curve of those who possess a stock of the commodity; and its reversal is merely a quick way of arriving at the results of addition. But in connection with it information is tacitly given us as to the surplus of the total stock over the amount required in order to gratify the whole market down to some given ordinate. The connection between these two pieces of information is arbitrary; for the vital information as to excess of supply over that required to bring the ordinates to a certain point, might just as well have been given us in connection with the other (so-called "demand") curve, or partly in connection with one and partly in connection with the other, or without any specified connection with either of them. Thus, if we had not had the two curves given us at all, but only the whole collective curve, without distinction between possessor and non-possessor, and had also been told that the stock was enough to satisfy all claims down to the ordinate of 40 with a surplus of 53, we should have obtained exactly the same result. And if we suppose curve (a) and curve (b) alike to be miscellaneous groups, both of them made up of some persons who possess and some who do not possess supplies of the commodity, we shall still have precisely the same results.

But the distinctions which are irrelevant to the determination of the market price and of the quantities ultimately possessed by the individuals constituting the market do affect, as we have seen,31 the specific steps by which the price is discovered and the equilibrium reached. It is in the failure to distinguish between the methods by which that price is discovered, and the ultimate facts by which it is determined, that the current analysis of the market appears to me to fail. Though the division between buyers and sellers is not absolute (for we have seen32 that a man may be a buyer or a seller according to circumstances in the same market, and that the buyer may be a possessor of stock also), yet it is undoubtedly the "higgling" of buyer and seller that discovers the actual price. Hence the seductive character of the current representation, and the insidious character of its concealment of the ultimate nature of the market and market prices.

We will now proceed to the examination in detail of examples of the way in which relevant and irrelevant facts are usually confounded in the analysis of markets and market prices.

In his book on The Economics of Distribution33 (pages 11 sqq.) Mr. Hobson supposes that in a horse-market there are eight "sellers" (of horses of uniform quality) who have reserve prices running from £10 to £26, and ten "buyers" willing to give prices running from £15 to £30. The details may be thrown into the form of Fig. 26. The figure is necessarily defective, for if H will sell at £26 and P will buy at £26, this involves a difference in the place of a horse upon the scales of preference of H and P, but Mr. Hobson does not tell us how great the difference is. It may be less than a farthing; that is to say, it may be that H would not sell at a farthing less than £26, and P would not buy at a farthing more. But that H would sell at £26 shews that he prefers £26 to the horse, though by never so little; and that P would buy at £26 shews that he prefers the horse to £26. A horse, then, stands on H's scale at a little below £26, and on P's at a little above. This is not shewn on our figure; but neither is it necessary for the purposes of our investigation.

Mr. Hobson proceeds to argue that if a price of anything above £21:10s. were set there would be more sellers than buyers, and if anything under £21 were set there would be more buyers than sellers, so that the price would settle somewhere between £21 and £21:10s. Anywhere within this range there would be an equal number of buyers and sellers.

This is all perfectly true, and it corresponds to our elaborate exposition of the market as a machinery for discovering the ideal equilibrating price.34 But if it is given as a statement of the data which determine that price it is quite needlessly complicated and gives us a number of irrelevant facts. If we know nothing at all as to who possess the horses but know the position a horse occupies on the relative scale of each of the persons concerned, we shall have, on Figure 27, a statement of what prices would rule for any supply of horses from one to eighteen, and shall see that for eight horses it might be anything from £21 to £21:10s.

The relevant facts for determining the price, in the case supposed by Mr. Hobson, are found to be that there are eight horses altogether, and that the places that a horse occupies on the scales alike of A-H and I-R are as stated, and as represented in the diagram. The irrelevant facts are that the eight horses are at present in the possession of A-H, and that I-R are all without horses. When I say that the possession or non-possession of a horse is irrelevant, I mean that it is irrelevant if we know the position of a horse on the scale of preferences of each of the persons concerned. The possession or non-possession of a horse may no doubt affect that position, but so may the man's health, or the health of his wife, or his age, or the fact that his wife has recently read Mrs. Hayes's Horsewoman, or that his daughter has read Xenophon On Horsemanship, or a thousand other things. There may, in short, be an indefinite number of reasons why the horse occupies just this position on his relative scale, but as long as we know the fact we are indifferent to the causes. Given, then, the relevant facts, you may distribute the items between the groups just as you like. You may arrive at your conclusion by the method of addition or the method of intersection. You may deprive the whole alphabet from A to R of horses altogether, and throw eight horses from some other source upon the market, without reserve price; you may suppose that some in group A-H possess horses and others do not; but you will always bring out the identical result that the market price, virtual or actual, will be somewhere between £21 and £21:10s., and that the ultimate possessors of the horses will be H, G, F, R, Q, P, O, N. Naturally. They are the eight persons on whose scales of preference a horse (whether they have him to begin with or not) stands highest, and there are only eight horses altogether.

If the fundamental method of addition is adopted, it is obvious at once that no hypothesis as to which of the persons brings the horses into the market will in any way affect the result, and, on examination, the same will be found true if we adopt the method of intersection. On Mr. Hobson's supposition, group I-R possess no horses, and group A-H possess eight. We know, then, that as there are eight horses altogether, we must so arrange the curves that between the highest of one group, R, and the highest of the other group, H (both included), there shall be eight units, so that whatever the point of intersection may be there shall be eight and only eight letters above it. This will give us Fig. 28,35 which will bring out the same ultimate possessors of horses and the same prices as we had in Fig. 27. But if we suppose that the eight horses were originally possessed by A, C, F, H, K, L, M, O, and that B, D, E, G, I, J, N, P, Q, R were without them, and proceed by intersection to determine the price and the ultimate possessors, we must again see to it that between R and H (both included) there are eight units, and again we shall obtain identical results (Fig. 29). But this rearrangement of the individuals is really superfluous. We may suppose the down and up sloping series in Fig. 28 each to include possessors and non-possessors, according to the data of Fig. 27. This will in no way affect the result; nor is it necessary to have any information on the subject in order to split up the data of Fig. 27 in any way we like and place the two groups cross-wise, with the interval between their highest members determined by the datum as to the total number of horses.

It will be noted that Mr. Hobson gives us the whole of the facts. Mr. Marshall (Principles of Economics, ed. 3, page 410) has a parallel example in which he only gives some of them. He supposes, in a corn-market, that at 37s. a quarter there will be "sellers" of 1000 quarters of wheat and "buyers" of 600; at 36s. "sellers" of 700 and "buyers" of 700; at 35s. "sellers" of 500 and "buyers" of 900.

The facts given us may be tabulated thus:—

A		B
Sellers will sell—		Buyers will buy—
1000	at 37s.	600	at 37s.
700 (keeping 300)	at 36s.	700	at 36s.
500 (keeping 500)	at 35s.	900	at 35s.

Therefore (subtracting from the B figures the 600 required to bring the B's to the 37s. point) we find that when all are satisfied down to the point of 37s., it will take—

A	B
300 more to satisfy the A's to the point of 36s.	100 more to satisfy the B's to 36s.
500 more to satisfy the A's to the point of 35s.	300 more to satisfy the B's to 35s.

It appears, then, that in the market altogether there are 1000 quarters more than would satisfy the group A, called "sellers," down to 37s. (for they have 1000 quarters that they value at less than 37s., or they would not sell them at that price). It would take 300 of these to satisfy them down to the point of 36s. (for we are told that at 36s. they would hold back 300), and 200 more to satisfy them down to 35s. What we know of the curve of the group called "sellers" is therefore represented on Fig. 30 (a). As to the group B, called "buyers," we do not know to what point they are already satisfied, i.e. we do not know at what price they would begin to buy, but we know that 600 quarters (or 600 more than they already have) would bring them to the point 37s., and then another 100 would bring them to 36s., and another 200 yet to 35s. What we know of their curve, then, from the 37s. point onwards is represented on Fig. 30 (b). In neither case do we know how far from the origins the curves start.

Let us add the two curves, starting at the points with the ordinate 37s. Fig. 30 (c) gives us the result. Now we know that after all parties are satisfied to the point of 37s. there are 400 quarters left; and these will satisfy all parties to the point of 36s. Or we might adopt the method of intersection, placing 400 quarters between the 37s. points of the two curves. The result, of course, will be the same (d). Both (c) and (d) can be constructed and read without reference to the initial distribution of the corn. If all the corn had originally been in the possession of the group A, or if half of it had been in A's possession and half in B's, or whatever the proportion had been, so long as the curves of significance remained the same, and the excess over the amount required to bring them all to the point 37s. remained 400, we should always have the same result. The course of the curves, then, and the amount of the excess, constitute our relevant information—relevant, that is, to the determination of the market price and the ultimate distribution of the excess. The irrelevant information is that the corn is now in the possession of group A.

A psychological objection may here be raised. It may be said that it is impossible that the curve of preference should be conceived irrespective of the possession or non-possession of the commodity. In the case of the horse-market it may be admitted that every man has a more or less determined relative estimate of the significance of a horse, and that we need not inquire how he came to form it. But in the case of the wheat we are asked to suppose that each man has a scale on which successive quarters of wheat are continuously registered with continuously declining significance. Now it may very well be that the man who comes into the market with the intention and hope of selling may buy when he becomes better informed of the facts, or vice versa, yet some mental friction would have to be overcome, so that the curve would not decline regularly, but would break at certain points determined by the amount of corn the man possessed. The answer is that this may be, though it need not be, the case; but that in a large market such individual considerations will counteract each other, and the whole body of persons conducting the business will present a sensibly continuous curve.

The final outcome of these investigations is that the diagrammatic method of taking a buyers' curve and a sellers' curve and shewing by their intersection what the market price will be is perfectly legitimate if properly understood, but that if it is supposed to represent the ultimate facts which determine the price, it embodies and emphasises irrelevant matter. If it is supposed that the two curves are different in kind and represent two principles, that they could not equally well be represented as a single curve, or that the transference of any constituent elements from one to the other would affect the result, or that either curve might not contain the register of both buyers' and sellers' preferences, then the method is misleading and mischievous. In the higgling of the market the price emerges as the result of the play of a conflict between buyers and sellers as such, which is not relevant to the ultimate facts and forces which constitute that price. The method of intersection is, in fact, a mere disguise of the method of addition, and it might ignore the distinction between buyer and seller without affecting the result, as far as price and ultimate distribution are concerned. If adopted to shew the amount of business done under given conditions, the distinction between buyers and sellers and the intersection of their curves is a legitimate method; if adopted to shew the ultimate considerations that determine the market price, it is, to say the least of it, seriously misleading.

Our main conclusions are nothing new. They merely restate the results of the analysis of markets entered upon in Book I. Chapter VI. Given the total supply of the commodity, the market price that any single customer finds established is determined in the main by the demands of all the other purchasers, but in some degree by his own. If his demand is, in bulk, a very small portion of the whole, then its effect on the price will be correspondingly small, that is to say, the total curve will decline so slowly that the addition or withdrawal of an amount of the commodity sufficient to carry this one purchaser from his initial to his final increments will not perceptibly raise its ordinate. And therefore in dealing with any one individual separately we may assume the market price as already fixed by all the other individuals, and may then simply measure it off on the axis of Y of the particular curve we are examining, and may draw a parallel to the axis of X through that point. The abscissa of the point at which this parallel cuts the curve will measure the amount that this particular purchaser will take. We may put it in this way: the amount of any commodity which will flow, in obedience to the economic forces, to the satisfaction of any one consumer's wants will be determined by his curve of preferences, by the similar curves of all the other claimants, and by the total amount of the commodity. This is the general law of distribution.

If we go on to ask what determines the quantity of the commodity, we find ourselves dealing once more with the identical problem that we have just solved. The flow of the productive forces into this or that industry is determined on exactly the same principles as the flow of the stock of any single commodity to the different consumers. To breed horses you need land, buildings, corn, apparatus of many kinds, and trained human faculty. In supplying horses, therefore, you demand all these things. To raise corn you need land, buildings, ploughs, waggons, gates, ships, machinery, and human faculty. In supplying corn, therefore, you demand these things. And so with all other commodities. Thus the supply of any commodity is itself a demand upon other commodities and services, and if we separate out the demand, say, for woodwork implied in the supply of each of the commodities into which it enters, we shall be doing just the same thing that we did when we separated out the demand for potatoes from all the individual budgets of the persons that composed the market. Here, as there, the share that each one gets is determined by the curve representing the urgency of the want it satisfies, by the similar curves of the other industries, and by the total available resources of the community. Thus the supply of any commodity is regulated by the combination of productive factors needed for its production and the rival claims of other commodities for the factors of this combination. Ultimately, then, we have at one end the undifferentiated and unmanipulated forces and materials of nature, the faculties (trained and untrained) of man, and the various modifications of the former by the latter, which exist at the moment. This constitutes the total available stock. And at the other end are the tastes and resources of each individual. The amount of the supply, at any moment, of this or that commodity (in its final and united form, or in any of its intermediate states or constituent elements) is determined by the attempts of the commercial community to gauge and anticipate individual wants and to regulate the flow and the combinations of the ultimate sources of supply in accordance with them.

We have seen that all the different items of the ultimate sources of supply, and all the existing products, can, at any given moment, be expressed in a common unit. Therefore, in considering any single industry, we have first to determine what unit we will take to measure amounts of the productive agents. We might take, for instance, the amount that would exchange for an ounce of gold, or a ton of pig-iron, or a quarter of wheat of given quality, or any combination of these or other articles we choose to select. This will be our arbitrary unit-of-products-and-factors-of-production, and as we are now applying it exclusively as a measure of factors of production we will call it the unit-factor of production. The unit of the special product we will take as that amount of it which the unit-factor of production can produce. What will the unit on the axis of Y be? It will represent the general command of articles in the circle of exchange which corresponds to the ounce of gold, ton of pig-iron, or what not, that we have taken to measure our unit-factor of production. We may think of it in terms of money. It may be a pound's worth or a shilling's worth of anything that is in the circle of exchange, including the factors of production themselves. The curve, then, will indicate the place on the communal scale of preferences of each successive unit of the commodity; and the flow of productive forces into that industry will be regulated exactly as the flow of fish or carrots to this or that purchaser's larder is regulated. It will bring it down to the (objective) level determined by its marginal significance elsewhere. If the total amount of the resources of society which will in any case be deflected to this particular industry is an infinitesimal portion of the whole, we may take this margin as independently fixed. The curve (Fig. 31) gives us the rate at which the unit-factor of production will satisfy human wants (measured objectively) in this industry at any margin.

At what rate (measured by the same standard) will it satisfy human wants in other marginal applications? Whatever that rate may be it can be represented by a line. Measure off that line on the axis of Y, draw through the point thus determined a parallel to the axis of X, and the abscissa of its point of intersection with the curve will determine the flow of the productive resources to this industry, and the corresponding amount of the product. The curvilinear space above this line will represent (objectively) the satisfaction which the creation or destruction of this particular industry would add or subtract from the community. Its revenues of enjoyment (or at least of anticipated or estimated satisfaction) will be increased to that extent by the existence of this industry. It follows, of course, that whereas the communal curves of demand for, say, a certain kind of timber in the furnishing, the building, the shipping trades, and so forth, can be added, under the conditions laid down on pages 494 sq., the communal curves for different commodities (houses, ships, race-horses, diamonds, books, fruit, music, etc.) cannot be added, since each such curve assumes that all other conditions remain the same, and to travel along any one of them constitutes a change of the conditions for some or all of the others.

If the demand (estimated significance) for a commodity increases, as represented by the upper dotted line in Fig. 31, the product will be increased from Ox to Ox₁. If it declines, as in the lower dotted line, the industry will shrink to Ox₂. If, while the demand remains the same, some invention is made which doubles the quantity of the commodity which could be produced by the unit-factor of production, or, which is the same thing, halves the amount of the productive forces required to produce the units we have hitherto registered along Ox, the dotted line parallel to the axis of X will indicate the quantity which will be produced. We might equally well represent this latter change by retaining the length Oy unchanged and doubling the height of the ordinate at every point, because the factors that would give the value Oy in other industries will now be producing the units of our product, and therefore the anticipated satisfactions they yield, at double the previous rate. The unit of Ox, therefore, will represent twice as much of the commodity, measured in its own proper unit, as before (Fig. 32).

We have now to note that any very extensive departure from the existing state of things might affect the whole constitution of the unit on which we are working, for it might disturb the marginal relations between different kinds of human effort and different products or gifts of nature. And, as the value of anything can only be expressed objectively in terms of something else, changes or discoveries that affect the general fertility of human effort, and the significance of natural products and agents, cannot be recorded by any consistent objective method. Further, the diagrammatic illustrations which we have been using can only be regarded as applicable to cases in which we are examining a very small part of the whole field, so that we may consider the general conditions as stable. An attempt to draw up the whole scale of significance of any one of the main factors of production, carried back to the origin, would of course be quite futile. It would be impossible to imagine the origin at all nearly approached without such a disturbance in other conditions as would deprive our units of all continuous significance.

One other point of theoretical interest remains for investigation here. We have seen36 that the creation of the supply of undifferentiated human capacity is to be regarded in the main as itself constituting a branch of expenditure or "consumption." It is determined, at any moment, by the scale of relative significance of this particular form of expenditure, "consumption," or expression of impulse, which has ruled in the past. But the total capacity-for-effort that exists is not employed "economically." What determines the amount that is devoted to the production of things that enter, or might enter, into the circle of exchange? Here, as in previous instances, we must begin with individual curves. Writers who have paid attention to the subject have usually regarded the output of human effort (spoken of under the rather dangerous abbreviation of "labour") as limited by its irksomeness, and have represented its significance (at least after a certain point) as a negative quantity.

We will begin with Robinson Crusoe. Along the axis of X (Fig. 33) we measure units of effort. The proper basis for such a unit would be foot-pounds if we were considering mere muscular effort, but it will be convenient to take an hour's work as our unit, including all physical and mental effort, and ignoring the fact that during different portions of the day, and so forth, the actual output of effort made per hour, measured by any objective standard, will vary. The p curve will now represent the marginal significance to Crusoe of the result of successive unit-outputs of effort, and the l curve will represent the marginal irksomeness of the output of effort itself. The unit on the axis of Y is essentially psychic, and we may for the present read the figure as meaning simply that at the margin of six hours' work per day the value of the product compensates threefold the irksomeness of the effort; that is to say, Crusoe would make the effort even if its results accrued at only a trifle above one-third the rate at which they actually accrue. Thus the balance is favourable up to 9 on the axis of X; after that it would be unfavourable, and therefore the output of effort is carried to that point and no further.

Leaving the island and returning to civilisation, we take the remuneration of each man's effort per hour as a datum, fixed by the general laws of the market, and, still reading the curve psychologically, we find that at the margin of six hours a day the individual whose curve we are examining estimates the advantage of the increased supplies of all commodities and services in the circle of exchange as threefold compensation for the irksomeness of the work that secures them. And the advantage is on the side of doing more work for wages up to nine hours a day, but no further. This, then, is the amount of labour he chooses to supply on the terms which it will command in the market. Well, then, he sells his time with a system of reserved prices, which constitutes his own demand for it; just as the stall-keeper sells her plums.37 Each individual can get for his work economically as much as his doing it is worth to others, and he will require for it as much as his not doing it is worth to himself. The total supply of any kind of effort is the whole capacity of the persons capable of making it, and this supply is distributed between economic and other applications in accordance with the general laws we have studied so fully.

This way of putting it at once suggests that the man who sells his labour is selling something for which he himself has a demand of some kind, and that this demand should be represented as a positive, not a negative quantity. Reflection fully justifies this suggestion. The irksomeness of the labour by which we earn money is not really the only thing that we have to set against the advantages the money secures. It is only a negative expression of one element in the desirability of rest or leisure. This latter is a positive conception, and it includes all output of effort upon the direct securing of things not in the circle of exchange, as well as rest. Our previous studies38 of the relations of positive and negative satisfactions and their diagrammatic representation will remove all difficulties from our path in this matter. We may treat "desirability of leisure" as positive, and may represent the l curve with positive ordinates, as in Fig. 34. We shall then get the same point as before, viz. 9, by intersection, and shall see that the whole diagram is no more than another disguise of the process of addition of curves.

We may read the l curve, whether in Fig. 33 or in Fig. 34, thus:—We have no information as to the total of exchangeable commodities which the man could conceivably secure to himself by his extreme output of effort, reducing his leisure to the minimum requirements of rest and nutrition which would enable him to continue at the same level. But we know that if he had already reserved as much leisure as would reduce its marginal significance to 7, he would still have thirteen hours a day, to distribute between the further gratification of his desire for more leisure and the total gratification of his desire for things in the circle of exchange. The p curve shews us that it will take seven of those thirteen hours to bring his desire for things in the circle of exchange down to the point of 7. That is to say, the marginal value of leisure, when eleven hours have been reserved for it, and of the reward of labour, when seven hours have been devoted to it, stand alike at 7. There are six hours more to be distributed between them. Add the curves together from this point, reversing l (Fig. 35), and we shall obtain our former result as to the point to which both sets of desires will be gratified. Two more hours will be devoted to work, making nine hours altogether, and four more to leisure, making fifteen hours altogether.39

For obvious reasons we have not carried our curves back to the origin. The assumption that "other things are equal" would be patently absurd at any great distance from the actual point of equilibrium. Even the range that we have actually allowed our curves to cover can only be justified by considerations of facility of demonstration.

