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William Stanley Jevons, The Theory of Political Economy [1871]Edition used:The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
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PREFACE TO THE FIRST EDITION
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| Popular Expression of Meaning. | Scientific Expression. | Dimensions. |
|---|---|---|
| (1) Value in use | Total Utility | MU. |
| (2) Esteem, or Urgency of Desire for more | Final Degree of Utility | U. |
| (3) Purchasing Power | Ratio of Exchange | M0. |
Definition of Market.
Before proceeding to the Theory of Exchange, it will be desirable to place beyond doubt the meanings of two other terms which I shall frequently employ.
By a Market I shall mean much what commercial men use it to express. Originally a market was a public place in a town where provisions and other objects were exposed for sale; but the word has been generalised, so as to mean any body of persons who are in intimate business relations and carry on extensive transactions in any commodity. A great city may contain as many markets as there are important branches of trade, and these markets may or may not be localised. The central point of a market is the public exchange,—mart or auction rooms, where the traders agree to meet and transact business. In London, the Stock Market, the Corn Market, the Coal Market, the Sugar Market, and many others, are distinctly localised; in Manchester, the Cotton Market, the Cotton Waste Market, and others. But this distinction of locality is not necessary. The traders may be spread over a whole town, or region of country, and yet make a market, if they are, by means of fairs, meetings, published price lists, the post office, or otherwise, in close communication with each other. Thus, the common expression Money Market denotes no locality: it is applied to the aggregate of those bankers, capitalists, and other traders who lend or borrow money, and who constantly exchange information concerning the course of business.1
In Economics we may usefully adopt this term with a clear and well-defined meaning. By a market I shall mean two or more persons dealing in two or more commodities, whose stocks of those commodities and intentions of exchanging are known to all. It is also essential that the ratio of exchange between any two persons should be known to all the others. It is only so far as this community of knowledge extends that the market extends. Any persons who are not acquainted at the moment with the prevailing ratio of exchange, or whose stocks are not available for want of communication, must not be considered part of the market. Secret or unknown stocks of a commodity must also be considered beyond reach of a market so long as they remain secret and unknown. Every individual must be considered as exchanging from a pure regard to his own requirements or private interests, and there must be perfectly free competition, so that any one will exchange with any one else for the slightest apparent advantage. There must be no conspiracies for absorbing and holding supplies to produce unnatural ratios of exchange. Were a conspiracy of farmers to withhold all corn from market, the consumers might be driven, by starvation, to pay prices bearing no proper relation to the existing supplies, and the ordinary conditions of the market would be thus overthrown.
The theoretical conception of a perfect market is more or less completely carried out in practice. It is the work of brokers in any extensive market to organise exchange, so that every purchase shall be made with the most thorough acquaintance with the conditions of the trade. Each broker strives to gain the best knowledge of the conditions of supply and demand, and the earliest intimation of any change. He is in communication with as many other traders as possible, in order to have the widest range of information, and the greatest chance of making suitable exchanges. It is only thus that a definite market price can be ascertained at every moment, and varied according to the frequent news capable of affecting buyers and sellers. By the mediation of a body of brokers a complete consensus is established, and the stock of every seller or the demand of every buyer brought into the market. It is of the very essence of trade to have wide and constant information. A market, then, is theoretically perfect only when all traders have perfect knowledge of the conditions of supply and demand, and the consequent ratio of exchange; and in such a market, as we shall now see, there can only be one ratio of exchange of one uniform commodity at any moment.
So essential is a knowledge of the real state of supply and demand to the smooth procedure of trade and the real good of the community, that I conceive it would be quite legitimate to compel the publication of any requisite statistics. Secrecy can only conduce to the profit of speculators who gain from great fluctuations of prices. Speculation is advantageous to the public only so far as it tends to equalise prices; and it is, therefore, against the public good to allow speculators to foster artificially the inequalities of prices by which they profit. The welfare of millions, both of consumers and producers, depends upon an accurate knowledge of the stocks of cotton and corn; and it would, therefore, be no unwarrantable interference with the liberty of the subject to require any information as to the stocks in hand. In Billingsgate fish market there was long ago a regulation to the effect that salesmen shall fix up in a conspicuous place every morning a statement of the kind and amount of their stock.1 The same principle has long been recognised in the Acts of Parliament concerning the collection of statistics of the quantities and prices of corn sold in English market towns. More recently similar legislation has taken place as regards the cotton trade, in the Cotton Statistics Act of 1868. Publicity, whenever it can thus be enforced on markets by public authority, tends almost always to the advantage of everybody except perhaps a few speculators and financiers.