CHAPTER V

THE THEORY OF "INCREASING AND DIMINISHING RETURNS"

Summary.—The laws of "increasing and diminishing returns," as currently stated, are in no sense co-ordinate, and do not form an antithesis. The use of the terms in economic argument seldom coincides with the definitions given to them. As applied to "cost of production" the conception of diminishing returns is often misleading and confused; and a fatal graphic resemblance between two intersecting curves of demand on the one hand, and a curve of demand intersected by a curve of "cost of production" on the other, has (together with other misleading influences) produced a habit, in graphic demonstrations, of treating increasing cost of production, as the amount produced increases, as the normal case. Other and less academic influences are at work to foster an irrational dread of "decreasing returns" to labour in the near future.

Diagrams of intersecting curves have been used with many different meanings, and a failure to distinguish precisely between them has given rise to much confusion. Our path to the further investigation of this subject lies through a consideration of what are known as the laws of "increasing" and "diminishing" returns.

In books on Political Economy our attention is called to the following facts. If successive doses or increments of labour (or labour and capital) are applied to a piece of land, we find that, at any rate after a certain point, doubling the amount of labour does not double the product. As we increase the amount of labour, therefore, each successive increment secures a smaller return in the shape of product. This is called the "law of diminishing returns," and is said to apply generally to agricultural and extractive industries. On the other hand, if an industry such as that of the cotton or iron trade so increases that, say, twice as much labour (or labour and capital) is employed in it as before, it will generally be found that the result is a more than doubled output. This is said to illustrate the "law of increasing returns," and to apply generally to manufactures.

When the statements are made thus baldly the reader can hardly fail to see that the two "laws" are in no sense co-ordinate, and cannot be regarded as standing side by side and proclaiming "divisum habemus imperium." The cases are not parallel. In stating the law of diminishing returns, it is assumed that the factor of land is constant, and if, when a number of factors co-operate to produce a result, you double some of them without doubling others, of course you cannot expect to double the result. If you double the pastry without doubling the apples, you do not double the pie. If you double the diners without doubling the dinner, or double the dinner without doubling the diners, you do not double the dining experience. In like manner if you double the land without doubling the operations on it, or double the operations without doubling the land, you cannot expect to double the crop. This principle would apply to manufactures just as much as to agriculture. If, for example, you had doubled the number of hands, retaining the same machinery and buildings, or if you had doubled the raw material without doubling the labour bestowed upon elaborating it, or if you had doubled the labour bestowed on the same raw material, you could in no case expect the exact doubling (or other proportionate increase) of the product. Or if a tradesman doubles his accommodation without doubling his stock and staff, or doubles his stock without doubling his accommodation and his staff, he will not double the effectiveness of his whole establishment. There are circumstances under which any of these operations might more than double the total result. If a business were desperately under-staffed or under-stocked, for instance, doubling the defective factor might more than double the effect of the whole; but if doubling any one of these factors without doubling the others exactly doubled the efficiency of the concern, it could only be a coincidence; and "after a certain point" it would certainly less than double it. The "law of diminishing returns," then, is really no more than an axiomatic statement of a universal principle that applies equally to all forms of industry, and to a great range of non-industrial experiences and phenomena as well.

The law of increasing returns, on the other hand, includes all those cases in which economies may be effected in one or more of the factors by increasing the scale of production. There is no kind of parallel or contrast between the two principles. If you double some of the factors and not the others you will not exactly double the product (except by a coincidence). If you increase all the factors in a suitable proportion you will in many cases be able to secure double the product without more than doubling any of the factors and without as much as doubling some of them.

The law of increasing returns, then, is an intelligible formulating of a very interesting and important phenomenon. Production on a large scale makes certain economies possible. A man who is cultivating 50 acres of land may require a waggon, but if he were cultivating 200 acres he might only require two, not four. And if, instead of supposing one man to increase his holding, we imagine four holders of 50 acres each to be working in co-operation, we may still suppose the same economy to be effected. Or, without any "co-operation" in the technical sense, a man may own a steam thrashing-machine, and may do the thrashing for all the farmers and holders in the neighbourhood more economically than they could do it for themselves; but it is only if there is a great deal of wheat grown in the district that this can be done. No limit seems yet to have been reached to the possibility of economising in one direction or another as the bulk of any industry increases. It seems always possible, at every stage, to introduce some new process of specialising or division of labour, and so to effect some new economy for which the industry was not ripe until it had reached its present dimensions. And note that the phenomenon we are now examining is independent of the question how far the business of a single concern, or under a single management, may be carried advantageously. The economies which a large volume of production, as such, renders possible are in principle independent of the question whether the industry is in few or many hands.

The principle of increasing returns, therefore, is intelligible and important; and it directs our attention to a significant point in the analysis of the processes of production. The "law of decreasing returns," on the other hand, as ordinarily stated, is, as we have seen, the mere enunciation, with special reference to land, of an axiomatic and sterile proposition. Of course you cannot indefinitely increase a product in proportion to the increase of certain selected factors of production if you do not increase the other factors.

This utter disparity of the two "laws" is sometimes veiled by stating the case merely in terms of "labour," or, it may be, of "labour and capital." Thus it is said that in agricultural and extractive industries the increase in the output will not be proportional to the increase in labour and capital, whereas in manufactures it will be more than proportionate. But manifestly this is only a partial statement. There is a suppressed assumption that you do not (or a suppressed postulate that you cannot) contemporaneously increase the other factors in the one case, and that you do (or can) increase them in the other. The enunciation of the "law" of diminishing returns, then, reduces itself to a veiled statement, or hypothesis, as to facts. Sometimes writers perceive this, and base their argument on explicit statements as to the actual limitation of the supply of land on the surface of the earth, or place their whole investigation on the footing of a hypothetical isolation, say, of England in time of war. On the relevancy or legitimacy of these statements or hypotheses we may have something to say presently,40 but meanwhile it is abundantly evident that there is no possibility, along any of these lines, of formulating two co-ordinate "laws," in the proper sense, parallel one to the other. The only "law" is that (within limits that do not appear as yet to have been ascertained or realised) successive economies in the administration of the factors of production may be introduced as the volume of production increases. But of course that does not mean that these economies are always such as to secure an increase in the product more than proportionate to the increase of some of the factors, if the other factors are not increased at all. The two "laws" therefore hold united, not divided, sway over industry.

But the semblance of a parallel in the statement of the genuine law of increasing returns on the one hand, and of the axiom and the disguised assumption (or hypothesis) which jostle each other under the cloke of a "law of diminishing returns" on the other, has led to a frequent treatment of the two as parallel, and this has reacted upon the conception of the "law of diminishing returns" itself. This "law" accordingly has made a series of masked movements by which it has in some degree approximated itself to a parallelism with the other.

If we were to construct an interpretation of the phrase law of diminishing returns in strict analogy to the rational use of law of increasing returns, we should formulate it thus:—"There are some industries of such a nature or in such a stage of development that you could double the output without more than doubling any of the factors of production, and by less than doubling some of them; but there are other industries of such a nature, or in such a stage of development, that you cannot double the output except by as much as doubling all the factors of production and more than doubling some of them." This would be an enunciation of two parallel principles which really might divide the realm of industry between them. It would remain to be shewn what industries, if any, came under the latter law. But this completely consistent use of the terms has never, so far as I am aware, entered either consciously or unconsciously into books of Political Economy; and that for a very sufficient reason. The terms in which we have attempted to give precision to the law of increasing returns are not the terms in which we habitually think. "No more than doubling any of the factors of production, and less than doubling some of them," is not a working formula. We might more than double some, but the economies effected by the reduction of others might more than compensate this increase; and, moreover, the question is complicated by substitutions, by the introduction of totally fresh factors, by the partial or complete elimination of existing factors, and so forth. And in order to make comparisons we need a common denominator to which all these entering and vanishing, waxing and waning factors can be reduced. This common denominator, as we have already seen,41 we have; and its index is the value in exchange of the several factors, that is to say, their marginal efficiency in other industries; and this we measure in terms of gold. What we practically mean, then, by the law of increasing returns is that in certain industries (or conditions of an industry) an increased output means a cheaper production, as measured in gold values; and, by analogy, we should interpret the law of decreasing returns to mean that in certain other industries (or conditions of an industry) an increased output would mean an increased cost of production.

Here, then, we have an intelligible use of the two terms in a parallel and consistent sense; and in most generalisations and inferences concerning "industries which obey the law of increasing returns" and "industries which obey the law of diminishing returns" this seems to be what is in the mind of the writers. But the reader will see that by a process of attraction the meaning of the "law of diminishing returns" has been drawn completely away from its original basis. Both laws have effected a masked movement from terms of specific factors of production, measured in their proper units, to terms of generalised productive resources measured in the unit of gold. And the law of diminishing returns has effected a further, and if possible more important movement, from the statement that if you do not adequately increase some important factor you must not expect an increase in the product proportional to the increase in the other factors, to the statement that in certain industries it will not be normally possible largely to increase certain important factors or to find adequate substitutes for them, except on terms so unfavourable, pecuniarily, that the net result will be an increase in the cost of production as the volume of the output increases.

These ambiguities would hardly have maintained their place in the textbooks had they not been supported by the assumption that in the case of agriculture there really is a normal difficulty or impossibility in obtaining at will an increased command of land, whereas in the case of manufactures there is no such normal and permanent limitation to the increase of any factor. Thus, the axiomatic statement that if you do not increase the land you will not increase the product in proportion to the increase of the other factors, coupled with the postulate that you cannot increase the land, yields the result that you cannot increase agricultural products except at an increase in the cost of production; and this result (flagrantly as it contradicts the facts in many instances) is accepted as representative of an important though undefined class of industries, the characteristics of which are often developed without further challenge, and without examination as to the extent to which such industries, or such conditions, actually exist. The generalisation, which still seems to pass loosely current, that the law of "increasing returns" applies to manufactures and the law of "decreasing returns" to extractive and agricultural industries, when translated into terms of cost of production, seems to derive little or no support from history, nor is it easy to apply it to the analysis of the actual phenomena of industry. It is true, of course, that land is ultimately limited in quantity, but at present there is plenty of land to be had for any specific use, either by withdrawing it from other uses,42 or by taking in fresh land not at present used for anything. And, on the other hand, if any specific manufacturing industry calls for an increase of labour, that labour can only be had by being withdrawn or withheld from other occupations, or taken up from labour-power that is not at present being used at all. As a matter of fact, no practical difficulty has been found in increasing to any required extent the area of the earth's surface applied to the production of wheat. And seeing that the men who, in an English manufacturing centre, construct thrashing-machines or other agricultural implements for use in Russia, are just as truly and certainly taking their part in the agricultural industries of Russia as the peasants who are on the spot, we cannot even say that the land of the great wheat-growing countries of the old and new worlds is out of the reach of the inhabitants of English cities; for they are actually harvesting the crops. In truth, the great industry of wheat-growing might be taken as affording a typical example of the economies of large scale production, and the abundance and cheapness of wheat in the world market indicates the fact. And, on the other hand, it is monstrous to assume it as self-evident that all the factors of production in a manufacturing industry can be increased at will. The raw material of many of them, as of the cotton industry, is itself an agricultural product, and none of them can at short notice indefinitely increase the factor of adequately skilled labour.

The most general case alike in manufactures and in extractive industries appears to be that a large and sudden increase of output must be made at an industrial disadvantage, because the supply of one or more important factors cannot be largely increased at a moment's notice. The increase, therefore, must be made at more than proportional sacrifice, since the proportions of the factors will necessarily be disturbed; and unless a sufficiently higher price is offered an increased product will not be forthcoming at all. On the other hand, if an increased demand continues for a long period, an increased flow of all the requisite factors will set in, and ultimately the advantages and economies of large production, with the factors of production duly balanced against each other, will be realised. Hence, whether in agriculture or manufactures, it seems to be a fairly general rule that when an increased demand causes an increased production that presses against the existing limits, at first cost of production will rise, but ultimately it will fall. There may, of course, be numerous and important exceptions; for there may be real and permanent difficulty in increasing the supply of certain materials; but the cereals, and generally the great vegetable staples, are a singularly unfortunate example to allege. Here at any rate there is no theoretical difficulty, and has been no practical difficulty, in increasing all the factors of production ad libitum.

We are now in a position to examine various diagrammatic methods which have been employed to exhibit the relation between value in exchange and cost of production, determining the normal price of an article by the method of intersection. It is usual to speak in this connection, as in that of the market,43 of a demand curve and a supply curve, but to distinguish between the cases that illustrate diminishing and those that illustrate increasing returns. Thus, we might take Fig. 36 to illustrate the case of an industry following the law of increasing returns. This would mean that if the quantity Ox of the commodity were produced its market value would be xp per unit, and the cost of production of a unit would be xc. Under these conditions there would obviously be an inducement to extend the industry. As Ox increased xp would, of course, fall. But so, by the action of the law of increasing returns, would xc; for as the output increased, economies could be introduced which would bring down the cost of production. There is a limit, however, to the decline of xc, whereas there is no limit to that of xp, and therefore a point of intersection must ultimately be reached. If the production were carried beyond this point, the cost of production would be greater than the price; that is to say, the effect of applying the necessary combination of factors of production at the margin of this industry would be the sacrifice of (objectively) higher values at the margin of other industries; and there would consequently be a tendency for these factors to flow from this industry to others, and so to contract the supply.

We may note, once for all, that what appears to be in the mind of writers who use this diagram is prevailingly cost of production as measured in the standard unit (gold). But as the distinction between this measurement and the measurement of the factors of production themselves, in their proper units, has seldom been kept steadily in view, there has naturally been some ambiguity in this matter.

Apart from this, we must carefully note that the two curves cannot be interpreted in the same manner. The demand curve represents a group of facts or possibilities which all of them exist contemporaneously. It is a synopsis. The high values near the origin represent possibilities as to market price, should an isolated change take place in the supply of this particular commodity, and they represent actualities in the shape of the (objective) value of certain units of the commodity to the persons who actually consume them; whereas the supply curve does not represent a series of co-existing facts. It is not true that some units are produced at the high cost represented by the points of the curve near the origin. The economies resultant on the larger output affect the conditions of production generally, and if the amount produced is Ox, the cost xc (except for temporary and individual reasons) will apply to one unit as much as to another. Scrupulous writers are also careful to note that the curve is often used with a historical significance, and in that case the high values near the origin no longer represent even potentialities in case of a reduced supply, for many of the economies which have been effected are permanent and might be applied even to a smaller supply. The supply curve, in such a case, represents a historic development on which the industry has travelled forward, but on which it could not travel backward without modification. This being so, it would be an altogether grotesque supposition that during the whole of this historical process the demand curve had remained constant. Thus the two curves could hardly be regarded as co-existing on the same plane, and no satisfactory interpretation can be given to their intersection.

It is undoubtedly true, however, that in some cases economies can at once be effected, if the scale of production is increased, without awaiting the elaboration of new methods. In such cases all the possibilities represented by the declining cost of production curve may be conceived as actually co-existing, qua possibilities, though not as actualities. In the same way an amount-of-the-supply and market-price curve represents a series of prices that co-exist as possibilities but not as actualities; whereas a curve of marginal significances represents, if properly constructed, a group of co-existing actualities. With these limitations a curve (as in Fig. 36) may be accepted as theoretically giving a closer approximation to the truth than the straight line of Fig. 31, in cases where the whole curve of demand is given from the origin onwards, or in which a large part of the whole curve is under consideration. Within the limits of actual oscillation, while "other things remain the same," a straight line will often best represent the facts.

The case is far worse for the application of the method of intersection of supply and demand curves, as in Fig. 37, to instances that are supposed to illustrate the "law of diminishing returns," and this unfortunately has been its favourite application. We have seen that it is normal for a sudden increase in the demand which provokes a sudden increase in the supply to meet with the check caused by the difficulty of suddenly increasing certain of the factors of production, whether land, or skilled labour, or elaborate machinery, or premises. Hence an up-sloping curve will represent the immediate effect on cost of production of an expansion of the supply. We have seen, however, that these effects are transitory. It is only a question of time; for if time be given, all the factors of production will probably be made to flow into this particular industry in proportions corresponding to, if not identical with, those that prevailed before; and the increased scale of production will give scope to all the usual economies. Broadly speaking, then, the up-sloping curve of supply, as contrasted with the down-sloping one, represents not a class of industries, but the condition that the increased demand is recent and has been sudden. There is not only a difference but a contrast between the immediate and the ultimate effect of an increased demand accompanied by an increased supply. The obvious application, however, of the up-sloping curve of supply to the immediate effects of an increased demand has, I think, misled students into the assumption, never sufficiently examined, that there is a large and normal class of industries to which this form of curve permanently applies.

The remark which has been made with reference to Fig. 36 is also applicable here. The lower curve represents a succession of facts and is not a synopsis of co-existing ones. Lower ordinates of the supply curve nearer the origin do not represent any actual facts which exist contemporaneously with those represented by the ordinate of the point which the production has actually reached; whereas the higher (objective) significance of the units nearer the origin, as represented by the demand curve, does represent facts that co-exist with the lower objective significance of the marginal units.

But the same form of curve has often been used for quite a different purpose to which this last objection does not apply, but which is open to other objections still more grave. If we select some factor, such as land, to exclude from consideration, and then draw a curve on which we arrange the individual units of the product in order of the proportion in which they depend on this factor and not on the others, we shall again obtain a curve of the form presented in Fig. 37. Thus, if land were the factor excluded from representation in our supply curve, we should register at the origin that individual unit, say of wheat, which had been produced by the smallest output of labour and capital because it was raised on the most fertile land; that is to say, the land employed in its production, having the highest marginal efficiency, would have been combined with the smallest amount of the other factors.

In every industry the different units will be produced under very different conditions, and when they are brought to market the ratio in which wages, rent, transport, expenses of management, and so forth, enter into their costs of production will be different in each case, whether we measure some or all of these agents in their proper units, or measure all of them in the general standard (gold). And we may of course arrange them if we like in the order dictated by the proportion in which any one selected factor or factors (or all the factors except one or more selected ones) have entered into the process of their production. We should then have a curve of the form represented in Fig. 37. Here the ordinate of a certain unit would not be xc because the total number of units produced is Ox, but that particular unit would be registered in that place because its ordinate is xc. It is as if you were to collect a number of men and arrange them in order of their heights. A certain man would not be, say, 5 ft. 11 in. because he was the twentieth man originally brought in, but would be put into the twentieth place because he was 5 ft. 11 in.

The habit of treating land as something wholly exceptional that does not enter into production on the same footing as other factors has led to a frequent use of this form of diagram as though it represented cost of production. It will be worth while to dwell on this point for a moment. It is usual to speak of wheat which has been grown on specially fertile ground as having been raised "under favourable conditions." This is quite natural and intelligible in itself, but if we translate it into a statement that the cost of production of this wheat has been less than that of other wheat grown on less fertile ground, we at once land ourselves in a tangle of confusion. There is no presumption that the cost has been less to the man who raised it, for he has had to pay higher rent for the more fertile land. Nor is there any reason to suppose, from the communal point of view, that a smaller sacrifice of open alternatives has been made for this unit of wheat than for any other. Just as in a broad generalisation we assume that labour might be withdrawn from the margin of any one industry and applied at the margin of other industries, not indeed without loss, but without great and conspicuous loss if the transfer were only small, and with a loss that diminishes without limit as we suppose the transfer to be smaller, so we must also assume that if land were withdrawn in small quantities from any given use, agricultural or other, it could be applied to some other use where it would be only a little less valued. The cost of production of any commodity, as we have seen, is determined by the significance of the alternatives sacrificed in its production, and there seems to be no kind of justification for excluding land, and the other purposes that it might have served, from the cost of production either of wheat or of anything else. If we ask the origin of so strange a practice as that of excluding land (which, moreover, we cannot separate from capital) from consideration when estimating the cost of production, the answer seems to be as follows: It was taken as an axiom that cost of production determined the value of the product. It was then seen that wheat raised upon land for which a high rent had been paid sold for no more than wheat of the same quality that had been raised on inferior land. Hence the syllogism: "Cost of production determines exchange value; rent does not affect the exchange value of wheat; therefore rent is not part of its cost of production." The major premise was false and the conclusion absurd, but so firmly was the premise established as an axiom that even a reductio ad absurdum did not lead to its revision. The argument, such as it is, would of course apply just as much to labour, raw material, or capital, as to land. For some wheat less has been paid in wages than for other wheat of the same quality; it would follow that if cost of production determines exchange value, wages are not part of the cost of production. The general truth is, as we have seen, that the value of the factors of production is derivative from the value of the product. The price or hire of some land is higher than that of other land because its products or services are more valued, but the same is true of all raw material and of all kinds and grades of skill. Their value is derivative from the value of the commodity, or ultimately the experience, they produce. This derivative nature of the value of factors of production was perceived in the case of land earlier than in other cases; and thinkers who were still under the impression that in general the product derived its value from the value of the factors of production, and who perceived that this was not true in the case of land, at once set land on a footing of its own, with the resultant confusions which we have been examining.

A certain semblance of rationality has been given to this arrangement of the units of wheat in the order of the decreasing ratio in which the cost of land stands to the cost of the other factors in their production, by dwelling on the idea that the most fertile land is likely to be occupied first, so that every extension of agricultural industry will be from more to less suitable land; and then the reaction of the considerations already dwelt on44 in relation to the immediate effect of a rise or fall of demand has enabled writers to pass from this specific conception of progressive recourse to inferior land in wheat-growing to the general conception of the necessity of progressive recourse to less and less favourable conditions as any industry expands; and so again a rising curve has been taken, without adequate examination, as representative of a large and normal class of industries. But this whole conception is illusory. The conditions that are favourable or otherwise to any particular industry are constantly changing, and an increasing scale of production is itself a factor in the change. A man may be at a positive disadvantage because he set up his machinery yesterday as against the man who is to set it up to-day. Manitoba may offer more favourable conditions for growing wheat for the London market than Essex does. It is quite as likely that the established man has to work at a disadvantage because he is committed to less favourable conditions than are now open, as it is that the man who is entering upon the industry is at a disadvantage because he finds all the most favourable sites and conditions preoccupied.

But probably the most deeply seated of all the predisposing causes which keep the up-sloping curve of cost of production in favour is one that has no connection whatever with the theory of decreasing returns. Neither of the intersecting curves of Fig. 20, on page 499, has any connection with production, or cost of production, at all. Yet one of them slopes up as the other slopes down. If we place all the holders on the up-sloping curve, so that all the "supply" is in the hands of the persons whose desires it represents, it is easy to fall into the habit of calling it the "supply" curve. We have seen that it is no such thing. It is the demand curve of a certain number of the persons in the market arbitrarily grouped together. The supply is not represented by a curve at all, but by a length on the abscissa. But once use crossing curves to illustrate the determination of the market price, and call the up-sloping one the "supply" curve, and you have at once a figure that you can transfer bodily, and without knowing that you are doing it, to the illustration of the regulation of "supply" as determined by cost of production. Thus crossing curves may come to be used indifferently to represent "demand and supply" or "demand and cost of production," the term "curve of supply" may be used indifferently in either case, the up-sloping curve of the one (which is merely a down-sloping curve of exactly the same nature as the other, reversed for convenience, and having no constitutional connection with "supply" whatever) may be transferred to the other; it may then be read as a curve of diminishing returns and increasing cost of production, and may create a habit of mind to which cases of "increasing return" present themselves as graphically inconvenient phenomena which must be recognised from time to time but can generally be comfortably neglected. A more disreputable origin for a respected figure in the economic world it would be difficult to conceive!

It remains true, however, that there may be industries in which an increased volume of production must normally imply increased cost, and under the limitations insisted on in the parallel case of decreasing cost of production45 such industries might legitimately be illustrated by a diagram such as that of Fig. 37. But when this very ambiguous diagram is employed without examination to represent unspecified industries that obey the "law of decreasing returns"; when that law, as originally defined, has been the mere statement of a truism that applies to all industries; when the unwarrantable exclusion of rent from a place amongst the costs of production, and unwarranted assumptions and delusive analogies as to increasingly unfavourable conditions and as to the nature of supposed "supply" curves, have presided over the construction and the interpretation of the curve and strengthened its hold on the imagination, and when purely geometrical deductions from it have then been applied to important practical matters, it is surely time to submit all the emergent theories to a thorough revision, based on a severely precise definition of the meaning to be assigned to the curve, and a demonstration that it actually represents an important body of industrial fact.

We may now summarise our results. A curve representing the conditions of increasing or diminishing returns, if properly constructed, would be an attempt to register a continuous series of changes of the nature of that represented by the transition in Fig. 31, page 519, from the unbroken to the dotted lines parallel to the axis of X. It might be in the same sense (increasing returns) or in the opposite sense (diminishing returns) to what is there represented. It would have no connection or relation whatever to the up-sloping curve on Figs. 20, etc.

A final word as to the processes illustrated in Figs. 19, etc., may be introduced. We must distinguish between the process by which the ordinate Oy was obtained, and the merely graphic presentation of the quantities which each of the consumers, A, B, C, etc., will take out of the market. The height Oy was only obtained by a process which involved the securing by A of the precise amount Oa, and by B of the precise amount Ob. These amounts were determined by the form of the curves (a), (b), etc., and the device of adding them together indicates that a claim is met or is not met, without reference to whose claim it is, according as its position is high or low on the relative scale. The shares which A, B, etc., have respectively taken in determining the final result are registered on the curves (a), (b), etc., but though the results may be registered separately, the process could only be conducted in combination. We start with the marginal significance of the commodity to A at about 8½, to B at 36½, etc., and we learn from combining all the curves that if the total quantity of the commodity is Ox (d), the market will tend to bring the marginal significance to all the consumers to the magnitude Oy, and in proportion as its action is frictionless and effective will actually do so.

In the same way if we take any individual industry, the price is determined by the collective curve of demand and the quantity possessed. This corresponds to the ordinates of the points a, b, g in the curves of Fig. 19. It may be, like the ordinate of b, above, or like the ordinate of a, below the ideal equilibrating ordinate, but the curve itself enters, together with other curves, into the determination of that ideal ordinate; and the amount produced, that is to say, the amount of the productive resources which flows into this particular industry, tends to coincide with the abscissa corresponding to that ordinate.

If the amount of the product can be increased or diminished by the inflow or outflow of the productive resources of the community in relatively fluid forms, the approach to the equilibrating ordinate will be rapid. If the forms in which the factors of production can be added or withdrawn are such as require a long period of time to mature or to wear out (deep shafts, for instance, or extensive premises and elaborate machinery), the movement will be slow; but in any case the price will only be changed by a change in the amount produced. Except as it affects that, the ideal equilibrating ordinate can have no influence on the price. Thus, if we know the course of the curve in the neighbourhood of the actual point reached by the supply, and know what the supply is, we know the price. If we wish further to know whether the tendency will be in the direction of expanding or contracting the supply we must know what the cost of production in the existing state of the industry actually is. This cost of production is represented by the ideal equilibrating ordinate and is no other than the marginal value of other commodities, measured for convenience in the standard (gold); just as the equilibrating point to which A's desire for plums can be satisfied is determined by the place of plums on the relative scales of B, C, etc. If by any combination of factors (and there will probably be a number of different combinations realisable under different conditions, and equivalent to each other as measured by the standard) a unit of the commodity can be produced at a cost less than its present price in the market, the tendency will be for the supply to increase. If no such combinations will produce it except at a cost which exceeds its present price, the tendency will be for the supply to contract.

But as we advance from individual curves to the collective curves of great industries it comes out more and more clearly that all the elements of a commercial civilisation mutually determine each other; that any marked change in the conditions disturbs the whole structure, composition, and significance of our units; and that the diagrammatic method can only be regarded as precise, even ideally, when it refers to an industry or a portion of an industry that is too insignificant a fraction of the whole to cause serious disturbance in general relations. In other words, it is only in the neighbourhood of present margins that our standard units can be regarded as stable. In an individual curve we may fruitfully imagine ourselves, if due caution is exercised, as travelling far; but only on the supposition that the general margins are maintained. In great collective curves we must never think of ourselves as commanding, even conjecturally, more than a minute portion of the tracing, in the neighbourhood of the actual point of realisation.

We have been engaged throughout almost the whole of this chapter in the discussion of theories about increasing and diminishing returns, and our conclusions have been almost entirely negative. One important point, however, remains, as to which we may hope for more positive results. The habit of isolating "labour," and tacitly assuming sometimes that it is, and sometimes that it is not, proportionately backed by other factors, has caused us a great deal of trouble, but it is not difficult to explain. It is the reward of labour, in the general sense of output of human effort, about which we are ultimately concerned, and all the questions about increasing and diminishing returns derive their interest from attempts to estimate or to forecast the conditions under which humanity conducts or will conduct its attempt to secure the satisfaction of its desires from the resources and opportunities of nature. If the law of diminishing returns to labour is, or will ever become, dominant, these conditions will become less favourable, and the thought of this possibility has sometimes been a nightmare to the speculative thinker. I am not about to enter upon any investigation of the terrors that haunt many minds as to the ultimate limitation of the resources of the planet. Though it be true at the present moment that the whole of the inhabitants of the globe could stand shoulder to shoulder on the surface of the Isle of Wight, it is of course easy to shew that if the increase of the population proceeded uniformly at a moderate rate, a state of things would come about within a calculable and imaginatively not a very remote period at which there would be no room for them to stand shoulder to shoulder on the face of the dry land and on the floor of the ocean. For the matter of that, it would be equally easy to shew that within a calculable period the atmospheric envelope of the planet would not contain sufficient nitrogen to renew the tissues of the population, if all other obstacles to their increase were removed; and possibly the one speculation may be found as suitable food for melancholy as the other to one whose temperament promotes "going far to seek disquietude."

But apart from these speculations which are too remote to cause any rational anxiety if they stood alone, there is a reason why a perpetual suggestion of the possibility of decreasing returns to labour, as an instant possibility, should force itself upon our minds irrespective of any foundation that it may or may not have in reality; and if we can rob this dismal suggestion of the unfair advantage it derives from a wholly irrelevant group of phenomena we may perhaps have contributed in some modest degree to the gaiety of nations.

Let us then suppose that some individual industry illustrates the law of increasing returns in the sense that if an increasing volume of human effort were devoted to it, land, capital, and so forth, could be obtained on such terms that the marginal effectiveness of labour, measured by product in bulk, would increase. Now, taking Fig. 38 in which as usual we measure on the axis of X units of the product, and on the axis of Y their marginal exchange value, we are to suppose that if we double, treble, or quadruple the amount of labour devoted to this industry we shall in each case more than proportionately increase the material output. The divisions of the paper then represent the selected unit of the commodity, and the numerals, 1, 2, 3, 4, placed at increasing intervals, represent the successive additions to the product caused by the doubling, trebling, or quadrupling of the output of effort. The figure would then mean that whereas a given number of men, which we take as our unit, properly backed by capital and so forth, would produce an amount of the commodity represented by 10, double that number of men would produce not 20 but 25, three times the number not 30 but 45, and four times the number not 40 but 70. But we are dealing with the material product in bulk, not with its value, and as the amount of the product increases, its marginal significance per unit will decline. If the curve takes such a form as that indicated in the figure, we see that doubling the number of men will give a more than proportional increase not only to the amount of the output, but also to its value, for the declining height of the ordinates is more than compensated by the increased length of the basis from 1 to 2. But when we pass from doubling to trebling, and from trebling to quadrupling, the original number of men, the still increasing proportional bulk of the output is now more than compensated by its decreasing value. Thus, although the industry obeys the law of increasing returns as interpreted in the return to labour of the material product, the law of diminishing returns is illustrated in the return to labour as measured in command of other commodities. For the units on the axis of Y which represent the value of the product must be interpreted in terms of other commodities. Men will give less of them in return for a unit of the commodity under investigation, because they are now better supplied with it.

But suppose they were better supplied with other things also. Suppose that the gradual increase of the population, accompanied by a suitable increase of capital and applications of fresh land or fresh and improved applications of land, enabled all the other industries to increase in volume also; and suppose that all likewise obeyed the law of increasing returns of material product to labour. Every one, then, having not only more of the particular commodity we first took into consideration, but having in suitable proportion more of all other commodities as well, will give as much of these other commodities for a unit of the first as they did before, and every one, therefore, will have more of everything, including opportunities of leisure and every form of self-expression. This would be the ideal condition of a progressive community, in which every generation, partly because of progress in the arts, but partly also from the mere increase of population and the resultant economies in every industry, would find itself wealthier than the last, and able to secure the co-operation and alliance of nature on ever pleasanter and easier terms. But it would still remain true that in each individual industry the position of its members would be strengthened if the other industries absorbed a relatively larger amount of the new energies and resources, and weakened if it absorbed a relatively larger amount itself. Every one would be aware that however much the ordinates of his industry were being raised by general processes that made all other commodities more abundant, and therefore to be had on easier terms, they would be falling in virtue of his own advance along his own line.

Thus generalising from his own industry every one will argue that the law of decreasing returns is already in full swing, that the more persons there are engaged in producing things, and the more abundantly they produce them, the poorer every one will be.

Thus we have arrived at a more exact analysis of the phenomenon which we have already described as the microbe of the disease of civilisation,46 the fact, namely, that every man is convinced (except in exceptional periods) that his own industry or profession is overstocked. However true it may be that an increase in the numbers engaged in every industry, accompanied by a suitable increase in tools and appliances, would secure a larger general command of resources, it remains true that in any industry, taken in isolation, the reverse must seem to be (and in a sense must really be) the truth. Hence it is to the interest of the existing members of every industry, taken severally, that every other industry should recruit its staff and increase its output, while they themselves retain the exclusive right of ministering to the increased demand for their own product thus created. They will then reap the full benefit of the raising of their own curve which the advance of other industries down their declining slopes secures, and will themselves escape the obligation of raising the curves of others by advancing on the down-slope of theirs. But it is obvious that if the advance were even in all industries the remuneration of each factor of productivity, measured in the sum of things in the circle of exchange of which it represented the command, would increase.

CHAPTER VI

THE DIAGRAMMATIC EXPOSITION OF THE LAW OF RENT AND ITS IMPLICATIONS

Summary.—The current exposition of the law of rent, based on a diagram of "decreasing returns" to labour, for a constant of land, mistakes the characteristics of the constant for those of land. Hence many errors in nomenclature and in thought have arisen. It is equally easy and equally legitimate to represent the same facts in the form of a diagram with labour for the constant and land for the variable. This will shew that both rent and wages are shares in the product determined by marginal efficiency; and that when all the factors have received their share in this marginal distribution there is no surplus or residuum at all.

The roots of the error concerning the exceptional treatment of land, which we examined in the last chapter, go down far deeper than the point to which we have as yet traced them, and the process of extirpation cannot be completed without an elaborate examination of the current exposition of the theory of rent. We will therefore go on to the examination of the ordinary diagram given to illustrate both the supposed "law of decreasing returns" and the "law of rent" derived from it. In Fig. 39 increments of "labour" applied to a constant of land are reckoned along the axis of X, and rates of increment to the crop per unit increment of labour along the axis of Y. The total yield for Ox₁ "labour" is Orw₁x₁, and labour being rewarded at the rate of x₁w₁ per unit receives the area Ow₁ altogether, the balance y₁rw₁ being rent. If Ox₂ only had been applied to the same amount of land the total yield would have been the smaller area of Orw₂x₂, but the reward of "labour" per unit would have been higher, namely, x₂w₂. Rent would only be y₂rw₂, a smaller proportion of a smaller total. Thus decreasing returns to land per unit and increasing returns to "labour" per unit are read as we recede from the margin, and decreasing returns to "labour" per unit and increasing returns to land per unit as we advance from the origin. More labour bestowed on the same land means less land under the same labour. So we have these results: More labour on the same land or less land under the same labour means a larger rent per unit of land and a less "wage" per unit of "labour"; whereas less labour on the same land or more land under the same labour means a lower rent per unit of land and a higher "wage" per unit of "labour." Those of the results just formulated which are directly illustrated in the figure are very familiar to all students of Political Economy, and familiarity has made them appear axiomatically true. But those of them which are just as explicitly contained in the data, but are only indirectly illustrated by the figure, and which have been italicised in the statement just made, are unfamiliar to most students of Political Economy, and may appear startling and perplexing, though they are absolutely identical with those expressed in the more familiar form and at once accepted as axiomatic.

Thus every one sees that if (after a certain point) more labour is applied to the same land the return to the land will be higher. But every one does not see that this is exactly the same as saying that after that point if more land is brought under the same "labour" the return to labour will be higher.

In our figure rent appears as a mixtilinear area and "wages" as a rectilinear one; and this has usually been assumed to be due to some special characteristic of land, but if we work out our data under the other form of statement we shall find that these graphic forms are simply due to the fact that land was taken as the constant. Had we thought in terms of less or more land under the same cultivation instead of more or less cultivation bestowed upon the same land, we should have found "wages" represented by a mixtilinear area and rent by a rectilinear one. This I shall go on to shew in detail. But before proceeding to the demonstration it will be well to note certain special points.

I have explained why certain phrases have been italicised above. I must now explain why I have put "wages" and "labour" between inverted commas. It is because labour is taken to include capital. In short, "labour" means all the factors of production except land. And "wages" means the remuneration of all these factors. To measure them all in one unit implies that they have all been reduced to a common denominator, and this must have been done on some such principle as that expounded in Book I. Chapter IX. It would be useless to attempt to express such a unit accurately every time we have occasion to speak of it. Even to call it a "unit of labour-and-capital-reduced-to-a-common-denominator" would be too cumbrous. To call it a unit of labour is in the highest degree dangerous; but the danger is reduced, though not altogether avoided, by systematically writing "labour" for this complex of factors, and "wages" for its remuneration. We must add that the distinction between "labour" in this sense and "land" is artificial and arbitrary; for all the land we ever deal with embodies capital, and so does "labour" as now defined.

We have next to note that the figure, and the argument that usually accompanies it, do not really give us any theory of rent at all. They assume our own law of remuneration in proportion to efficiency for all the other factors (tacitly reduced to a common denomination), and then simply tell us that whatever is not anything else is rent.

Further, we must note with extreme care that the number of units of "labour," Ox₁ or Ox₂, applied to the constant of land, will be fixed by the alternatives open to land and "labour" respectively. "Labour" is devoted to, say, wheat-growing till the marginal return is only x₁w₁, because it cannot find any more eligible alternative, and it is not devoted to it beyond that point, at a lower marginal significance, because it can find alternatives as eligible. And in like manner so much land and no more offers itself at a declining marginal significance to a given amount of wheat-growing "labour," because it cannot find anything else better, but can find other things as good, to do with itself. So land will not come to a man unless he offers it as good terms as it can get anyway else, and men will not come to land unless it offers them as good terms as they can get anyway else. The quantities Ox₁, x₁w₁, y₁rw₁, are determined by the general conditions of industry and the markets; and if under conditions which would justify these proportions an individual should choose to take land and work on it at the rate represented by Ox₂, instead of earning Ow₂ and paying y₂rw₂ in rent, he would find that out of his total crop of Ow₂ he would have to pay a rent of y₁rw₁, and would only have Om minus the mixtilinear triangle w₂mw₁ for himself. If rent were at the rate of y₂rw₂, and "wages" at x₂w₂, it would be because more eligible alternatives had been opened to "labour," or a more abundant supply of land had become available to it as against the conditions that determined y₁rw₁ and Ow₁. It should be noted incidentally that any such change would be sure to affect the internal constitution of the complex unit of what we have called "labour"; it would not act upon interest on capital and wages for every different grade and character of work, for instance, in exactly the same proportion.

Lastly, we may note that the figure deals with yield per unit of land of a given quality, as it is plied with more and more "labour." It takes no account of different grades of land, each of which would present a curve of different form. Neither does the figure take account of the different conditions that might prevail on larger and smaller holdings.

With reservations, the nature of which will presently appear, as to the general form of the curve, we may now proceed to the detailed demonstration promised on page 552. It will be well to begin from the beginning and build up our curves step by step.

Suppose a man holds 50 acres of land and bestows 3000 hours' personal work upon it in the course of the year, backed by tools and apparatus of every kind, stock, seed, manure and so forth, and also hired labour. An hour's labour will in this case be a mere symbol of an aggregate of factors of production, of defined magnitude, expressed under a common denominator, and will mean "the totality of the applications and combinations which may be supposed to accompany, or to be included in, the expenditure of an hour's work on the land by the tenant." Let us suppose that the crop is about equivalent to 5 quarters (or 1280 quarts) of wheat per acre. For convenience of subsequent operations we will take it at 1260 quarts, and this would be 630 quarts per half-acre. Thirty "hours" a year will be devoted to each half-acre. So the crop will be at the rate of 21 quarts per "hour" expended. We will take this as our starting-point. But it will be convenient to take a smaller unit of land than the acre or half-acre. Let it be the twentieth of a rood (which would be two poles), or the fortieth of a half-acre. The selection of the unit is determined merely with a view to diagrammatic convenience. Then our supposition will be: Land cultivated to the point of 60 "hours" to the acre yields the equivalent of 1260 quarts of wheat per acre, which is at the rate of 21 quarts per hour, or 15.75 per (two-pole) unit of land.

The scale of

1260 quarts per 80 land-units under 60 hours' cultivation

is the scale of

630 quarts per 40 land units under 30 hours' cultivation,

and the yield is at the rate of

630 ÷ 30 = 21 quarts per hour, or

630 ÷ 40 = 15.75 quarts per land-unit.

Here the reader must note carefully that these rates per unit of land and labour are not shares which fall to each of the factors, nor estimates of the value of their respective contributions. They simply indicate the ratio of the gross crop to the land or to the labour, taken severally. Yield per unit of land is a familiar conception. Yield per unit of labour is equally important for our present investigation, and the reader must try to make himself equally familiar with it.

Let us now suppose that if the man only cultivated at the ratio of 25 "hours" per half-acre his crop would be at the rate of 531.40 instead of 630.47 Here note that we are imagining our cultivation to be less intensive than on the first supposition; that is to say, the cultivation or "labour" is spread thinner on the land. This we may think of in terms either of the unit of land having less labour spread on it, or of the unit of labour being spread over more land. Thus, if we pass from 30 "hours" on 40 land-units to 25 "hours" on 40 land-units, we get the same ratio (5 to 8) which we should have got had we passed from 30 on 40 to 30 on 48 (5 to 8 again); but of course the total crop on 48 land-units under 30 "hours' "; cultivation will be greater by a fifth than that on 40 land-units under 25 hours' cultivation.

Thus if, as we have (arbitrarily) supposed, the crop on 40 land under 25 labour is 531.40 quarts, it follows that the crop on 48 land under 30 labour will be 637.68 quarts (six-fifths of the other); and whichever way we measure it we shall have a yield of 13.285 quarts per unit of land and of 21.256 quarts per unit of labour.