[Back to Table of Contents]Definition of Trading Body.
I find it necessary to adopt some expression for any number of people whose aggregate influence in a market, either in the way of supply or demand, we have to consider. By a trading body I mean, in the most general manner, any body either of buyers or sellers. The trading body may be a single individual in one case; it may be the whole inhabitants of a continent in another; it may be the individuals of a trade diffused through a country in a third. England and North America will be trading bodies if we are considering the corn we receive from America in exchange for iron and other goods. The continent of Europe is a trading body as purchasing coal from England. The farmers of England are a trading body when they sell corn to the millers, and the millers both when they buy corn from the farmers and sell flour to the bakers.
We must use the expression with this wide meaning, because the principles of exchange are the same in nature, however wide or narrow may be the market considered. Every trading body is either an individual or an aggregate of individuals, and the law, in the case of the aggregate, must depend upon the fulfilment of law in the individuals. We cannot usually observe any precise and continuous variation in the wants and deeds of an individual, because the action of extraneous motives, or what would seem to be caprice, overwhelms minute tendencies. As I have already remarked (p. 15), a single individual does not vary his consumption of sugar, butter, or eggs from week to week by infinitesimal amounts, according to each small change in the price. He probably continues his ordinary consumption until accident directs his attention to a rise in price, and he then, perhaps, discontinues the use of the articles altogether for a time. But the aggregate, or what is the same, the average consumption, of a large community will be found to vary continuously or nearly so. The most minute tendencies make themselves apparent in a wide average. Thus, our laws of Economics will be theoretically true in the case of individuals, and practically true in the case of large aggregates; but the general principles will be the same, whatever the extent of the trading body considered. We shall be justified, then, in using the expression with the utmost generality.
It should be remarked, however, that the economical laws representing the conduct of large aggregates of individuals will never represent exactly the conduct of any one individual. If we could imagine that there were a thousand individuals all exactly alike in regard to their demand for commodities, and their capabilities of supplying them, then the average laws of supply and demand deduced from the conduct of such individuals would agree with the conduct of any one individual. But a community is composed of persons differing widely in their powers, wants, habits, and possessions. In such circumstances the average laws applying to them will come under what I have elsewhere1 called the "Fictitious Mean," that is to say, they are numerical results which do not pretend to represent the character of any existing thing. But average laws would not on this account be less useful, if we could obtain them; for the movements of trade and industry depend upon averages and aggregates, not upon the whims of individuals.
[Back to Table of Contents]The Law of Indifference.
When a commodity is perfectly uniform or homogeneous in quality, any portion may be indifferently used in place of an equal portion: hence, in the same market, and at the same moment, all portions must be exchanged at the same ratio. There can be no reason why a person should treat exactly similar things differently, and the slightest excess in what is demanded for one over the other will cause him to take the latter instead of the former. In nicely-balanced exchanges it is a very minute scruple which turns the scale and governs the choice. A minute difference of quality in a commodity may thus give rise to preference, and cause the ratio of exchange to differ. But where no difference exists at all, or where no difference is known to exist, there can be no ground for preference whatever. If, in selling a quantity of perfectly equal and uniform barrels of flour, a merchant arbitrarily fixed different prices on them, a purchaser would of course select the cheaper ones; and where there was absolutely no difference in the thing purchased, even an excess of a penny in the price of a thing worth a thousand pounds would be a valid ground of choice. Hence follows what is undoubtedly true, with proper explanations, that in the same open market, at any one moment, there cannot be two prices for the same kind of article. Such differences as may practically occur arise from extraneous circumstances, such as the defective credit of the purchasers, their imperfect knowledge of the market, and so on.