We may tabulate these results:—

		Quarts per "hour."	Quarts per land-unit.
30 to 40	gives a yield of	21	15.75
25 to 40	" "
or		21.256	13.285
30 to 48

Thus as we pass from 25 to 30 units of cultivation on 40 units of land we have decreasing returns to labour, but increasing returns to land. To say that we have a decreasing or increasing "total yield" would have no sense unless we had established some common denominator (pecuniary or other) under which we could express land or labour indifferently, or both collectively. This lies outside our present inquiry; and we see that "increasing" and "decreasing" returns, from our present point of view, are merely relative terms and may be applied to the same phenomenon simultaneously according to whether we are speaking of land or of "labour." To this important conception we will presently return, but meanwhile we are to follow our investigations along another track.

Our hypothesis is that at 30 "labour" to 40 land we have a crop of 630; so that we may call this the return either to 30 "labour" or to 40 land, on the supposition of the ratio of 3 to 4. When we alter the ratio to 5 to 8, we may keep either 40 land (with 25 "labour" spread on it), or keep the 30 "labour" and spread it over 48 land. In the one case we shall have a crop of 531.40 instead of 630, and in the other a crop of 637.68 instead of 630; that is to say, if we spread so much less labour on the same land we shall decrease the yield to the land by 98.60 quarts, and if we bring so much extra land under the same "labour" we shall increase the yield to the "labour" by 7.68 quarts.

We may now begin to plot out our results on Fig. 40. In (a) we may assume that the half-acre (40 of our land-units) is constant. We mark along the axis of X the number of "hours" per half-acre put in annually, and on the axis of Y rates of yield measured in quarts, so that the crop per half-acre, for any ratio between land and labour, will be represented by areas in which every small square is a quart. In (b) we will take 30 "hours" of cultivation per annum as our constant, and will measure along the axis of X the units of land (twentieths of a rood) over which it is spread. The meaning of the units on the axis of Y will still be rates of yield measured in quarts, and areas will represent the crop per 30 "hours' "; cultivation, for any ratio between land and "labour." In (a) as we advance from 25 "hours" to 30 we secure by hypothesis an addition of 98.60 quarts per half-acre, or if we move in the opposite direction, from 30 to 25, a diminution of that amount. This may be plotted on (a) by erecting a rectangle of an altitude 19.72 on the base line between 25 and 30. This means that, land remaining constant, the addition or withdrawal of these 5 hours per half-acre will make the difference we have assumed in the crop. But, as we have seen, to pass from 30 to 25 on (a) is equivalent to passing from 40 to 48 on (b), since each of them means changing the ratio of 3 : 4 into that of 5 : 8; and the effect of this change is to increase the yield to 30 "hours" of labour by 7.68. In (b), on the base line between 40 and 48, we must therefore erect a rectangle of area 7.68 or altitude 0.96, which means that, "labour" remaining constant, the addition or subtraction of these eight land-units will make a difference of 7.68 quarts in the crop.

Note that movement towards the origin in (a) corresponds to movement away from it in (b). We may either start with the ratio 3 : 4 and move to the left in (a) and to the right in (b), or we may start with the ratio 5 : 8 and move to the left in (b) and to the right in (a). That is to say, our data imply that if we increase the number of "hours" spread over the same land we shall increase the yield per unit of land and decrease the yield per unit of "labour," whereas if we bring more land under the same output of cultivating labour we shall increase the yield per unit of "labour" and decrease the yield per unit of land.

Let us now change the ratio of 3 : 4 in the contrary sense. Let us suppose (as an arbitrary datum) that a ratio of 7 : 8, that is to say, of 35 "labour" to 40 land, or 30 "labour" to 34.286 land, would yield a crop of 705.98 per half-acre, or six-sevenths of this, viz. 605.13 per 30 "hours." This would mean that the difference made to the crop by the addition or subtraction of these five "hours" on 40 land-units is 75.98, and may be represented on (a) by a rectangle on the base line between 30 and 35 with an altitude of 15.20; whereas the difference made by the addition or subtraction of these 5.714 land-units under 30 "hours" of cultivation is 24.87, and will be represented on (b) by a rectangle whose base is the line between 34.286 and 40 on the abscissa, and its altitude 4.35.

We can now tabulate and extend our results. If we start with the rectangle on the left in (a) and move to the right, and with the corresponding rectangle on the right in (b) and move to the left, we shall have a series of increments to record on (a), and of decrements to record on (b). But the figures may be read either way, and if we read (b) towards the right and (a) towards the left we should have increments to record on (b) and decrements on (a). We shall therefore not mark positive or negative signs on our table; for if we read it down the differences in column 6 will be positive and those in column 7 negative, and if we read it up it will be the other way, and either reading is equally legitimate.

Ratio of "Hours" to Land-units.	"Hours" to Constant of 40 Land-units.	Land-units to Constant of 30 "Hours."	Crop to Constant of Land (on Arbitrary Hypothesis).	Crop to Constant of "Labour" (on same Hypothesis).	Difference in Yield to Constant of Land.	Difference in Yield to Constant of "Labour."	Height of Rectangle on (a).	Height of Rectangle on (b).
5 : 8	25	48	531.40	637.68
					98.60	7.68	19.72	0.96
3 : 4	30	40	630	630
					75.98	24.87	15.20	4.35
7 : 8	35	34.286	705.98	605.13
					53.18	35.76	10.64	8.34
1 : 1	40	30	759.16	569.37
					31.85	42.03	6.37	12.61
9 : 8	45	26.667	791.01	527.34
					12.99	44.94	2.60	16.85
5 : 4	50	24	804	482.40

Now, as the effect of increasing the labour bestowed upon the same land in the one case, or increasing the land brought under the same expenditure of cultivation in the other, will obviously be continuous, we may trace curves on the principle fully explained on page 447, which in the case of (a) will correspond to the ordinary curve given to illustrate rent in the books, and in the case of (b) will be the complementary curve in which labour is supposed to be constant. Thus, for any abscissa on (a) the corresponding ordinate will mark the marginal efficiency of labour per hour, at that point, in increasing the yield to a constant of half an acre of land (40 land-units); and for any abscissa on (b) the ordinate will represent the marginal efficiency of land per unit, at that point, in increasing the yield to 30 "hours" of labour.

What we have got in (a), therefore, is a portion of the familiar rent curve. It shows us the "decreasing returns" to "labour" as successive increments or doses are applied to the same piece of land; and since "labour" is remunerated at the rate of its marginal efficiency, the rectangle of the ordinate multiplied by the abscissa, that is to say, the rectangle contained by the curve, is the total amount that would be paid in "wages." There remains the rest of the crop for rent; and if the curve were completed, that would be represented by the mixtilinear area above the rectangle.

This last point may easily be established. The land would produce no crop at all unless some labour were expended on it. Thus, if we start with the crop for x "hours" per land-constant, and successively account for, and register as an area, the part of the crop dependent on the difference between x and (x - 1) "hours," the part dependent on the difference between (x - 1) and (x - 2), and so on, up to the part dependent on the difference between 1 and 0, we shall have accounted for the whole crop. Now our curve is constructed precisely on these principles. Over each successive base it bounds an area which represents, by construction, the part of the crop for which the corresponding portion of the abscissa is responsible. Thus, if we had completed it, it would account for the whole crop. For example, at the ratio of 3 "labour" to 4 land, or 30 "labour" to 40 land, we take the abscissa 30 on (a) and read 17.50 as the marginal significance of "labour" per hour. If this represented a state of equilibrium, 17.50 × 30 = 525 would be the amount of the crop that would fall to "labour," and the rest would measure the rent of half an acre.

In (b) we should have a portion of a precisely analogous curve shewing the "decreasing returns" to land as successive increments are brought under the same amount of "labour"; and since land will also be remunerated at the rate of its marginal efficiency the rectangle contained by the curve is the total paid for rent. The rest of the crop will remain for "wages." The point 40 on the abscissa of (b) corresponds to the point 30 in (a). Reading the ordinate for the abscissa we find it to be 2.625. The rent then will be 40 × 2.625 = 105, and the rest of the crop will be the "wages" of thirty "hours" of labour.

If our curves have been accurately drawn and correctly read these results must coincide. And so they do. For returning to page 554, where the total crop for 30 "hours" bestowed on 40 land-units is taken at 630 quarts, we find from (a) that wages will be at 30 × 17.5 = 525, and from (b) that rent will be at 40 × 2.625 = 105. And 525 + 105 = 630.

Let it be clearly understood that all we have proved is that the same data may be diagrammatically expressed in two different ways; and that these two representations, if correctly made, will be consistent. That our sum comes out right proves nothing; and if it came out wrong it would disprove nothing. The curves are to be drawn in accordance with the calculations, and they can be calculated more accurately than they can be read. They illustrate the calculations; but they do not prove them to be correct. The calculations, as legitimate inferences from the data, must stand or fall on their own merits. The curves simply illustrate the relation in which the different inferences stand both to each other and to current (or recently current) economic teaching.

The essential and all-important point of the demonstration, up to this point, is that in the ordinary diagrams rent is set forth as a mixtilinear and "wages" as a rectangular area, not because there is any inherent appropriateness in these geometrical forms as representatives severally of the respective industrial factors, but simply because return to the constant, whatever it happens to be, will always come out as a mixtilinear area, and that to the variable as a rectangular one. And whether a distributive share is represented as a mixtilinear or a rectangular area, it is the same quantity and it is marginally determined.

This will become still clearer if we plot the total crop (for each ratio of land and "labour") to 40 land-units and to 30 "hours" respectively, in conjunction with the marginal returns to "labour" and to "land." I must refer my readers to the short mathematical treatise already mentioned48 for the detailed justification of the general form of the curves which our data imply; but it is sufficiently obvious that the form of figure usually given (as in Fig. 39) is an exceedingly crude representation of the facts. The more careful writers always state that the law of diminishing returns will only come in "after a certain point," and assume that when we are near the origin increments of labour will produce more than a proportionate increase in the product. Further, it is clear that if I were to distribute a few hours' labour over many acres of land (really distributing it over the whole, not selecting a portion of it), I should produce no appreciable effect at all. The difference between giving so much labour and no labour would not be perceptible. If, on the other hand, I were already giving 300 days' work to a holding of 40 acres, every extra hour of work would produce an appreciable result. Thus I have attempted, in the work referred to, to shew that our curves will pass through the origin, will rise for a time, and then decline. Our data have hitherto been assumed in accordance with this theory, and we may now extend them so as to carry our data for (a) back to the origin in one direction, and some way farther to the right than it has yet reached in the other.

We will assume, then, the following data, some of which have been already tabulated, the rest being now introduced for the first time:—49

TABLE I.—Land-Constant at ½ Acre (40 Units).
Ratio of Labour to Land.	"Hours" of Cultivation per Constant of Land.	Crop per Constant of Land (Assumed).	Total Crop per Unit of Land (Derived).	Total Crop per Unit of "Labour" (Derived).
1 : 8	5	46.26	1.16	9.25
1 : 4	10	152.36	3.81	15.24
3 : 8	15	282.24	7.06	18.82
1 : 2	20	413.08	10.33	20.65
5 : 8	25	531.40	13.28	21.26
3 : 4	30	630.00	15.75	21.00
7 : 8	35	705.98	17.65	20.17
1 : 1	40	759.16	18.98	18.98
9 : 8	45	791.01	19.78	17.58
5 : 4	50	804.00	20.10	16.08
11 : 8	55	800.91	20.02	14.56
3 : 2	60	784.74	19.62	13.08
13 : 8	65	758.22	18.96	11.66
7 : 4	70	724.01	18.10	10.34

If we take the figures in the second column as a series of abscissas and those in the last column as the corresponding ordinates, we shall have a series of points in a curve the rectangle contained in which gives the total crop per half-acre (40 units) at any ratio of land to labour. And if we add the curve of marginal significance of "labour" applied to a constant of 40 units of land, we shall have on our Fig. 41 (a) one curve c (which stands for "crop") containing the rectangle of the total crop per 40 units of land, and another curve w (which stands for "wages") containing the rectangle of the share of labour in that total. The first of these rectangles minus the second will obviously represent the share of land, also as a rectangle. And this last rectangle will be equal to the total area of curve w minus the rectangle it contains. If we divide it by 40 we shall have the figure in the last column but one of our table.

But the assumed data of Table I. can be presented in Table II. for a constant of 30 "hours" and a variable of land-units. We have taken our points on the abscissa of (a) at uniform intervals of 5 units and assumed data to match them. The corresponding intervals on (b), being reciprocals will not be uniform. It would, of course, have been equally easy to have gone the other way about, so the regularity in one case and the irregularity in the other has no theoretical importance. We will tabulate for 30 "hours' "; constant the data corresponding to the abscissas from 60 to 15 in Table I.

TABLE II.—For 30 "Hours' " Constant.
Ratio of Labour to Land.	Land.	Crop per Constant of "Labour" (Derived).	Crop per Unit of "Labour" (Derived).	Crop per Unit of Land (Derived).
3 : 2	20	392.37	13.08	19.62
11 : 8	21.818	436.86	14.56	20.02
5 : 4	24	482.40	16.08	20.10
9 : 8	26.667	527.34	17.58	19.78
1 : 1	30	569.37	18.98	18.98
7 : 8	34.286	605.13	20.17	17.65
3 : 4	40	630.00	21.00	15.75
5 : 8	48	637.68	21.26	13.28
1 : 2	60	619.62	20.96	10.33
3 : 8	80	564.48	18.82	7.06

Here again, by taking the figures in the second row as abscissas and those in the last row as the corresponding ordinates, we shall obtain a series of points on a curve c, Fig. 41 (b), the rectangle in which gives the total return to 30 "hours' "; cultivation applied to the amount of land marked by the abscissa; and if we add the curve of marginal significance of land, we shall have in (b) a curve c (crop) containing the rectangle of the total crop to 30 "hours," and a curve r ("rent") containing the rectangle of the share of land in that total. The first of these rectangles minus the second will represent the share of "labour," also as a rectangle. And this last rectangle will be equal to the total area of curve r minus the rectangle it contains. If we divide it by 30 we shall have the figure in the last column but one of Table II.

Thus the readings of (a) and (b), either in Fig. 40 or Fig. 41, will give absolutely identical results, if the figures are correctly and consistently drawn. The reader will be able to check this roughly by reading the curves for any two corresponding points that lie between the tabulated points. For example, on (a) take the rate of 35 "labour" to 40 land. This gives us 12.9 for wages per hour; and 7.3 × 35 for the rent of 40 units of land, or about 6.4 per unit. Now 35 to 40 is 30 to 34.3. Therefore the corresponding point on (b) will have the abscissa 34.3. If we read the ordinates we find that rent is about 6.4 and the wages 11.3 × 34.3 for 30 hours, or 12.9 per hour.

We have now thoroughly established the important conclusion that there is no special propriety in regarding rent as a residual share in the product, nor is there any special or necessary appropriateness in representing rent diagrammatically as a mixtilinear area, in contrast to the representation of wages, for example, as a rectilinear area. But the mistaken conceptions now dissipated have led to what I cannot but regard as disastrous confusions both in thought and nomenclature which may long impede the progress of Economics. It has been assumed, in the first place, that every economic quantity that presents itself graphically, under any treatment, in the form of a mixtilinear area has some specific analogy to rent. And here we may note that what is known as the "Ricardian" law of rent may be presented in this same form. Thus a diagram of the form in Fig. 39 (page 551) might be regarded not as shewing the relation between marginal-return-per-unit-of-labour-and-capital and ratio-of-labour-and-capital-to-land, but as an arrangement of the several units of labour and capital employed in the wheat industry, referred to the varying fertility of the land to which they are applied. We should then have the mixtilinear area representing the excess of the yield of the more fertile over the yield of the least fertile land under cultivation. The Ricardian theory of rent usually (though quite unnecessarily) assumes that the least fertile land will bear no rent at all, and in that case the mixtilinear area would represent the whole rent; otherwise it would represent the excess of rent over a minimum. Now, if you take a number of persons who possess different talents and arrange them in the order of the marginal value to the community of the exercise of their talents, you will have near the origin an individual the product of whose efforts per annum is relatively high, and as you go forward you will come to individuals the exercise of whose talents produces a smaller and smaller pecuniary return. If we draw a line on the level of the return to the efforts of the least efficient of the men in question, the area above it will represent the excess over that minimum return that accrues to the more able individuals; and simply because this is a curvilinear figure the revenue it represents has actually been called "rent of ability."

It is clear that at this rate any excess in the value of one article above another that is nominally the same would be entitled to the name of "rent." Thus, if a pound of one kind of manure produces the same result as two pounds of another, and so forth, you might register pounds of the different manures, in order of their efficiency, along the axis of X, and treat the excess of efficiency of a pound of the one over a pound of the other as "rent of superior efficiency." Indeed, if any two things could perform the same function, but one of them could perform more of it than the other, you might regard the excess of the price of one over the price of the other as a case of "rent." And in very truth that is all that the Ricardian law of rent amounts to. If two pieces of land can each of them yield wheat to labour and capital, but one yields more wheat than the other, the value of that land will be proportionately higher, just as the value of an apple-tree that bore an average of two hundred apples of given quality per annum would be higher than that of one that only bore an average of one hundred and fifty of the same quality. In fact the Ricardian law of rent is nothing whatever but a statement that the better article commands an advanced price in proportion to its betterness. The introduction of the hypothesis that the lowest quality of the article is to be had for nothing would make the whole price of the better article due to its "betterness." If there is no such gratuitous supply, then only the excess of the price of the more expensive article in the market would be due to its "betterness," and the rest to its "goodness" up to the point of lowest goodness in the market.

Again, reverting to our former interpretation of the figure (waiving all scruples as to the course of the curve in the neighbourhood of the origin), and bearing in mind that the form of the mixtilinear area is determined simply by the fact that land is constant, we shall see that by representing any other factor as constant we shall obtain a representation of it as a mixtilinear area. Thus, in all the individual and communal curves which represent the declining marginal significance of successive supplies of any commodity, we may regard the psyche or sensitive organism as the constant, and the areas as psychic. If the sensitive organism, or body of sensitive organisms, remains constant, successive increments of the provocative or stimulus will, after a certain point, produce decreasing revenues or volumes of the experience in question, and we shall therefore have the mixtilinear area representing an excess in the experience provoked by the earlier over those provoked by the marginal increments. When students perceived this they promptly dubbed that excess "consumer's rent."

But misleading as these uses of "rent" appear to me to be, they constitute but a small part of the evil that we have to deal with.

We have seen that the figure constructed on the hypothesis of land being constant, and labour and capital variable, may equally well be regarded as an illustration of the Ricardian theory of rent when associated, as it usually is, with the hypothesis of "no-rent" land being under cultivation. The general attitude of mind with regard to rent that results from all this may be thus described:—Rent is a residuum which is determined by the subtraction of the shares of the other factors of production, and what those shares are is determined by the remuneration they can secure on "no-rent" land—that is to say at the margin of cultivation.

We may notice in passing that this treatment of rent as a residuum incidentally stultifies the claim of the current economic science to have established a "law of rent" at all. For if rent is simply what is left when the other factors have been satisfied, we have not established a law of rent, but have assumed that we know how to determine the shares of everything except land, and then simply stated that what is not anything else is rent. If we start from x = a + b + c + etc., we cannot determine a simply by the equation a = x - b - c - etc., unless we have independently determined the values of b, c, etc. Thus, what is usually given as a derivation of the law of rent from the law of decreasing efficiency of successive doses of labour and capital on the same land is really an assumption that every other factor of production obeys the law of marginal efficiency which we have taken as our guide to the whole theory of distribution. Instead of elaborating a theory of rent the current exposition tacitly assumes a (correct) theory with reference to everything except land, and then claims that no theory at all is necessary for land. But our elaborate examination has shewn that the diagrammatic exposition strictly involves the conclusion that that same law really applies to land just as much as to the other factors. In truth, then, the mixtilinear area represents rent, not because it is all that is left when the other claimants have been satisfied, but because it represents the marginal efficiency of land, and would be represented by an ordinate if we had taken labour as the constant, just as labour is represented by an ordinate when we take land as the constant.

But we are concerned at present not with the inconsistencies already involved in regarding rent as a residuum, but with the further conclusions that have flowed from it. If rent, it is argued, is a surplus or residuum which can be arrived at by deducting the remuneration of the other agents, as measured by the return to them on marginal or "no-rent" land, why should not profits be regarded as the residuum or surplus to be arrived at by deducting the remuneration of other agents, as measured by their returns in a marginal or "no-profit" business? And when, by these or similar processes, we have arrived at satisfactory "laws" which determine rent, profits, and so forth, surely we can determine wages (as General Walker did) by making them, too, a residuum when the other factors have been paid off. It is clear that all such attempts are based on the system of equations a = x - b - c - etc., b = x - a - c - etc., c = x - a - b - etc., and so on, none of which adds anything to the original datum x = a + b + c + etc., but each of which assumes that data have been independently obtained, with respect to all agents except that one to which it specially refers.

Nor is this the last or the worst of it. The reader will have noticed that the use of " margin" or "marginal" which we are now examining is quite different from that in which we have defined it on page 40 sq. and used it throughout this work. "Marginal land," for instance, or "marginal ability," in this connection, is not land or ability considered with reference to the volume of the supply, at the margin of which it is added or subtracted, but land or ability of the lowest intrinsic quality which is devoted to the industry in question. And the marginal conditions are not the conditions determined throughout the industry by the "margin" in our sense, that is to say, by the marginal significance of adding or subtracting a small increment, but are certain specified conditions applying to the production of specified units of the product. On this conception of margins many writers have conceived of one distributive category after another as consisting of an actually existing "surplus," mounting backwards towards the origin from the "margin," and constituting a great reservoir untapped by marginal distribution; and bewildered and bewildering attempts have been made to get at the marginal (least efficient) man working with the marginal (least efficient or least abundant) capital on the marginal (least efficient) land, and to calculate everything backwards from this point. But it must now be clear to the reader that all such attempts are based either on the mere arrangement of units on the abscissa in the order of their efficiency, which neither illustrates, nor proves anything except that the better article commands the better price, or else are based on a misunderstanding of the geometrical form necessarily assumed by the area that represents the constant, whatever it may happen to be, in a diagram constructed on the principles of Fig. 39 (page 551). The ambiguous use of the term "margin" has obviously added to the confusion. We now see once for all that the marginal distribution in our sense (that is to say, the distribution of the product amongst the claimants in proportion to the significance of the addition or withdrawal of a small increment, at the margin determined by the present supply), exhausts the whole product. The curvilinear area represents a margin just as much as the linear ordinate does, and may just as well be represented in the same geometrical form.

In our phraseology a unit "at the margin of x" is not contrasted with the other units in the group, which are in some way superior to it. All the units in the group are at the margin. The distinction is not between the x units of the group severally, but between the significance of each of a number of qualitatively indistinguishable units when forming one of a group of x and when forming one of a group of x + 1. The one use of the term implies qualitative differences, the other presupposes qualitative identity, within the group. In our sense of the term, therefore, all the units of every group are always marginal units, whatever the margin may be; and therefore, naturally, the marginal distribution accounts for the whole product.

It is open to any one to examine or to dispute the ethical or social claim of any factor of production to a share, in accordance with its marginal significance, or to argue that there is no industrial necessity to allow such a claim; but it is not open to any one who understands the facts to argue that when, by a marginal distribution, every factor, reduced to the common term (on the principles of equivalence of marginal significance expounded in Book I. pages 368 sq.), has been satisfied, there remains any residuum or surplus whatever to be divided or appropriated. The vague and fervid visions of this unappropriated reserve, ruling upward as we recede from the marginal distribution, must be banished for ever to the limbo of ghostly fancies.

Before we bid farewell to the current or recently current expositions of the law of rent, we have still to notice one curious and instructive point. There is no connection whatever between the definition of rent given by the economists and the demonstrations by which they seek to determine its amount; for the economists first carefully define land as the primitive and inalienable properties of the soil, and explain that any ordinary piece of agricultural land is, to an indefinite extent, not land at all, but capital; and then proceed to examine the law of rent (almost invariably drawing their illustrations from agricultural land) on principles that take no account whatever of this distinction; for, as far as concerns the "Ricardian" law, it is clear that if one man commands a rich alluvial soil, and another man commands soil which by drainage, permanent manuring, and other devices, has been made equally desirable, both the one and the other, and both in equal degree, will pay a higher rent than they would pay for unmanipulated moorland which it is just worth while for some one to cultivate. And again (to take the law of rent as expounded in connection with the principle of "decreasing returns"), whether the land which we rent has been made what it is by mixing marl with the original soil, by drainage, or by other deliberate process, or is what it is by virtue of its original properties, or has become valuable because of the opening of a railway line or the building of a number of houses in the neighbourhood, in any case it will be cultivated more or less intensively on exactly the same principles. The law of rent, then, as expounded by the economists, has no connection with land as defined by them, but connects itself readily enough with land in the popular sense, which is an amalgam of economic land and economic capital.

There is nothing surprising in this, for we have seen over and over again that it is impossible to draw the line either between land as a primitive gift of nature and land as embodying capital or the results of human effort, or between a change in the value of a piece of land caused by something that has been done to it and that caused by changes that have taken place elsewhere. And, finally, since we know that land and capital are remunerated on one identical principle, in conformity with their marginal efficiency, we can see that the attempt to distinguish accurately between them is as unnecessary as it is hopeless.

Indeed it may be roughly said that everything that we read in Economic books as to the pure theory of distribution, whether it refers to wages, interest, rent, or profit, is either false when asserted of the category under discussion, or else true of all the others as well.

CHAPTER VII

BANKING. BILLS. CURRENCY

Summary.—Banking had its origin in the practice of depositing money with goldsmiths for safe custody. It was found that most of the money so deposited was never taken out again, but was transferred from one credit to another. Hence it was found safe to invest the greater part of it in revenue-yielding ways, and only to hold a comparatively small reserve in gold. The miscellaneous forms of property held by the bank represent the sums that their clients hand over to each other by cheques and so help to transact the business of the country, and are in truth media of exchange. The actual transfers of gold necessary to settle balances, after all the obligations in the country have been "cleared" as far as possible, is undertaken by the banks without specific charge. But not so in the case of balances between one country and another.

International trade is generally carried on under the denomination of gold (or silver), but the Englishman who owes money in France might buy goods in England to the value of his debt, export them to France, sell them there, and ask his correspondent to pay his debt for him. Thus gold transactions within the countries would be substituted for cross gold transactions between them. And if an Englishman owes gold in France he would find an advantage in liquidating his debt in this way, even if he made no independent profit on this subsidiary transaction, so long as he lost less on it than it would cost to transport the gold. This machinery for discharging debts in goods when it is cheaper to do so than to pay for them in gold is simplified and generalised by the use of "bills," and its action is registered by the "rates of exchange" prevailing between different countries.

We measure changes of value in commodities by changes of price, and as all prices are measured in gold and the price of gold therefore cannot vary, it is difficult to realise that gold varies in value just in the same way and on the same principles as other commodities do. The resistance of retail prices, and other relatively fixed scales of payment, to change, prevents the ratio of exchange between gold and certain classes of commodities and services from adapting itself rapidly to changed conditions. But in principle all values are determined by the same considerations of quantity and place on the relative scale. But whereas the use of gold as a standard of value does not affect its place on the relative scale, its use as a medium of exchange does, for it withdraws a portion of it from other uses and so raises its marginal significance. A minted sovereign is a piece of gold certified by the Government as to weight and quality. The certificate may be of value, and persons may be willing to pay for it. Hence a sovereign may be worth a little more than the gold it contains. But its cost of production (i.e. the expense of minting it) cannot maintain its price if for any reason the certificate should fall in value. This only happens rarely, for short periods, and within narrow limits. A paper currency can only be maintained so long as the paper is directly or indirectly convertible into actual commodities or immunities. A Government cannot make it circulate by saying it shall, unless it puts some actual meaning and power into it by effectively relating it to actual values.

We have now closed our critical investigations directly relating to the construction and interpretation of diagrammatic curves and the economic problems they suggest; but a somewhat isolated branch of inquiry, indicated by the title of this chapter, still demands our attention. It is not my purpose to enter in detail upon questions of finance and currency, but the very short examination of the subject with which we contented ourselves in Book I.50 must be supplemented by notes on a few topics, selected partly for their fundamental nature, partly for their important bearing on current discussions, and partly because, as I believe, false conceptions of a peculiarly insidious kind are current concerning them. Much will be omitted that would have to appear in even an elementary treatment that aimed at completeness within its own limits.

We have already distinguished between two functions of gold. It is a standard of value by which a survey of the terms on which all manner of alternatives are offered can be facilitated, or, in other words, it furnishes the scale on which exchange values are expressed; it is also an actual medium of exchange, inasmuch as it constitutes a universally acceptable commodity, and is thus a convenient means of dividing into two stages the operations by which we transform the things we have into the things we want; for it enables us first to generalise the special forms of wealth or capacity we have, and then specialise this generalised wealth into what we want. It is obvious at once that the former function is of the wider scope, for two persons directly exchanging their wares might do so in terms of gold without using gold as an intermediary. A farmer who has hay which he will have to sell at the market price in order to buy turnips at the market price may find another farmer with turnips to sell who wants hay. In this case there may be no necessity for the material intervention of gold at all, even though it be employed mentally as a means of enabling each of the farmers to realise the other alternatives that are open. Each of them may estimate both the hay and the turnips in gold to help him in determining their relative values. When they have both determined that they can do no better than exchange, the one so much hay for so many turnips, and the other so many turnips for so much hay, they have simply to make the exchange; and if each farmer makes out a bill of the same amount to the other and they then exchange receipts, though in form there will be two distinct transactions in which each farmer assumes that the other will pay him in gold, as a matter of fact this is a mere customary fiction, and there are not two transactions but one. The turnips and the hay are exchanged for each other, but their values are expressed in terms of gold.

Now it may well be that two men have frequent dealings with each other in which each receives goods from the other, without at the time giving him anything in exchange for them, but promising to pay him gold to the amount required. Here the obligation to pay gold is not a mere fiction. There is no agreement to give anything else and no obligation to enter into further transactions, and the gold promised may ultimately be paid. But if at the end of six months one man finds that forty sovereigns are due from him to his neighbour, and thirty-eight sovereigns due from his neighbour to him, there is obviously no necessity for him to hand over forty sovereigns and to receive thirty-eight; it will be the same if he pays over two and the men exchange receipts. And if some such approximate balancing of claims can be anticipated with confidence there will be no occasion for each of the two to keep by him a stock of sovereigns in order to meet the claims of the other. And of course the mere fact of A owing fifty pounds to B may suggest to A the possibility of hitting upon something that he can sell him. And if (as may probably be the case) it would be inconvenient to him to find the ready money he may try to tempt B by offering him a slightly advantageous bargain. Thus he goes a little out of his way to create a counter obligation against which he may cancel his. Thus, one way or another, instead of requiring between them to keep eighty or a hundred sovereigns in order to be able to settle with each other, the two men will find it enough if each of them has five or six sovereigns ready to pay any balance that is likely not to be cancelled when they compare their mutual claims. This is a great advantage, for each wants to put all his available wealth into his land and crops. Here all the accounts are kept in terms of gold, but very little of the business is transacted through gold as a medium. Nevertheless each transaction is in itself a promise on the one side to deliver the goods and on the other side to pay gold. Now this incurring of obligations to pay gold which never have to be fulfilled is a phenomenon of extreme importance in the industrial world, and the machinery by which such obligations are met without the transfer of gold repays careful study.

The simplest case would be such as the one we have already examined, where A has supplied B with commodities or services and has a claim for gold against him, and B in like manner has supplied A with other commodities and has a claim for gold against him.

These two claims for gold, so far as they go, will cancel each other, and only the balance need be paid. Gold as a standard of value and a potential medium of exchange has been associated with the whole transaction; gold as an actual medium of exchange, only with a small part of it. But suppose A is under obligation to pay gold to B, and B is under obligation to pay gold not to him but to C, who in his turn is under obligation to pay gold not to B but to A. Then A is to receive gold from C and pay gold to B, B is to receive from A and pay to C, and C is to receive from B and pay to A—

so that in the end the gold will be exactly where it was at the beginning, if the obligations are equal; and if the various transactions are not of the same value in gold, the final state will only differ from the initial state by the margin beyond the area of coincidence. Here again it is clear that a sum of gold passing from A to B, and from B to C, and from C to A again, is making the same superfluous journeys that it was found easy to avoid in the simpler case when it passed from A to B and then back again from B to A.

Now any one of these three, B for instance, might say to C: "I owe you money, but A owes me money. Instead of paying you I will tell A to pay you, and will accept your assurance that he has discharged my obligation to you in lieu of his payment to me." If C accepts this arrangement, then the form has been reduced to the form and, as we have seen, these claims cancel each other; so that the whole of the three transactions can be cancelled, so far as the gold is concerned, except for the settlement of the balances. If A, B, and C are in easy connection with each other, it does not matter whether they live in the same house or in the same city or in the same country. They might be one in New York, one in Berlin, and one in London; or they might be next-door neighbours; or they might be (as they often are) members of the same family liquidating their obligations across the table. It is easy to see that the same principle might be successfully applied to any number of persons and to any network of cross obligations and combinations if a system of cancelling could be established that involves less expense and inconvenience than the keeping and transferring of the metal would. Now the actual transfer of gold may be a more serious matter between Glasgow and London than between two streets in Glasgow, and a more serious matter between Glasgow and Berlin than between Glasgow and London. Therefore if two persons, A₁ and A₂, live within easy access of each other and are in habitual communication, and two other persons, B₁ and B₂, are similarly situated with respect to each other, then suppose A₁ is under obligation to pay gold to B₂, and B₁ under a similar obligation to pay gold to A₂, we should have that is to say, A₁ and B₁ are to pay, and A₂ and B₂ are to receive. Then let A₁ pay A₂ on behalf of B₁, and let B₁ pay B₂ on behalf of A₁— the result being the same, namely, that A₂ and B₂ have received money, and A₁ and B₁ have paid it. Thus, if we regard A₁ and A₂ as a single group, and B₁ and B₂ as another single group, the form may be regarded as reducing itself to the form and only the balance between the total obligations of the A's to the B's or the B's to the A's will have to be settled by the transfer of gold. And in the same way the A, B, and C of a former example may be groups of persons living respectively in London, Berlin, and New York.

This is the whole theory and principle of foreign exchanges and international trade, but we must further examine the machinery through which it is applied. Before proceeding with this branch of our inquiry, however, we must consider another closely connected but also contrasted financial scheme.

Let us suppose that a man who has numerous transactions with his neighbours both buys and sells with most of them, though there are some from whom he buys only and others to whom he only sells. This still is, or recently was, very much the case in remote country districts. Such a man may, by the cancelling process already described, conduct a great part of his exchanges under the denomination of gold but without the intervention of gold as an actual medium. But he both receives and pays in gold to some extent, and he must take care to keep by him enough of the gold that he receives to enable him to make his payments. And there are periods during which a considerable amount of coin is simply lying in his cash-box in anticipation of claims that will be made before any more cash has come in. Indeed, to be safe he always aims at having a little more than he is at all likely to want. If he could be sure of its safe custody he would be glad to be rid of the anxiety and risk of keeping this cash himself; and we are told that it was the lodging of sums of money with goldsmiths for safe custody that first gave rise to the system of banking. Let us suppose, then, that a bank is established and that it receives the greater part of the stock of money which the community finds it convenient to have available for paying their balances in gold. The banker credits each of his clients with the amount of his stock. When A has to pay a sum in gold to B, instead of handing over the sovereigns he now gives him an order for those sovereigns upon the banker, and B, if he likes, can go to the bank and get them out. But if he too wants gold chiefly for paying balances, and if he too lodges the greater part of his stock with the banker, it is unlikely that he will draw the sovereigns out at all; he will simply hand over to the bank A's certificate that so many sovereigns are now his, not A's, and the banker will transfer the amount from A's credit to B's.

This system could be carried on either in conjunction with the cancelling process described above, or apart from it; for A and B may either give each other orders on their bankers for the full amounts of their obligations, or may exchange their bills as far as they go, and only settle the balance by an order on the banker for the transfer of credit from one to the other. And where the accounts of a whole community are thus kept by the banker, it is obvious that machinery is at once established by which many cross transactions may be simplified. Thus, in the instance given on page 579, if A has given an order on his banker to B, B may simply transfer the order to C without knowing that C owes money to A. C, in any case, may go to the bank and draw out the money, or he may leave it there to his own credit. Or if B prefers it he can draw a cheque on his bank in C's favour, and at the same time pay in A's order, so that he would at once have the credit transferred to him from A's account out of which he can meet C's claim. The more complicated the transactions are the greater the simplification that can be effected by one central recipient who has the whole field under his survey. The transactions of the community, therefore, when banking is firmly established, will be to a very great extent conducted without any physical transfer of gold at all. But so far we have not seen that the banking system effects any further economy in the amount of gold required to carry on the business of the community. It is true that the gold need not be shifted. If it lies at the bank and is now B's, whereas it was A's, the shifting is only in the books, not in the cellars, of the bank; but A, B, and C must severally, and therefore collectively, have credit at the bank for the full number of sovereigns that they must otherwise have kept at home. Indeed in some ways the banking system rather tends to limit than to extend the cancelling of obligations, in the strict sense, as between individuals. Every one knows that it often conduces to simplicity and clearness of account-keeping actually to go out of the way to avoid cancelling transactions, and to exchange cheques as well, when exchanging receipts; so that a man may have to keep a larger balance at his banker's than the reserve of sovereigns that would be necessary if he did business with his neighbours by cancelling accounts. Otherwise there would be danger of overdrawing, at any rate for a few days or hours. For if A owes B £40, and B owes A £38, and neither of them has more than three or four sovereigns, they can settle their accounts when they meet; but if they avail themselves of the conveniences of banking, and without waiting till they meet send each other cheques, if one presents his cheque at the bank a few hours before the other there will be no credit to meet it unless balances of £40 or so are kept at the bank. Thus in some cases the conveniences of banking may be an alternative to those of cancelling, and may involve the maintaining of a larger balance of money in hand. But it is also possible that banking may be resorted to in conjunction with a system of private cancelling, and in any case it may obviously facilitate the interchange of obligations by which A can make his credit with B discharge his obligations to C, and so forth. But all the while it would appear as yet that the gold, whether for paying of balances or total amounts, must exist in the hands of the bankers though it is not transferred. The economy is in moving the gold, not (so far as we have yet seen) in the amount of gold that is kept.

But now we must take another step. The banker finds that only a comparatively small part of the gold with which his clients are credited is ever taken out: the greater part of it is left with him and is simply transferred now to one credit and now to another. The consequence is that he does not find it necessary actually to keep all the gold which stands to the credit of his clients. He can transform the greater part of this wealth into revenue-yielding forms, provided he keeps enough cash to meet all claims that he can in reason expect will be made on it. For, as we have seen, if A gets an order for gold from C, whether he wants it immediately to settle B's claims, or wishes to keep it ready for any other and future purposes, he will generally not draw out the actual sovereigns, but will simply leave the credit he has received in the banker's hands, or request him to transfer it to some one else.

But the persons in the neighbourhood of Bank A will not deal exclusively with each other. They will deal to some extent with persons in other parts of the country; so that persons dealing with Bank A may be under obligation to pay sums of money to the clients of Banks B, C, etc., and customers of these banks will be under similar obligations to the clients of the others, including A. All these transactions may also be carried on by means of orders to the bankers to transfer credits, only now the client of Bank A will order his banker to transfer his property not to another of his own clients but to a client of Bank B. Here then is an actual order to transfer gold from his cellar to that of another banker, not from the credit of one of his clients to the credit of another, and it would seem that the gold must be shifted. But there will be a number of such obligations on the part of Bank A to Bank B, and a number of counter obligations on the part of Bank B to Bank A, and now, so far as the transfer of gold is concerned, a genuine cancelling of obligations may take place. Bank A sends a number of orders for gold on Bank B, and Bank B meets a part of these by counter orders for gold on Bank A. Perhaps a balance is still due from Bank B to Bank A in gold, but a balance may be due to Bank B from Bank C, and so forth; and—since all the banks will be connected with each other directly or indirectly, through local branches of the Bank of England, through their agents in London, or otherwise, and since they will all (as we shall see) ultimately have balances at the Bank of England,—partly by a system of cancelling obligations and partly by a system of cheques on the Bank of England, they will probably arrange all their affairs without the material transfer of any coin whatever.

Thus it is only a portion of his property (if he is in trade a small portion) that each individual will wish to command in the form of gold; and of this portion, again, he will only desire to have a fraction, probably a small one, actually in his cash-box in the form of gold; the rest he will hold as a balance at his banker's, which he is entitled to realise in gold at any moment he chooses. Now of these balances the banks will hold the larger portion in the shape of revenue-yielding forms of wealth; and of the portion which they desire to command in the form of gold the branch banks will, again, only keep a fraction in their tills; the rest will be held by the great houses in Birmingham, Liverpool, Manchester, and so forth; and these, again, will hold only a portion of their reserves in gold, and the rest in the form of credit with the Bank of England. The Bank of England in its turn will hold the greater part of the property with which it is entrusted by the other banks, and which they may at any time claim in the form of gold, in the shape of revenue-yielding forms of property, only maintaining such a reserve in actual coin and bullion as it deems sufficient both to meet the claims that will actually be made upon it and to maintain its credit unshaken.

Thus we see that enormous economies in the use of gold as a medium of exchange are effected. The whole metallic reserve held by all the banks constitutes a very small fraction of the collective liability of the banks to pay gold on demand; for note that every depositor in every bank is entitled at any time to draw out the whole of his property in coin of the realm, or in Bank of England notes, which in their turn he may present at the Bank of England, demanding gold in exchange for them. Every one, then, is entitled to draw out the full amount of his balance in gold, and any one can actually do this as long as the machinery is working smoothly; but it would be impossible for every one to do it, because the immensely greater part of the property does not exist in the form of sovereigns or gold at all; it consists of all kinds of property and obligations, of a value equivalent, at the marginal terms of exchange, to the total sum which the public has the theoretical right to draw out in gold. It all exists, however. Every man's balance severally, and the whole amount of the deposits in the banks collectively, represent real property, and all this property is in the possession of the banks at every moment, to its full amount. It is the greatest mistake to suppose that the whole body of banking transactions reduces itself to mere entries and transfers in books, and that if the banker had simply squandered the property entrusted to him, everything would go on just the same so long as nobody knew it. For it is just because the property is there, and is most of it yielding revenue, that the banker is able to pay his staff and support his own expenses. The property of the clients, represented by their balances at the bank, is real property and is doing real work; and the revenues that accrue to it in virtue of that work are paying for all the privileges and conveniences that the clients enjoy. If five hundred people draw cheques on the same bank on the same day to the extent of £5000, and only 50 sovereigns, one per cent of the whole, are actually drawn out of the bank, nevertheless, each individual cheque has behind it a basis of actual property to which the drawee has received a valid title. If the bank is solvent, then even if it had to "stop payment," that is to say if it were unable to meet all the simultaneous claims for actual coin made upon it, the holder of credit in it would be the holder of actual property. Thus the man who pays a cheque, hands to his correspondent a document which gives him a substantial claim; and the sum of these substantial claims (unlike the formal right to draw coin) can be met simultaneously; for the holders of the cheques and credits in the bank are entitled, in the last resort, to enter into acknowledged and legal possession of miscellaneous property that is actually bearing revenue and is negotiable, like all other property, in the public markets. So when I receive a cheque in exchange for valuable possessions or services, though I do not thereby enter into possession of the commodities and services that I myself require, yet I do get actual property, not a mere pretence or symbol of property. The actual property I get is valued by some one else, and I can hold it until I find it convenient to exchange it for property that I value myself. Thus by the banking system a vast amount of miscellaneous claims and possessions other than gold are converted into "media of exchange" just as real as gold itself; for they mediate between the things I have and the things I want, and enable me to transform the one into the other without the necessity of a double coincidence between my wants and those of my correspondent. The whole mass of cheques which is exchanged day by day is therefore not an economy of "media of exchange" at large. It is a calling into partnership with gold, as a medium of exchange (but not as a standard of value), of an immense amount of other property. To regard the banking system of England as consisting in a cunning device to make sovereigns that only exist as entries in a book do the work of real sovereigns, is a fundamental misconception.