The principle above expressed is a general law of the utmost importance in Economics, and I propose to call it The Law of Indifference, meaning that, when two objects or commodities are subject to no important difference as regards the purpose in view, they will either of them be taken instead of the other with perfect indifference by a purchaser. Every such act of indifferent choice gives rise to an equation of degrees of utility, so that in this principle of indifference we have one of the central pivots of the theory.
Though the price of the same commodity must be uniform at any one moment, it may vary from moment to moment, and must be conceived as in a state of continual change. Theoretically speaking, it would not usually be possible to buy two portions of the same commodity successively at the same ratio of exchange, because, no sooner would the first portion have been bought than the conditions of utility would be altered. When exchanges are made on a large scale, this result will be verified in practice.1 If a wealthy person invested £100,000 in the funds in the morning, it is hardly likely that the operation could be repeated in the afternoon at the same price. In any market, if a person goes on buying largely, he will ultimately raise the price against himself. Thus it is apparent that extensive purchases would best be made gradually, so as to secure the advantage of a lower price upon the earlier portions. In theory this effect of exchange upon the ratio of exchange must be conceived to exist in some degree, however small may be the purchases made. Strictly speaking, the ratio of exchange at any moment is that of dy to dx, of an infinitely small quantity of one commodity to the infinitely small quantity of another which is given for it. The ratio of exchange is really a differential coefficient. The quantity of any article purchased is a function of the price at which it is purchased, and the ratio of exchange expresses the rate at which the quantity of the article increases compared with what is given for it.
We must carefully distinguish, at the same time, between the Statics and Dynamics of this subject. The real condition of industry is one of perpetual motion and change. Commodities are being continually manufactured and exchanged and consumed. If we wished to have a complete solution of the problem in all its natural complexity, we should have to treat it as a problem of motion—a problem of dynamics. But it would surely be absurd to attempt the more difficult question when the more easy one is yet so imperfectly within our power. It is only as a purely statical problem that I can venture to treat the action of exchange. Holders of commodities will be regarded not as continuously passing on these commodities in streams of trade, but as possessing certain fixed amounts which they exchange until they come to equilibrium.
It is much more easy to determine the point at which a pendulum will come to rest than to calculate the velocity at which it will move when displaced from that point of rest. Just so, it is a far more easy task to lay down the conditions under which trade is completed and interchange ceases, than to attempt to ascertain at what rate trade will go on when equilibrium is not attained.
The difference will present itself in this form: dynamically we could not treat the ratio of exchange otherwise than as the ratio of dy and dx, infinitesimal quantities of commodity. Our equations would then be regarded as differential equations, which would have to be integrated. But in the statical view of the question we can substitute the ratio of the finite quantities y and x. Thus, from the self-evident principle, stated on pp. 91, 92, that there cannot, in the same market, at the same moment, be two different prices for the same uniform commodity, it follows that the last increments in an act of exchange must be exchanged in the same ratio as the whole quantities exchanged. Suppose that two commodities are bartered in the ratio of x for y; then every mth part of x is given for the mth part of y, and it does not matter for which of the mth parts. No part of the commodity can be treated differently to any other part. We may carry this division to an indefinite extent by imagining m to be constantly increased, so that, at the limit, even an infinitely small part of x must be exchanged for an infinitely small part of y, in the same ratio as the whole quantities. This result we may express by stating that the increments concerned in the process of exchange must obey the equation
The use which we shall make of this equation will be seen in the next section.
[Back to Table of Contents]The Theory of Exchange.
The keystone of the whole Theory of Exchange, and of the principal problems of Economics, lies in this proposition—The ratio of exchange of any two commodities will be the reciprocal of the ratio of the final degrees of utility of the quantities of commodity available for consumption after the exchange is completed. When the reader has reflected a little upon the meaning of this proposition, he will see, I think, that it is necessarily true, if the principles of human nature have been correctly represented in previous pages.