The great bulk of the business of the country, therefore, is still carried on by the intervention of media of exchange, but only a little of it by the medium of gold; whereas almost the whole of it is carried on under the denomination of gold. Gold, therefore, has a far wider application as a standard of value than as a medium of exchange. But even in this last capacity it is still active. Actual transfers of gold are constantly made from individual to individual, from bank to bank, and from city to city. The obligations of the bankers in Edinburgh and the bankers in Liverpool may not accurately balance each other, and even if the balances are settled by cheques on the Bank of England the receiving banks may find it convenient to demand cash and not a credit from the Bank of England itself. Or at any time and independently of other banks any given bank may desire to draw cash from the London (or other) agent with whom its reserve is deposited. So there will be a pulsation and ebb and flow of gold not only within any given district but from one district to another, and the banks undertake, as part of their business, to convey the actual coin from one part of the country to another, as may be needed.

Thus if I live in Birmingham and owe money to a man in Leeds, I may send him a cheque on a Birmingham banker, and this will save me the expense and risk of actually sending him the gold. It may turn out, as the result of the whole series of transactions between Birmingham and Leeds, that gold actually has to be transferred directly or indirectly from Birmingham to Leeds, or it may turn out the other way. In the first case the fact that I have transferred a portion of my credit in Birmingham to the credit of some one in Leeds will aggravate the situation. In the other case it will relieve it. And this will make a difference to the bankers, but it will make no difference to me. The banker will conduct my business on the same terms whether this particular transaction happens to increase or to diminish his own expenses. It is indeed possible that if I am dealing with a distant part of the kingdom he may charge a special commission on all cheques, but this commission will be uniform and will not depend on whether this particular transaction tends to involve him in the expense of the transfer of gold or tends to relieve him from it. The expenses of the transfer of gold, then, whenever it may be necessary, are a part of the general obligations incurred by the bank to its clients, and no individual dealing with other individuals through a bank in the United Kingdom has to consider whether this particular transaction is likely to involve the expense of a transfer of gold, for if it does he will not have to pay anything extra, and if it saves such a transfer he will derive no benefit from the fact.

But if a London merchant is under obligation to pay gold to a Paris merchant there is no machinery by which he can once and for all contract himself out of the liabilities or privileges that may be incidental to the money being due in Paris and the gold being in London, when the time of settlement comes. And it is here that the economic difference between home and foreign trade clearly emerges.

There is obviously no reason why the purely economic forces which urge men to further the purposes of others in order that they may thereby further their own, should in any way be limited or qualified by national boundaries. And from the economic point of view it therefore seems impossible to conceive that there should be any essential difference between foreign and domestic trade. Whatever differences there are must apparently be differences of condition or of machinery, not of economic principle or theory. But what are these differentiating considerations? Some of the conditions under which, and obstacles in the face of which, the economic forces act may indeed be determined by a difference of government or language, or both. But it is difficult to assign any general or dominant efficacy to them even when they coincide with the areas of "home" and "foreign" trade. Familiarity and confidence are essential elements for the carrying on of business, and this may, in a vague way, be furthered by a common nationality, language, or government; but it is hard to see why a merchant in Dover should necessarily have more familiarity with or confidence in a merchant in the Hebrides as against a merchant in Calais. English and Americans speak the same language, yet their dealings constitute a branch of foreign trade. Englishmen and Welshmen deal with each other, and their dealings are a branch of domestic trade, even if they habitually speak different languages. English and Irish trade is domestic, and English and French trade foreign quite irrespective of the cordialité or otherwise of any entente that may exist between the peoples. Colonial trade is usually (and rightly, as we shall see) classed with foreign rather than home trade, though by the sentimental tests it should belong to the latter. Tariff boundaries seem to promise a more important distinction; but the trade between England and Denmark is foreign trade though there are practically no tariff barriers to overcome, and the trade between Florence and the surrounding agricultural districts is domestic although a tariff barrier is drawn round the city. Where, then, are we to look for any essential differences? Is it in the different systems of currency? No; for the standard coins minted by any one of the countries forming the "Latin Union" were made legal tender in the public treasuries of all the others by a treaty of 1866, and were practically received as such in all private transactions. Moreover, even where there is no such legal or conventional equivalence of currencies, transactions are conducted under a common standard. The affairs between Germany and England are conducted in terms of gold, and the sums of gold which people in London and people in Berlin have engaged to pay each other can be cancelled directly or indirectly, as between Liverpool and Glasgow; the balances in either case being ultimately paid in gold which has to be physically transported from the one centre to the other. But, as we have seen, there is a real difference in the machinery by which the cancelling is effected and the form in which the individual trader meets his share in the expense of the necessary transfers; and it is to the examination of this point that we must now return.

Let us revert to the case examined on page 579. We suppose that three persons, A, B, and C, are in such relations with each other that A owes to B, B to C, and C to A. That is, B having supplied things to A, sends him in a bill, C sends in a bill for the like sum to B, and A to C. Let A send in his bill to C and request him not to pay it, but simply to acknowledge that he owes the money and will pay it to any one A may nominate. Let C send back A's bill with this undertaking endorsed on it, and then let A write on it a statement that it is B to whom the money is to be paid, and let him then forward the document with these two endorsements upon it to B. B has now a claim upon C for the money which A owes him, and as C has a claim for the same amount on B, the two claims meet each other and there is no transfer of coin at all. A has settled his account with B by giving him a bill upon C; and this is the type of the instruments by which international obligations are cancelled. We have only to suppose that A lives in London, B in Bombay, and C in Amsterdam to transform this into an actual case of settlement of international accounts by bills.

We may note exactly equivalent ways of settling such a group of accounts.

may be resolved into

into

or into

according as A "draws a bill" on C, B draws a bill on A, or C draws a bill on B. All these processes are identical in principle and in effect. Custom determines the prevailing practice in each important case.

But the "double coincidence" implied in this example will be rare. An English merchant may well export woollen goods to New York, a New York merchant wheat to Amsterdam, and a Dutch merchant dairy produce to London; but it is not likely that it will be the same English merchant that sells the woollen goods and buys the dairy produce. And so with the others.

We shall therefore have, in the simpler case of the two countries, dealing with each other both ways, resolving itself, by the agency of a bill, into That is to say: the Paris merchant B₁ who owes money to the London merchant A₂ will find another Paris merchant B₂ who has a bill against another London merchant A₁; he will pay it and will then send B₂'s order on A₁ in payment of his own obligation. B₂ will then have been paid by B₁, and A₂ will draw upon A₁, who will pay him.

In the more complex case we have An English merchant A₂ has bought dairy produce from a Dutch merchant C₁. C₁ finds another Dutch merchant who has bought wheat from a New York merchant B₂ and wishes to pay him. C₁ sells his bill on A₂ to C₂, who forwards it in payment to B₂. B₂ finds another New York merchant B₁ who owes money to an English merchant A₁ for woollen goods. He buys the bill on A₂ from B₂, and forwards it in payment to A₁, who presents it to A₂ and receives payment for it. Thus A₂ has paid A₁ instead of C₁; C₁ has been paid by C₂ instead of by A₂; C₂ has paid C₁ instead of paying B₂; B₂ has been paid by B₁ instead of by C₂; B₁ has paid B₂ instead of paying A₁; and A₁ has been paid by A₂ instead of by B₁.

The movement has been A₂, C₂, and B₁ have paid, and A₁, C₁, and B₂ have received, as was due; but the settlements have all been made without transfer of coin from country to country.

The instrument of liquidation has been a bill on London; but theoretically it might equally well have been A₁'s bill on B₁ in New York, or B₂'s bill on C₂ in Amsterdam. But it is manifestly unnecessary for more than one bill to circulate.

Thus we see that in international or colonial trade (for we might just as well have had Quebec as New York in our example), through the instrumentality of bills payments within a country may be substituted for payments from one country to another, even when all the transactions are conducted and all the obligations incurred in terms of gold, and even if every one of the creditors requires and receives full payment in gold.

But the most important and complex part of the investigation still remains. How are balances settled? They might be, and sometimes are, settled by the actual transfer of gold, but the expense of transferring gold from Berlin to London, for example, is about ¼ per cent. More closely, if a German has to fulfil an obligation to a London merchant for £1000, it would cost him about £1002:9s. if he actually sent the gold. Now in any given state of trade there will always be German merchants who would be prepared to export, say, musical instruments or glass to London, if they could get a very little better price than they can actually command. A German merchant who would just not be induced to accept a certain order at £1000 might just be induced to accept it at £1001. If such a man, having an offer of £1000 for certain goods, were to say to the German who owes £1000 in London, "I will discharge your debt for you by sending goods to London which will be accepted as the full value of £1000, if you will give me £1 for doing so," it would pay the German debtor to accept the offer. The German manufacturer would present him with a bill against his correspondent to the full amount of £1000, he would despatch it to London in payment of his obligation, and it would have cost him £1001 only, instead of £1002:9s. Thus the exports to England will increase, and the balance "against" Germany (that is to say, the obligations of Germany to England in excess of those of England to Germany) will be reduced. But it may be that in spite of this Germans are still buying more from England than England is buying from Germany, so that the obligations of Germany are still mounting, and German debtors, having exhausted all the possibilities of finding German manufacturers who are within £1 on the £1000 of striking bargains in England and so creating bills on her, will have to offer better terms and make use of those who are, say, only within £1:5s. on the £1000. And this process may go on until there is no German manufacturer or exporter who will undertake to deliver any goods in London which will have the market value of £1000 there, unless he receives a premium of £2:9s. for doing so. When it comes to this, if there is still a balance to be paid, the German debtor will have nothing to lose by despatching the gold, and he will therefore do so.

If the balance is the other way it will be the English debtor who may have to pay a premium on getting his debt discharged, and the English manufacturer of woollen or leather goods, or hardware, who may be induced to sell his wares in Berlin at a lower price, after allowing for transport, than he would accept in England, because he will receive a premium for discharging a debt in Berlin. In a word, when there is a balance due from London to Berlin, a claim for money in Berlin being worth more to a London merchant than a claim for money in London, the export trade will be stimulated. And when the balance is the other way of course the reversed relation holds.

Sums approximating to £99:16s. and £100:5s. are known as the gold points between London and Berlin. Naturally the gold points between any other two centres are different. They are the points to which the premium must rise either way in order to make the actual export of gold the cheapest way of settling a balance. Within the gold points balances are settled by exporting goods which would not have yielded a profit had exchange been at par.

The gold balance will, normally, be "against" gold-producing countries, where gold is a staple export and obligations are normally discharged in it, for these countries normally export gold and receive other commodities in exchange; whereas in other countries the balance will prevailingly be "favourable," that is to say, they will receive their share in the increasing supply of gold in return for export of other commodities.

On the basis of these actual "bills" a fabric of drafts and instruments of every kind is raised, by which international obligations are liquidated. Thus a cheque on my London banker sent to a friend in Berlin becomes a "bill" on London, that is to say, a claim for so much gold in London; and if such claims are at a premium in Berlin, it will sell for more than the metallic value of the gold it represents. And so, too, with Bank of England notes.51 The case of actual coin seems anomalous. By hypothesis gold in London is of more value to the Berlin merchant than gold in Berlin. Yet when, for that very reason, bills on London are at a premium, English sovereigns follow the bills and will exchange for more than their metallic weight in German coin. Qua gold they are worth less, but qua instruments by which obligations can be discharged in London they are worth more, and persons who are intending to go to London and spend money there will pay more for them, just as willingly as for notes. If there were a large number of them, and their export to settle obligations in London became a business, a man who undertook to send them to England for the convenience of others, instead of desiring to take them across for his own convenience, would have to be paid. But as there are not enough to satisfy all the wants of those who desire them, not as gold but as English coin, they remain at par with the notes this purpose of which they serve equally well. The chief centre of the "bill" business in the larger sense is London, and "drafts" on London are drawn by all nations in settlement of their accounts.

Expositions of the theory of foreign exchanges often dwell too much upon the form which the transactions take without connecting it sufficiently closely with the ultimate movements of trade which it represents. We do not find in practice that one man goes to another, as we have supposed, and says, "I will discharge your debt for £1000 in London if you will give me a commission of £1 for doing so." But the man who owes £1000 goes into the market to buy a bill by which he can discharge his debt, and finds he has to pay £1001 for it. This of course simply means that to induce some one to create a bill for £1000 on Berlin, that is to say, to supply goods for which he will receive £1000, he must offer him a premium of £1 for doing so. A man who has a bill must sell it for what it can fetch, but he will not create a bill, by a transaction which taken alone would involve a loss, unless he can sell it at a profit. If there is a profit of £1 to be made on creating a bill for £1000, any one can do it if it is worth his while. And as a matter of fact bargains are struck by telegraph all over the world in accordance with the rate of exchange, which varies from day to day; and the amount for which a man can negotiate a bill on such and such a centre is a material consideration in the terms which he can offer his correspondent. All this is perfectly understood, but a delusive simplicity can be given to the exposition by simply treating bills as though they were themselves commodities, and saying that if bills on Berlin are scarce they will rise in value like any other commodity, and if they are abundant will fall, only that they cannot rise or fall beyond the gold points because there would then be cheaper substitutes for them. The superficiality of this treatment need hardly be pointed out. The bill is not a commodity, and we must go behind the phenomena of the bill market to the actual commercial facts which it represents.

Our treatment of the principles of banking and of foreign exchange has necessarily been extremely brief and imperfect, and it is not compatible with the scope and aim of this work to go into further detail. There is, however, one branch of the subject which still remains for examination, and it cannot be wholly neglected. It is the question of the principles which regulate the distribution of the precious metals, and specifically gold, between its uses in the arts and in the currency.52 The difficulties that surround this question do not arise so much from the use of gold as currency as from its use as a standard of value, and with this we will therefore begin. There should be no real difficulty in understanding the fundamental relation between gold and other commodities. But it is extremely difficult not to be confused by the language in which we have to express the facts. Thus high gold prices mean low price of gold; for the gold prices of other things are the amounts of gold that must be given for them, whereas the price of gold is the amount of other things that must be given for it. Thus, abundant gold means high prices (in gold), and scarce gold means low prices (in gold). Whereas abundant wheat means low prices (of wheat), and scarce wheat means high prices (of wheat). This is perfectly consistent; but since, when we are speaking of gold, "prices" mean the prices in the commodity of which we are discoursing, and when we are speaking of other things prices mean the prices of the commodities of which we are discoursing, the terms constantly confuse and frequently betray us when we are considering the theory of finance and currency. The most experienced scalers of the Alpine heights of speculation in the currency have constantly to steady their heads in these regions of discourse, and the novice is almost certain to be the victim of aggravated vertigo. The facts, however, that lie behind these bewildering phrases are intelligible enough. We will approach them by forgetting gold for a moment and speaking of wheat. If there is a good wheat harvest, a given amount of wheat will exchange for less of any other commodity or service, and any other commodity or service will exchange for more wheat than if the harvest is bad. High wheat prices would correspond to a relative abundance of wheat; that is to say, a value which was expressed as ten pecks of wheat when wheat was relatively scarce might be expressed as eleven pecks when it was relatively abundant. Consequently if a man had a fixed income of so many quarters of wheat, independently of its abundance or scarcity, he would find when wheat was abundant that prices had risen against him, and although his nominal wheat income would be the same, his real income in the general command of commodities and services would have fallen. But if the man's nominal income were increased so as to make his real income the same, he would find that wheat being cheaper than before relatively to other things, that is to say, the sacrifice of other things involved in consuming a peck of wheat being smaller than before, there would be a tendency in his administration (imperceptible if he were rich, very marked if he were poor) to consume more wheat in proportion to other things than he had done previously.

On the other hand, if the crop of wheat relatively to the number and habits of the population remained constant for a long series of years, and the amount of gold increased, people would gradually discover that all articles made of gold became relatively cheaper, whether measured in wheat prices or in the equivalents of other services and commodities; and men who had hesitated to pay the extra price for the use of gold in dentistry, or publishers who had refrained from attractive touches of gold in the make-up of their cheap issues, would find that it was now worth their while to incur the lessened expense. Thus, if a man were considering whether he would order a set of artificial teeth, containing a certain amount of gold in the plate, he would find that whereas the extra cost would formerly have been a quarter of wheat, now that gold is cheaper it will be less by a few pecks. He may think this lower (wheat) price worth giving for the additional advantage, in durability and comfort, of having the gold in his plate, whereas at the former price he would not have ordered it. Gold being cheaper it can be had at less sacrifice of other things.

Now these consequences of an increased crop of wheat or an increased output of gold will remain exactly the same if gold, instead of wheat, is the standard. If gold becomes relatively more abundant, gold prices rise, and the man whose real income remains the same (his nominal income being raised, as in the case of the wheat standard) finds gold articles relatively cheaper because all other things are dearer in gold prices, so that the amount of other things he would be able to get instead of the gold in his plate is now smaller than it was, and the sacrifice of other things now involved in securing the plate being therefore smaller, he may be willing to incur it. If, on the other hand, the relative supply of gold remains constant for a series of years and wheat becomes more plentiful, there will be a tendency to substitute the consumption of wheat for that of certain possible alternatives. Thus the relative value of wheat or of gold in relation to other things, and the extent to which they are used by individual consumers, depend on the relative abundance of wheat or of gold, and are entirely independent of the standard in which values are measured, though the position of a man with a fixed income is naturally dependent on the article in which that income is fixed.

If our general thesis is correct that the economic forces tend to secure remuneration to every man and prices to all articles in accord with the marginal significance of the services they render, then there would always be a tendency for nominal wages in wheat to increase if wheat became more abundant and for nominal wages in gold to increase if gold became more abundant; but this tendency may have serious obstructions to overcome. Confining ourselves to the case of the gold standard and the gold prices with which we are familiar, it is obvious that even if a man has not a fixed salary expressed in terms of gold, there may be a traditional price of his services which will offer a certain opposition to change. It would not be easy for a man to change his terms from 7s. 6d. to 7s. 8d. an hour for some kind of instruction, or from 4s. or 10s. a thousand words for translation to the same sum for 1010 words, if the ratio in which gold exchanges for wheat and other commodities had changed. This inertia, or friction, affects all kinds of bargains, the terms of which ought, on the general principles of exchange, to fluctuate not only with the supply of the commodity or capacity concerned and its place on the communal scale, but also with the change in the significance of the unit in which it is expressed; and schemes of a complex standard of value that would automatically preserve the ratio between established prices and their purchasing power have been designed; but they have never come into use; and therefore any man may find himself prejudiced or advantaged by a contract or convention that only yields to the changing facts under severe pressure; and he may therefore be giving either more or less than the value of what he gets, because the terms of his bargain have ceased to correspond with the facts. There is a specially marked tendency to retain certain retail prices at a fixed nominal level, and the fact that this can continue—that the price of a hat, for instance, or the admission to an exhibition remaining fixed through great fluctuations in the purchasing power of gold—shews how much friction counts for, and how much the action of the general economic trends is impeded when it has to force itself through the narrower channels of the commercial system.

But when the amplest allowance has been made for all this friction the general proposition remains true that whether wheat or gold were the standard an increased crop of wheat would at once raise wheat prices and encourage the consumption of wheat, whereas an increased supply of gold would raise gold prices and encourage the use of gold. We have, therefore, to keep in mind that, under a gold standard, high prices correspond to cheap gold and low prices to dear gold; and that in principle and in the long-run this difference of expression is the only difference which the selection of gold as the standard of value really makes, except in so far as the use of gold as a standard of value involves its use as a medium of exchange. This use as a medium of exchange constitutes an extra use for gold, and consequently raises its value, just as every additional use for any other commodity would, and does. Every individual finds it convenient to hold a portion of his property in the form of gold (or the subsidiary currencies, into the relation of which with gold we need not enter), and therefore a certain amount of gold is withdrawn from other uses, and its marginal significance in these other uses rises. How much does each individual thus set aside? If he is living from week to week or from year to year upon his current earnings, he will practically desire to have the whole of his income immediately available in this form, for he never has enough property for a long enough time to enable him to invest it in revenue-yielding ways. But if he is engaged in any kind of trade or any occupation which involves the acquisition and maintenance of capital, or if he is spending less than his income, or if his earnings are considerable and his expenditure is irregular over long periods, there will be a perpetual question in his mind how much of his property to keep immediately realisable in gold and how much to employ remuneratively. He will not, indeed, in any case keep any large stock of actual coin about him, but he will keep a certain amount of his property as a fluctuating balance at his banker's, and all of this is available at any moment in the form of gold. This balance he will not make larger than necessary, for (neglecting the details of the arrangement with his banker) it will be practically "lying idle." The adjustment, then, of the portion of his income which he keeps available in coin to the rest of his income will be determined on exactly the same principles as all other distributions. A very small balance might be inconvenient, a somewhat larger balance less inconvenient, and the marginal inconvenience of this larger balance might not be sufficient to compensate the advantages of investment. When we come to the bankers we are in face of exactly the same problem. They must be prepared to meet all claims for coin. This they will do by keeping actual coin in their tills and by keeping a balance, that is to say, a claim for gold which will ultimately lie for the most part against the Bank of England. They do not wish this balance to be more than enough to keep them safe, for it is from the revenues derived from the rest of the property which they hold in trust that they derive their own incomes. And the same is true of the Bank of England itself.