Imagine that there is one trading body possessing only corn, and another possessing only beef. It is certain that, under these circumstances, a portion of the corn may be given in exchange for a portion of the beef with a considerable increase of utility. How are we to determine at what point the exchange will cease to be beneficial? This question must involve both the ratio of exchange and the degrees of utility. Suppose, for a moment, that the ratio of exchange is approximately that of ten pounds of corn for one pound of beef: then if, to the trading body which possesses corn, ten pounds of corn are less useful than one of beef, that body will desire to carry the exchange further. Should the other body possessing beef find one pound less useful than ten pounds of corn, this body will also be desirous to continue the exchange. Exchange will thus go on until each party has obtained all the benefit that is possible, and loss of utility would result if more were exchanged. Both parties, then, rest in satisfaction and equilibrium, and the degrees of utility have come to their level, as it were.
This point of equilibrium will be known by the criterion, that an infinitely small amount of commodity exchanged in addition, at the same rate, will bring neither gain nor loss of utility. In other words, if increments of commodities be exchanged at the established ratio, their utilities will be equal for both parties. Thus, if ten pounds of corn were of exactly the same utility as one pound of beef, there would be neither harm nor good in further exchange at this ratio.
It is hardly possible to represent this theory completely by means of a diagram, but the accompanying figure may, perhaps, render it clearer. Suppose the line pqr to be a small portion of the curve of utility of one commodity, while the broken line p'q
is the like curve of another commodity which has been reversed and superposed on the other. Owing to this reversal, the quantities of the first commodity are measured along the base line from a towards b, whereas those of the second must be measured in the opposite direction. Let units of both commodities be represented by equal lengths: then the little line áa indicates an increase of the first commodity, and a decrease of the second. Assume the ratio of exchange to be that of unit for unit, or
1 to 1: then, by receiving the commodity áa the person will gain the utility ad, and lose the utility ác; or he will make a net gain of the utility corresponding to the mixtilinear figure cd. He will, therefore, wish to extend the exchange. If he were to go up to the point 
, and were still proceeding, he would, by the next small exchange, receive the utility be, and part with b'f; or he would have a net loss of ef. He would, therefore, have gone too far; and it is pretty obvious that the point of intersection, q, defines the place where he would stop with the greatest advantage. It is there that a net gain is converted into a net loss, or rather where, for an infinitely small quantity, there is neither gain nor loss. To represent an infinitely small quantity, or even an exceedingly small quantity, on a diagram is, of course, impossible; but on either side of the line mq I have represented the utilities of a small quantity of commodity more or less, and it is apparent that the net gain or loss upon the exchange of these quantities would be trifling.
Symbolic Statement of the Theory.
To represent this process of reasoning in symbols, let Dx denote a small increment of corn, and Dy a small increment of beef exchanged for it. Now our Law of Indifference comes into play. As both the corn and the beef are homogeneous commodities, no parts can be exchanged at a different ratio from other parts in the same market: hence, if x be the whole quantity of corn given for y, the whole quantity of beef received, Dy must have the same ratio to Dx as y to x: we have then,
In a state of equilibrium, the utilities of these increments must be equal in the case of each party, in order that neither more nor less exchange would be desirable. Now the increment of beef, Dy, is 
times as great as the increment of corn, Dx, so that, in order that their utilities shall be equal, the degree of utility of beef must be 
times as great as the degree of utility of corn. Thus we arrive at the principle that the degrees of utility of commodities exchanged will be in the inverse proportion of the magnitudes of the increments exchanged.
Let us now suppose that the first body, A, originally possessed the quantity a of corn, and that the second body, B, possessed the quantity b of beef. As the exchange consists in giving x of corn for y of beef, the state of things after exchange will be as follows:—
A holds a - x of corn, and y of beef. B holds x of corn, and b - y of beef.