But we have still not quite come to the question of the currency. We have been speaking chiefly of gold rather than of sovereigns, and the great reserve in the Bank of England is, as a matter of fact, largely in bullion, not in sovereigns. What determines the amount of gold which is actually coined? The answer to this question is at bottom quite simple. The process of converting bullion into sovereigns or sovereigns into bullion is supposed to cost about 1½d. an ounce either way, and if any competent firm were allowed to undertake the minting of sovereigns, and were to do it at that price, it is clear that the value of an ounce of gold in sovereigns could not remain greater or less than that of an ounce of gold in bullion by more than 1½d. an ounce (which is about 0.16 per cent), for the one could be converted into the other at that price. For the purpose of actual currency the gold must be in the form of sovereigns, for that is the certificate (of the Government in the actual fact, of the issuing firm in the case we are supposing) of the quality and quantity of the gold, and such a certificate would be required by all persons, not experts, as a guarantee that they were really receiving the gold. Now it might be worth any one's while to pay something for this convenience; that is to say, he might be willing to receive a little less gold in a form in which it would be accepted and could be exchanged by any one, rather than a little more in a form in which it could only be accepted by or exchanged with experts. The ordinary man, indeed, desires to have no gold except in this form and incidentally in his bookbinding, jewellery, and so forth. But the goldsmith, the bookbinder, the dentist, and others who put gold into their business in the most literal sense, desire gold both in coin and otherwise, and they will not take a smaller quantity in sovereigns in preference to a larger quantity in bullion unless they derive some corresponding convenience from it. And this they will only find to be the case to a limited extent. Thus, with the goldsmith in particular, the balance which we have seen other men strike between the amount of property which they keep in their business and the amount which they keep at the banker's will resolve itself to a great extent in his case into a distribution between the amount which he keeps in bullion or manufactured articles and the amount he keeps in coin or as a balance with his banker. Now, seeing that it costs the equivalent of 1½d. an ounce to convert bullion into sovereigns, one might naturally expect under the conditions we have supposed that sovereigns would be worth more than bullion at the rate of 1½d. an ounce, for why should any one be at the expense of making them to such an extent as to bring their marginal significance below that point? Whereas until it has reached that point there will be a profit in coining; so it will not rest anywhere above it. But we have seen that there is always a risk of the price of manufactured articles being less than their cost of production, and it is therefore conceivable, in the abstract, that such changes should take place in the demand for sovereigns and the demand for bullion as to reduce the marginal value of sovereigns below the point which alone would have justified their manufacture. But neither could the departure in this sense be more than 1½d. an ounce, for if bullion rose above that point it would become profitable to melt sovereigns. Now the gold contained in sovereigns is at the rate of an ounce to £3:17:10½. It follows, therefore, that the price of gold, if any one were at liberty to mint it, could never, except for a short time and under quite exceptional circumstances, sink below £3:17:9 an ounce, or rise above £3:18s.

Now this state of things, which we should expect if coining were an ordinary industry, corresponds exactly to the actual facts. In explaining this we will confine ourselves to the conditions established by law in England. Every man has a right to take properly assayed and certified gold to the Mint and have it coined into sovereigns gratuitously, at the rate of £3:17:10½ the ounce. Any valuable alloy there may be in it belongs to the Mint, but per contra the Mint makes no charge for the alloy in the sovereigns.

But though the Mint is compelled by law to coin and return the gold handed in to it, yet it is not bound to give it back at once. It is to treat all customers without favour in the order of application; and since there are always orders on hand from the Bank of England that it would take months to execute, any one who should apply to have his gold coined would be likely to have to wait, say, six months for his turn. If you reckon interest at four per cent the delay would be equivalent to a payment at the rate of about 1s. 7d. an ounce for mintage. The consequence is that no one ever does take his gold to the Mint. There is, however, another legal provision by which the Bank of England is bound to buy all the gold that is offered to it at the rate of £3:17:9 per ounce. This is only 1½d. on the ounce, or a little above a third of a penny on £1. Any one, therefore, who wishes to have his gold coined can legally command better terms from the Bank of England than he can from the Royal Mint. The Bank of England is not bound to pay in sovereigns; it may pay in its own notes. But the cash department of the Bank of England is compelled to give gold for the notes of the issue department, on demand, and consequently any one who likes may take his gold to the issue department and receive notes for it at the rate of £3:17:9 per ounce, and may then go round the corner to the other department and receive the gold. If he does this it will not hurt the Bank of England, for the Bank of England does not pay for having its gold minted; nor will it be embarrassed by an excess of gold in its cellars, for the gold will be drawn out in sovereigns as rapidly as it is put into the cellars in bullion, and the Bank may have its gold coined as fast as it pleases by the Mint. The Bank of England, therefore, will be the gainer by 1½d. for every ounce of gold that is thus given it. The country, indeed, will be the loser by the expense of coining, for which it, not the Bank of England, pays. Whether by a coincidence or not, it happens that this 1½d. that the Bank of England may take off the value of the gold in the sovereigns it returns, coincides with the best estimates of the cost of minting, so that while the country loses and the Bank of England gains 1½d. on every ounce of gold that is minted, the net result to the man who sells the gold is exactly the same as if he had paid for the minting. There is, therefore, exactly the same check on reckless turning of gold into sovereigns that there would have been under the conditions we imagined of a country in which any firm might mint gold into coin, the cost of doing so being 1½d. an ounce.

As a rule, however, the persons selling gold to the Bank of England will not at once cash the notes. Bank-notes are legal tender, and it will be convenient to the man who has disposed of a large amount of gold (if he does not wish to open a credit with the Bank of England53 ) to take away the legal tender that he desires in the form of bank-notes rather than in the actual sovereigns. The Bank is compelled to hold actual gold against every one of its notes that is in circulation beyond the eleven millions guaranteed by the nation. Consequently, the Bank will hold the gold that is brought in, against the notes that it issues, and if the country already has as many notes in circulation as suits the convenience of the public a large fresh issue will determine, not immediately but in a short time, the presentation of a corresponding number of notes at the cash department, in which case the effect will be the same as if the sovereigns had been taken out directly. If the number of notes issued is not such as materially to swell the body of notes in circulation, no perceptible effect will take place, but in any case the Bank cannot be inconvenienced. It gains its 1½d. an ounce and loses nothing.

Our investigations so far would lead us to expect that the market price of gold bullion in the open market would be £3:17:9, and this may in truth be regarded as the normal state of things, but there are occasions on which the price rises not only to the metallic par of £3:17:10½, but even to £3:18s. We saw but now54 that such a state of things is not inconceivable, but the examination of the conditions under which it may arise will lead us to the most difficult part of our subject.

We have seen that the Bank of England holds a great part of the gold reserve of the world, and occasions arise on which the bankers of some one or more countries may wish to withdraw a large amount of the gold which stands to their credit. There may be danger that when called upon thus actually to pay an abnormal proportion of the claims for gold which some of its clients are in a position to make, the Bank may feel that the remaining reserve threatens to be reduced to an alarmingly low proportion of the total claim which it is still nominally liable to have to meet. It must, therefore, "protect its reserves," that is to say, prevent their being further depleted. Now what is really wanted is some means of inducing people not to draw gold, but to settle their affairs by transfers of credit; and a very small charge on actually cashing cheques in gold instead of paying them in to the accounts of the drawers, or on withdrawing gold from an account instead of transferring the credit, would suffice to accomplish this. But it is impossible to make such a charge. The value of a cheque or of a bank credit is due to the fact that though you are not likely to cash it you always can. And to place any obstacle in the way of cashing it would amount to a qualified "stoppage of payment," and it is of the essence of the security and credit of the Bank that it should be prepared at any moment and to any extent to meet its nominal obligations to pay gold. The difficulty, then, has to be met by circuitous and wasteful processes. In the first place the Bank of England does a great business in discounting bills. We have hitherto55 spoken of bills as though they were claims for the instant payment of money at such and such a place, and so they may be; but many of them are claims for money, not now, but six months hence; and a merchant who holds such a bill, that is to say, who has supplied goods to a customer, whether at home or abroad, for money that will not be due for three or six months, may want to have the money either in cash or, more probably, in credit with his banker, at once. If the Bank accepts his bill, that is to say, the promise of his correspondent for money three or six months hence, and gives him present cash or credit in exchange for it, it will, of course, make a charge corresponding to the interest on the money which it lends, so that when the bill becomes due it will not only repay the loan but pay interest on it also. This charge is discount. Now the Bank of England cannot prevent its clients who actually have credit from withdrawing as much gold as they choose, but it can discourage the formation of credits by raising the terms on which it discounts bills. It can, therefore, to a great extent regulate the proportion between its reserves and its liabilities by refusing to enter into fresh liabilities and so contracting its business. It thus limits the potential calls for gold, and thereby restricts the actual calls which stand in a definite relation to them. This is a wasteful and indirect process, and it affects the terms on which loans are made all over the country, often to the extreme embarrassment of business; but no more direct or economical device has yet been hit upon.

But the Bank has another means of protecting its reserves,—the very curious one of bidding for gold in the open market and offering more sovereigns for it than would make its own weight if melted. This may seem at first sight a strange way of increasing its reserves, for it is offering more than an ounce of gold in payment for an ounce; but the Bank will pay for the gold either in bank-notes or in acknowledgments, that is to say, in credit, and it calculates that the credit of the importer of gold will not actually be drawn out in sovereigns to any greater extent than the credit of its other clients will, and, therefore, by buying gold for notes or credit it will increase its reserves in larger proportion than its business. Thus, by buying gold and at the same time raising discount it protects its reserves from depletion, partly by contracting its general business and so reducing the claims on its reserve, and partly by increasing its dealings with a particular set of clients who will actually bring gold into its cellars, to the full amount of their accounts, and will only draw the ordinary proportion of them out again in gold. These are the conditions under which the value of bullion in the market per ounce rises above the value of sovereigns per ounce. But except for a very short time and in very exceptional circumstances this excess cannot exceed 1½d. an ounce, for if the Bank of England bought gold at a higher rate than this its clients would proceed to draw out sovereigns simply for the purpose of melting them down, and bringing them back again to sell at a profit as bullion.

But we have not even yet answered the question what determines the amount of gold that is actually minted into sovereigns. The whole reserve of the Bank of England need not be, and is not, coin; and the means the Bank takes to protect its reserves has no immediate connection with the amount of gold that is minted. What then determines this amount? The answer is simple. The private individual, who deals in gold little and indirectly except as coin, places an amount of his property determined by considerations already explained56 with his banker. It is registered in terms not of bullion but of sovereigns, and he can draw out absolutely as much of it as he chooses in the form of sovereigns. Provided he has a balance at the banker's, or a claim on any one else's balance, it costs him absolutely nothing to get it in the form of coin. Hence the celebrated declaration of a Member of Parliament: "We all of us have as much money as we want." So the depositors in the banks can, and do, take out as many sovereigns as it suits their convenience to have, and the Bank of England has to see to it that enough sovereigns are minted to meet the demands. The answer to the question, "What determines the number of sovereigns coined?" is therefore, "the estimate formed by the Bank of England of the number of sovereigns that the depositors in the banks collectively want to have." As it costs the Bank of England nothing to have the sovereigns coined, and as it always has plenty of gold, there is no reason why any one should be stinted. The country, therefore, bears the expense of providing all the depositors with as much coin as they call for.

But the importers of gold are in a different position. They cannot generally exchange their gold for sovereigns at weight par. They may have to pay .16 per cent premium. Thus there is generally a check, not indeed to the minting of gold, but to the flow of gold into the cellars of the Bank of England, where it lies ready to be coined. But the Bank may reduce or remove this check or substitute a stimulus for it within certain limits, whenever it conduces to its credit to do so. On the other hand, there should be a normal check to the flow of gold out of the currency into the form of bullion again, and so to a certain extent there is. If it were not for a certain abuse, to be explained presently, all persons who required gold for their business would have a slight advantage in buying it direct from the importers rather than drawing it out of the currency. For it would seem that if the market price of gold is £3:17:9 an ounce, a man would be able to get more gold by .16 per cent in return for his cheque if he paid it to an importer than he would get from his banker by drawing out the sovereigns and melting them. And there would be the additional expense of the melting. If we put that at 1½d. he would lose .32 per cent by drawing his gold out of the currency instead of out of the market. And if the market price rose for any reason, though this advantage would be diminished, it would still always be on the side of buying gold in the market. It is true that most persons whose business requires them to deal in gold will tell you that they are not conscious of being influenced by this consideration, and that whether they buy gold from a merchant or take it out of the currency is determined by considerations of convenience quite independent of this premium, even supposing that the market price of gold perceptibly affects transactions of the scale on which they conduct them. But in the nature of things this cannot be universally true. A market price is after all a market price, and means that gold or sovereigns are actually at a commercial premium, that is to say, that a preference for one or the other is actually felt by some one, presumably by the large dealers in bullion.

But this difference between the market price of gold and the gold weight of the sovereigns in which that price is paid, is crossed in the case of the working jewellers by a practice which we must now examine. Those of them who deal with branches of the Bank of England are in the habit of requesting their bankers to select the heaviest sovereigns and put them aside to meet the cheques that they draw in their own favour, for purposes of melting.57 Now the standard weight of a sovereign in England is 123.27447 grains. But a "remedy" is allowed to the mint-master; that is to say, an allowance for the imperfection of workmanship; so that if a sovereign does not weigh more than 123.474 or less than 123.074 it may be issued by the Mint; and it is legal tender, and may be issued by the Bank of England against its own notes and cheques, until it has sunk by abrasion to 122.50047. Between the heaviest and the lightest sovereigns paid out by the Bank of England and its branches there may therefore be a difference of .97353 grains, which is about .79 per cent. But presumably the Mint keeps very well within the allowed "remedy," and we may suppose that there are few sovereigns in the currency much above the standard weight, whereas the sovereigns issued against a cheque in the ordinary way would, on an average, be far above the lower limit. We shall therefore perhaps not be far wrong if we say that the average weight of the selected sovereigns exceeds the average weight of the unselected sovereigns by something less than .387 gr. or .315 per cent, which would be very close to the full amount of 3d. on the ounce, which marks the maximum theoretical advantage on buying in the market as against melting the currency. The subject is one as to which it would be a matter of some delicacy to make close inquiry, and I do not profess to have any accurate information. The practice, as far as it goes, is obviously an abuse, and together with the fact that the Mint (and therefore indirectly the Bank of England) throws in the excess of the alloy in the sovereigns which it issues above that in the gold it receives, it establishes a permanent leakage in the currency for which there is no theoretical necessity, and which constitutes a loss to the nation.58 The activity of the Mint must be sufficient to keep the public stocked with all the sovereigns it wants in spite of this leakage; and the Bank of England must maintain its reserves against it.

We have concluded our positive examination of the selected points of financial science; but one theory must still be examined, for it seems to be not only unsound in itself but a fruitful source of confusion throughout the whole range of monetary science.

A treatise on currency frequently expounds what is known as the "quantity law," as regulating the value of the currency. The supposed law may be stated as follows: "The exchange medium of every country (coined gold in the case of England) has to carry on the business of the country, and this business consists in the whole volume of exchanges conducted day by day or year by year. Seeing then that the whole body of the currency, consisting of so many pieces, has to conduct the volume of exchange, each passage of a coin from hand to hand will have to conduct a certain fraction of it, and this fraction will be determined by a division sum; the dividend being the volume of exchanges, and the divisor being the number of coins employed multiplied by the average number of times that each coin changes hands during the period over which the volume of business has been taken." Hence the name "quantity" law, from the supposed determination of the value of each unit of the currency in inverse ratio to the quantity of the currency as a whole.

The unsatisfactory character of the statement must be obvious at once, and it is noteworthy that there is (unless it has escaped me) no mention of any such law, nor any implication direct or indirect of its existence, to be found from end to end of the numerous works on currency and finance of the late Professor Jevons. To begin with we may eliminate all mention of the number of coins and the "average" number of times that each changes hands. For this "average" can only be arrived at by adding together the number of times which each coin has circulated and then dividing by the number of coins. When we multiply a (number of coins) by b (number of times each circulates on an average) to obtain c (total number of transactions) we have really already assumed c and obtained b by dividing c by a. We start with c then, and as it is c we want we may dispense with the process of first dividing by b to get a and then multiplying by b again to get back to c.

The simplified statement of the quantity law would then be: "A certain total volume of trade has to be conducted by a given number of changes of a sovereign from hand to hand. Therefore each one of those changes has to conduct a given volume of exchange, arrived at by division. And as it 'has' to do this, it will do it. The amount of work we set it to do determines the amount of work it does. That is to say, the value in exchange of a sovereign is determined by the work it 'has' to do every time it shifts."

Prima facie this is an inversion. How can we make a sovereign do a certain amount of work by telling it it must? The total business that the sovereigns collectively do is the sum of what each of them does whenever it changes hands. The business the sovereigns do, one would say, depends on their efficiency severally. How can their efficiency severally depend on the work they have to do amongst them? Obviously no one would suggest that the services rendered to the community by a pound of potatoes or a ton of iron could be arrived at by determining in the first place the total services that potatoes or iron have to render annually to the community, and then dividing it by the number of pounds or tons in existence; or determining the amount of earth that a navvy shifts by every swing of his spade by stating how much earth the whole body of navvies has to shift, and then reckoning up their number and the average number of spade-swings which each of them performs, and dividing the total work they have to do by the figure so obtained. It is obvious, then, that if any such law holds in the case of the currency, it must be owing to some special characteristic which completely differentiates it from every other article. And this is exactly what is asserted by the exponents of the law in question. Their contention is that currency is a purely legal institution. A government, it is supposed, can make anything currency by declaring that it shall constitute the legal discharge of obligations; and as a proof of this we are referred to the numerous instances in history in which paper currency has been maintained for indefinite periods. In these cases a piece of paper which has an inscription, corresponding to a certain weight of gold, passes as the equivalent of so much gold and is actually received as such an equivalent by persons who deal in gold as a commodity, although it carries no right to demand gold from anybody. A Bank of England note, of course, can be cashed at the Bank of England, that is to say, any one who likes is legally entitled to receive five sovereigns of full weight at the Bank of England in exchange for the note. But in countries where there is no such obligation on the part of any private or public body, nevertheless the dealers in gold are willing to part with it in exchange for paper, and all other persons are willing to receive the paper just as if it were gold. And it is further noted that the value of the notes will not sink below the par of gold unless there has been an over-issue. Thus it seems that the government, by itself giving its servants pieces of paper with the name of an amount of gold upon them, declaring that all its obligations are thus discharged, and that it will regard all other obligations amongst its subjects as discharged in like manner, can actually give a value to the paper that depends on the amount it issues. In other words, by enacting that its paper shall be received in payment of all debts and obligations it can cause all the business transactions of the country to be conducted by its means, and having thus determined the total amount of work that the paper shall do, it can further decree how much paper there shall be to do it; and since the habits of the industrial community determine how much of its business shall be done by the currency, and how much by cheques, paying of balances, and so on, the rate at which the paper will circulate, that is to say, the number of times, on an average, that each piece will change hands in the course, say, of a year regulates itself; and so the amount of the issue will determine the amount of business which each paper unit will conduct each time it changes hands.

These facts being supposed to be established, it would follow that if the business of a country is actually conducted in gold, that is to say, in an article which has an independent industrial value, apart from the enactment which makes it legal tender, this is an unessential incident. Because, as we have seen, all the functions of money can, by hypothesis, be conducted by a unit that has no primary industrial value. If (it is maintained) the currency of any country, England for example, consists of pieces of metal that happen to have a value in the arts and sciences, then there are two independent uses to which a piece of gold can be put, one of them being the natural and direct service which gold, as gold, can render in the arts and sciences; and the other being a fictitious or legally established value, which the legislature has chosen to affix to gold, but might just as well have attached to paper, leather, or anything else, provided it could so stamp its units of currency as to prevent their unauthorised issue by others than itself. Thus, according to this theory, a sovereign as a weight of gold, and a sovereign as a unit of legal tender, are indeed physically identical, but the values that the coin has in its capacity of a legal discharge of debt and in its capacity of a weight of gold have no direct or immediate connection with each other whatever.

But a government which chooses a valuable for its currency saves itself, it is admitted, from the temptation of over-issue; for if it over-issued, then its sovereigns, qua currency, would have less value than they would have qua gold, and whoever got hold of them would melt them until their contracting number threw more work upon each individual sovereign, and therefore raised its value in the currency; whilst the increased supply in the arts would lower the significance of gold in them. On the other hand, there can be no possibility of the value in the currency being permanently higher than the value in the arts if (as in England) there is a free mint. For any one who has gold can have it coined at will, and therefore if the amount of work thrown on each sovereign were such as to raise its value in the currency above what it bore in the arts, gold would be coined till the increasing number of sovereigns lightened the amount of work that each had to do, that is to say, reduced its value, whereas the deflection of gold from the arts and sciences would raise its value in them, and equilibrium would be restored. Thus, it is maintained, the two capital functions of gold (one primary and specific, the other wholly legal and independent of the natural properties and uses of the substance gold) will keep in balance with each other.

This theory of currency is fascinating by its ingenuity and neatness, and derives enormous practical support from its harmonising with the psychology of the ordinary man, in whose mind there is no practical connection between the value of gold as currency and its value in the arts. No man is conscious of being willing to work or to surrender his goods for a piece of gold, because gold is valuable for dentistry, for gilding picture frames or book leaves, for setting jewellery, or for making plate. His value of it for currency is something which, if he thinks about it at all, he regards as resting on custom or law. This theory then has the enormous polemic advantage of allying itself directly to the ordinary way of thinking, and as it is easy to expound and has a certain elegance, it is equally popular with teachers. But nevertheless the reasoning on which it rests is throughout topsy-turvy. From first to last it goes on the assumption that sovereigns, collectively and individually, will do what they have to do, and that the legislature can determine what that is; and throughout our exposition of the doctrine it has been obvious that we have been compelled to treat the value of a sovereign not as constituted by anything that it can and will do, but by something which in obedience to law it has to do. Now, that the law can enable any assemblage of things to perform a certain service, or conduct certain operations, collectively, simply by saying that it has got to do so, is so startling a proposition as to demand the closest inspection. If we maintained, for instance, that the government could by decree determine that all the agricultural operations of this country should be carried on by persons and with instruments authorised by itself, and if it were assumed that this would not affect the extent or nature of the operations, but that they would all be necessarily conducted by the authorised men and implements, and therefore if there were few men and implements each would do a great deal of work, whereas if the government issued more each individual would do less, but precisely the same amount would be done altogether, we should at once see the impossibility of supposing that the amount done by each unit was determined by dividing the sum of what they all do by the number of units; because as a matter of fact the amount that each of them does is the primary datum, and what they all do together is arrived at by addition or multiplication. If the government had any power of making each individual do more or less it could make a larger or smaller number of them capable of doing a given amount of work, but it cannot decree how much they shall do collectively, independently of their numbers, and then determine what each of them does by regulating those numbers.

What, then, are the supposed peculiarities of the work of the currency which have given rise to the belief that these exceptional possibilities exist in this case, though not in others? In the first place, the undoubted fact is pointed out that the amount of transference of goods or services which can be effected under the denomination of a sovereign depends solely upon the value of that sovereign. That is to say, if a quarter of wheat and a ton of hay are each worth the gold in one and a half sovereigns, they can be exchanged under the denomination of one and a half sovereigns. If, on the other hand, they are each worth the gold in a sovereign, they can be exchanged under the denomination of a sovereign. Thus the same amount of business, namely the exchanging a ton of hay for a quarter of wheat, might be conducted with the intervention of one sovereign, of one and a half sovereigns, or of two sovereigns, equally well. And therefore, if, for any reason, the stock of gold were so reduced that the gold in a sovereign should double its value, then the sovereign would be able to conduct twice as much business as it did before. The services that the currency renders to the community at large, therefore, seem to be independent of the number of sovereigns that are in the currency. And it is undoubtedly true that, within wide limits, the money function could be performed equally well, in any community, by a larger or smaller number of sovereigns. This then, we are told, constitutes a fundamental difference between the money function and the functions of other things, for a large or a small number of potatoes will not equally well perform the nutritive functions of potatoes, nor will a large or small number of men or tools be able to perform the same industrial functions equally well. The derivative nature of the exchange function of gold, therefore, seems to differentiate it from the primary functions of other commodities. But, as we have seen, this derivative value is not peculiar to the currency. To any man who is dealing in anything it is a matter of indifference, within wide limits, whether he receives a large or a small quantity of it for any given consideration, provided the small amount in one case is as valuable as the large amount in the other. If, for instance, a certain class of books is worth 5s. a volume in the second-hand trade, and a bookseller has a considerable trade in them, making on an average 10 per cent per annum on his turnover, and if presently this class of books, through a change in the taste of the public, becomes twice as valuable, and the bookseller with the same general apparatus and machinery, and with the same effort of attention and so forth, deals in half the number of books, his purposes will be just as well served, so long as he makes the same profit on his turnover. For neither his expenses nor his income depend on the value that he attaches to the books for his own use. They depend on the value that some one else attaches to them, so that this derivative function which they perform for him can be performed equally well by a smaller number that are highly valued and by a larger number that are valued low. But to the student purchaser of books it is by no means the same thing whether he has a thousand volumes for which he has given, on an average, 5s. each, or five hundred of the same volumes for which he has given, on an average, 10s. each. The five hundred at 10s. each do not facilitate his studies or serve his other purposes any better than if he had only given 5s. each for them. And he is without half the library he would have had on the other supposition. The distinction, then, that we are at present examining is not one between currency and all other commodities, but between primary and derivative values, between the value attached to an article by the user and the value attached to it by the dealer. And in all cases, whether of primary or derivative value, the total service consists in the sum of the individual services. We can in no case get at the individual services by saying that each individual has got to perform, and therefore will perform, its due fraction of the total, fixed as a total by some external power. Surely we should expect that if the government really has the power of making the currency do certain work, it must be by giving to a definite quantity of gold the power to do a definite piece of work, not by enabling an indefinite sum of gold, whether great or small, to do a definite amount of work by its fiat that it shall do it. If, as we have seen, a little gold can under certain circumstances do as much as a great deal under other circumstances, it must be because under those circumstances each unit of gold is made capable of doing a larger amount of work; not because it is told that there is more work for it to do. This is obvious enough in an ordinary way, and the example of the books will again serve our purpose. If the primary services of the books (to the readers) have mounted on the collective scale then their derivative services (to the dealer) mount too, and each book will convert a larger amount of his energy and thought into a correspondingly larger amount of the things he desires. Just so if the primary services of gold mount, either because of a falling off in the rate of production, or because of increased applications of gold to the satisfaction of tastes and wants, or for any other reason, each unit of gold will be able to conduct a larger amount of business.

These considerations suggest that we should begin our inquiry as to the connection between the amount of gold in the currency and the value of each sovereign at the other end from that by which it is usually approached. Granted that, in a general way, the total amount of work that the currency has to do is fixed by the general business habits of the community (though, as we shall see presently, this is a large assumption), it will follow that if the marginal value of an ounce of gold, in the arts, is high, then a small amount of gold will be enough to conduct that part of each man's transactions for which he employs the currency, and he will become a "dealer in gold" only in small volume. That is to say, the withdrawal of a small volume of gold from its primary applications will suffice to conduct the business of the country because each piece of gold, having a high value, will be able to transact a large amount of business. If, on the other hand, a large output of gold during a series of years, or any cause affecting the use of gold in the arts, should bring down the marginal significance of an ounce of gold in the arts, then each man will find that as a "dealer in gold" he needs a larger volume of gold to do his business for him, and a larger volume will be held out of its primary applications. Thus it is not the amount of gold in the currency that determines how much work each piece shall do, but the amount of work that each piece can do that determines the amount in the currency.

If we now turn to paper currencies, again, we shall remodel the statement thus: It is not true that a government can confer on pieces of paper, or other intrinsically worthless articles, the collective power of doing the business of the country, but it can within certain limits confer a defined power of doing business on certain pieces of printed paper. For the government, as general guardian of contracts and of property, has the power to enforce or to decline to enforce any contracts, and as guardian of the rights of property it can determine whose property anything shall be. It is possible, then, for a Government at any time to say: "There are in this country a number of persons under legal obligation to pay fixed rents for premises, fixed interest on capital, fixed salaries for services, over such periods as their several contracts cover. There are also a number of persons under definite obligations to pay such and such gold, at such and such dates, once for all. Now we, the Government, can, if we like, issue stamped papers bearing various face denominations of one, ten, a hundred, etc., units of gold currency, and we can decree that any one who possesses himself of such papers, to the face value of his debts, and hands them over to his creditor shall be held to have discharged his debt, and we will henceforth defend his property against his late creditor and declare that he has, in the eye of the law, paid the sum of gold which he owed." It is obvious that these pieces of paper will thereby acquire definite values to all persons who are under obligation to discharge debts or to pay salaries or rents or other sums due under contract; for to command one of these pieces of paper will be, for certain of their purposes, exactly equivalent to commanding a sovereign. As these persons constitute a large and easily accessible portion of the community, there will at first be no difficulty whatever in circulating the notes, for those who have no direct use for them themselves will know that there are plenty of people who have, and a certain number of these certificates can, in this way, be floated. Each will be able to transact business to the same extent as a piece of gold of its face value. But as the contracts gradually expire and the debts are gradually discharged, the original force that gave currency to the Government's paper will become exhausted. At first the holder of such a bond will from time to time come across men who will say: "Oh, yes, I was just looking out for paper in order to discharge my debt or pay my rent"; and if there were the smallest tendency to depreciation, competition would instantly rise amongst these persons who would be glad to get, at any reduction whatever, these things which their creditors would be compelled to receive at full value. If people chose to go on making fresh contracts and giving fresh credit, without specifying that the payment should be in gold, and thus went on perpetually bringing themselves under legal obligation to receive paper in full payment, the process might go on for a certain time, by its own impetus, but there would be nothing to compel any one to enter into such a contract; and if at any time, for any reason, there were a slight preference for making contracts in gold, so that there was a dearth of people of whom it could be definitely asserted that for their own immediate purposes, independent of the general understanding, the paper was worth the gold, there would obviously be no firm basis for the structure, and every one would become nervous and would want to make some allowance for the risk of not finding any one who would take the paper at or near the face value.

The Government has, however, a further resource. It has the means of maintaining a perpetual recurrence of persons thus desiring money at its face value, for the Government itself has more or less defined powers of taking the possessions of its subjects for public purposes, that is to say, enforcing them to contribute thereto by paying taxes. Ultimately it requires food, clothing, shelter, and a certain amount of amusement and indulgence for its soldiers and all its officials; and it requires fire-arms, ammunition, and the like. And in proportion to its advance in civilization it may have other and humaner purposes to fulfil. Now, as long as gold has any application in the arts and sciences it exchanges at a certain rate with other commodities, just as oxen exchange at a certain rate against potatoes, pig-iron, or the privilege of listening, in a certain kind of seat, to a prima donna at a concert. The Government, then, levying taxes upon the community, may say: "I shall take from you, in proportion to your resources, as a tribute to public expenses, the value of so much gold. You may pay it to me in actual metallic gold or you may pay it to me in anything which I choose to accept in lieu of the gold. If you do not give it me I shall take it from you, in gold or any other such articles as I can find, and which would serve my purpose, to the value of the gold. But if you can give me a piece of paper, of my own issue, to the face value of the gold that I am entitled to claim of you, I will accept that in payment." Now, as these demands of the Government are recurrent, there will always be a set of persons to whom the Government paper stamped with a unit weight of gold is actually equivalent to that weight of gold itself, because it will secure immunity from requisitions to the exact extent to which the gold would secure it. This gives to the piece of paper an actual power of doing the work that gold to its face value could do, in the way of effecting exchanges; and therefore the Government will find that the persons of whom it has made purchases, or whom it has to pay for their services, will not only be obliged to accept the paper in lieu of payments already due, and which it chooses to say that these papers discharge, but will also be willing to enter into fresh bargains with it, to supply services or to surrender things for the paper, exactly as if it were gold; as long as it is easy to find persons who, being themselves under obligation to the Government, actually find the Government promise to relinquish their claim for gold as valuable as the gold itself. The persons who pay taxes constitute a very large portion of the community and the taxes they have to pay form a very appreciable fraction of their total expenditure, and consequently a very large number of easily accessible persons actually value the paper as much as the gold up to a certain determined point, the point, to wit, of their obligations to the Government. Thus it is that a limited demand for paper, at its face value in gold, constitutes a permanent market, and furnishes a basis on which a certain amount of other transactions will be entered into. The Government, in fact, is in a position very analogous to that of an issuing bank. An issuing bank promises to pay gold to any one who presents its notes, and to a certain extent that promise performs the functions of the gold itself, and a certain volume of notes can be floated as long as the credit of the bank is good. Because bank promises to pay are found to be convenient, as a means of conducting exchanges. After this number has been floated the notes begin to be presented at the bank, and presently it has to redeem its promises as quickly as it issues them. The limit then has been reached and the operation cannot be repeated. After this people will decline to accept the promises of the bank in lieu of the money, or, which is the same thing, they will instantly present the promise and require its fulfillment. The amount of notes in circulation may be maintained, but it cannot be increased. The issuing Government does not, without qualification, say that it will pay gold to any one who presents the note, but, in accepting its own notes instead of gold, it says, in effect, that it will give gold for its own notes to any of its own debtors; and as long as there is a sufficient body of these debtors to vivify the circulating fluid the Government can get its promises accepted at par. Any Government which, even for a short time, insists on paying in paper and receiving in gold, that is to say, any Government that does not honour its own issue when presented by its debtors, will find that its subjects decline to enter into voluntary contracts with it except on the gold basis; and if its paper still retains any value whatever, it will only be because of an expectation of a different state of things hereafter that gives a certain speculative value to the promise. In fact a Government which refuses to take its own money at par has no vivifying sources to rely on except the very disreputable and rapidly exhausted one of proclaiming to debtors, and persons under contract to pay periodic sums, that they need not do so if they hold a certificate of immunity from the Government. Such immunity will be purchased at a price determined, like all other market prices, by the stock available (qualified by the anticipations of the stock likely to be available presently) and the nature of the services it can render. The power, then, of Governments to make their issues do exchange work depends on their power to make a note of a certain face value do a definite amount of exchange work; and this they can effect by giving it a definite primary value to certain persons, and then keeping the issue within the corresponding limits. It does not consist in an anomalous, and, in fact, inconceivable, power of enabling an indefinite issue to perform a definite work, and arriving at the value of each individual unit by a division sum.

Indeed, this division sum is impossible in any case to make; for the proposed divisor is arrived at by multiplying the number of units in the face value of the issue by the rate at which, on an average, they circulate. Now the Government can undoubtedly regulate the amount of the issue, but it cannot regulate the average rate at which the units will circulate. Nor indeed can it rely on the dividend, namely the amount of business which the circulating medium shall perform, remaining constant. For it is a matter of convenience how much of the business of a country shall be carried on by the aid of a circulating medium and how much without it; and as a matter of fact, at periods when there is a dearth of small change in a country a great amount of retail business is conducted on account, and balances are more often settled in kind. Thus business which would ordinarily have been carried on by the circulating medium is carried on without it, because of its rarity. In Italy, for instance, when coppers were rare the exchange value of a copper did not rise because a smaller number had to do a greater amount of work, but each unit did as much business as it could, and the rest of the business was done without them. Again, the history of paper money abounds in instances of sudden changes, within the country itself, in the value of paper money, caused by reports unfavourable to the Government's credit. The value of the currency was lowered in these cases by a doubt as to whether the Government would be permanently stable and would be in a position to honour its drafts, that is to say, whether, this day three months, the persons who have the power to take my goods for public purposes will accept a draft of the present Government in lieu of payment. It is not easy to see how, on the theory of the quantity law, such a report could affect very rapidly the magnitudes on which the value of a note is supposed to depend, viz. the quantity of business to be transacted and the amount of the currency. Nor is it easy to see why we should suppose that the frequency with which the notes pass from hand to hand is independently fixed. On the other hand, the quantity of business done by the notes, as distinct from the quantity of business done altogether, and the rapidity of the circulation of the notes may obviously be affected by sinister rumours. Two of the quantities, then, supposed to determine the value of the unit of circulation are themselves liable to be determined by it.

[1.]Compare the qualifications to the Principle of Superposition on page 204.

[2.]Pages 34 sq.

[3.]Cf. pages 66 sqq.

[4.]For a worked-out example see my Alphabet of Economic Science (London, 1888), pages 128 sqq.

[5.]Page 54.

[6.]For the full justification of this statement, see below, pages 440 sqq., especially pages 446 sqq.

[7.]Cf. page 101.

[8.]See Chap. II. of this book, and cf. Chap. III.

[9.]See page 85.

[10.]"Origin" is the technical term for the point marked O in all our figures.

[11.]See pages 21, 82, etc.

[12.]Cf. page 441, and the whole of Chap. II.

[13.]Chapters II. and III., though important from the theoretical point of view, are of an abstract and somewhat academic character, and some readers may prefer to go on at once to Chapter IV.

[14.]See page 60.

[15.]This analytical proof is, strictly speaking, unnecessary; for since we have ah = aeok and ks = kogd, we have also aegd = ah + ks = ac; and this involves the equality of bef and fgc. But the proof by substitutions may probably be found the more enlightening.

[16.]At the bottom of page 451.

[17.]Cf. page 426.

[18.]But see below, pages 467 sqq.

[19.]Cf. pages 45-47.

[20.]Cf. page 435.

[21.]Cf. pages 552 and 568 sqq.

[22.]But compare the following chapter.

[23.]Cf. Appendix to Chapters II. and III. pages 490-492.

[24.]See page 477.

[25.]See pages 15 sqq. and 423 sqq.

[26.]Cf. further pages 521 sq.

[27.]Cf. page 483.

[28.]Cf. pages 485 sq.

[29.]Cf. pages 218 sqq.

[30.]Pages 229 sqq.

[31.]Page 498.

[32.]Pages 233 sqq.

[33.]Macmillan, 1900.

[34.]Pages 219 sqq.

[35.]I have preserved the convention by which the "demand" curve is made to run down and the "supply" curve to run up, from left to right. Of course it has no significance and might just as well be neglected or reversed.

[36.]Pages 336 sq.

[37.]Pages 229 sqq.

[38.]Pages 414 sqq.

[39.]It is necessary, however, to note that in thus reversing our original l curve we have assumed a stability in our psychic unit on the axis of Y that was not granted in our first construction of the figure. The ordinates of the p and l curves for any abscissa were determined with reference to each other, at that point, and consequently our ordinate of 7 for the l curve, when the abscissa is 13, means that irksomeness of effort (or desire for its cessation) at that point is seven times as great as the advantage accruing from labour at that point. It does not follow that it is just equal to the advantage accruing at the abscissa 7, unless we can be sure that the psychic value of the unit remains stable for p throughout its course; and we have seen (pages 469 sqq.) the extreme difficulty of securing even a fair approximation to such stability in far simpler cases than this. If we retain the form of the p curve, and reversing the l curve relate each ordinate to the now corresponding ordinate of p, we may get a different form of the curve, representing the same relations and the same psychic values. But the point at which the two ordinates are equal to each other must obviously be the same.

[40.]Pages 533 sq., 539 sq.

[41.]Pages 361 sqq.

[42.]Cf. below, page 540.

[43.]Page 504.

[44.]Page 538.

[45.]Page 537.

[46.]Pages 345 sqq.

[47.]It is of course admitted and understood that such minuteness of estimate takes us absolutely away from all contact with practical business or practical possibilities. It is adopted merely for graphic purposes and to illustrate the principles involved in the current expositions.

[48.]Co-ordination of the Laws of Distribution, London, 1894.

[49.]As a matter of fact the assumed data throughout conform to the formula, crop = 2.248x2e-(7/180)x, in which x stands for the number of "hours" put in per annum per 40 land-units. The corresponding formulæ for the pair of curves on Fig. 41(a), page 566, will naturally be 2.248xe-(7/180)x for the curve containing the rectangle, and 2.248[2 - (7/180)x]xe-(7/180)x for the curve the integral of which equals the rectangle.

[50.]Pages 127-141.

[51.]Notes that are at a discount, and will not discharge gold debts to their face value, in their own country, will of course be at a discount elsewhere too, independently of the balance of indebtedness.

[52.]As I believe that the line of investigation here pursued is somewhat novel, and as I have no technical knowledge of minting or of the gold market, the whole of this section should be regarded as a tentative suggestion rather than a dogmatic exposition. My reason for giving it at all is that I believe the usual treatment of the subject to be theoretically unsound (cf. pages 610 sqq.), and therefore it seemed desirable to attempt a fresh analysis.

[53.]See below, page 606 sq.

[54.]Page 603.

[55.]Pages 590 sqq.

[56.]Pages 600 sq.

[57.]The prevalent idea that private melting is illegal is without foundation. It is illegal to deface or intentionally abrade (sweat) sovereigns. Any one may melt them.

[58.]This is only a particular case of the general phenomenon which is defined under "Gresham's law" as the tendency of bad money to drive out good. This is not really a special law affecting the currency. It is merely a special application of the general principle that if S1 and S2 are units of two specified commodities (in this case heavy and light sovereigns) which are equally capable of serving the purposes of A (who cannot indeed distinguish between them), whereas S1 will serve certain purposes of B (who can distinguish between them) better than S2 will, there will be a tendency, as they pass in exchange, for B to "secrete" the S1's for his own special purposes and pass on the S2's to A. Or in more general terms, if S1 will serve some purposes as well as S2 and other purposes better, there will be a tendency to assign S1 to those purposes which it can serve better than S2 rather than to those it can only serve as well. A light sovereign (within the limits of legal tender weight) will serve the purposes of the ordinary citizen as well as a heavy one, but the latter will serve the technical purposes of the jewellers best.

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