Let f1 (a - x) denote the final degree of utility of corn to A, and f2x the corresponding function for B. Also let y1y denote A's final degree of utility for beef, and y2 (b - y) B's similar function. Then, as explained on p. 96, A will not be satisfied unless the following equation holds true:—
Hence, substituting for the second member by the equation given on p. 95, we have
What holds true of A will also hold true of B, mutatis mutandis. He must also derive exactly equal utility from the final increments, otherwise it will be for his interest to exchange either more or less, and he will disturb the conditions of exchange. Accordingly the following equation must hold true:—
y2 (b - y). dy = f2x.dx:
or, substituting as before,
We arrive, then, at the conclusion, that whenever two commodities are exchanged for each other, and more or less can be given or received in infinitely small quantities, the quantities exchanged satisfy two equations, which may be thus stated in a concise form—
The two equations are sufficient to determine the results of exchange; for there are only two unknown quantities concerned, namely, x and y, the quantities given and received.
A vague notion has existed in the minds of economical writers, that the conditions of exchange may be expressed in the form of an equation. Thus, J. S. Mill has said:1 "The idea of a ratio, as between demand and supply, is out of place, and has no concern in the matter: the proper mathematical analogy is that of an equation. Demand and supply, the quantity demanded and the quantity supplied, will be made equal." Mill here speaks of an equation as only a proper mathematical analogy. But if Economics is to be a real science at all, it must not deal merely with analogies; it must reason by real equations, like all the other sciences which have reached at all a systematic character. Mill's equation, indeed, is not explicitly the same as any at which we have arrived above. His equation states that the quantity of a commodity given by A is equal to the quantity received by B. This seems at first sight to be a mere truism, for this equality must necessarily exist if any exchange takes place at all. The theory of value, as expounded by Mill, fails to reach the root of the matter, and show how the amount of demand or supply is caused to vary. And Mill does not perceive that, as there must be two parties and two quantities to every exchange, there must be two equations.
Nevertheless, our theory is perfectly consistent with the laws of supply and demand; and if we had the functions of utility determined, it would be possible to throw them into a form clearly expressing the equivalence of supply and demand. We may regard x as the quantity demanded on one side and supplied on the other; similarly, y is the quantity supplied on the one side and demanded on the other. Now, when we hold the two equations to be simultaneously true, we assume that the x and y of one equation equal those of the other. The laws of supply and demand are thus a result of what seems to me the true theory of value or exchange.
[Back to Table of Contents]Analogy to the Theory of the Lever.
I have heard objections made to the general character of the equations employed in this book. It is remarked that the equations in question continually involve infinitesimal quantities, and yet they are not treated as differential equations usually are, that is integrated. There is, indeed, no reason why the process of integration should not be applied when it is required, and I will here show that the equations employed do not differ in general character from those which are really treated in many branches of physical science. Whenever, in fact, we deal with continuously varying quantities, the ultimate equations must lie between infinitesimals. The process of integration, if I understand the matter aright, only ascertains other equations, the truth of which follows from the fundamental differential equation.
The mode in which mechanies is usually treated in elementary work tends to disguise the real foundation of the science which is to be found in the so-called theory of virtual velocities. Let us take the description of the lever of the first order as it is given in some of the best modern elementary works, as, for instance, in Mr. Magnus's Lessons in Elementary Mechanics, p. 128. We here read as follows:—
"Let AB be a lever turning freely about C, the fulcrum, and let P be the force applied at A, and W the force exerted, or resistance overcome, or weight raised at B. Suppose the lever turned through the angle ACA', then the work done by P equals P × are AA', and work done by W equals W × arc BB', if P and W act perpendicularly to the arm. Therefore, by the law of energy,
P × AA' = W × BB', and since
we have P × AC = W × BC,
or, P × its arm = W × its arm."
Now, in such a statement as this, we seem to be dealing with plain finite quantities, and there is no apparent difficulty in the matter. In reality the difficulty is only disguised by assuming that P and W act perpendicularly to the arm through finite arcs. This condition is, indeed, carried out with approximate exactness in the problem of the wheel and axle,1 which may be regarded as combining together an infinite series of straight levers, coming successively into operation. In this machine, therefore, the weights, roughly speaking, always act perpendicularly to arms of invariable length. But, in the generality of cases of the lever, the theory is only true for infinitely small displacements, and no sooner has the lever begun to move through any finite arc AA', than it ceases to be exactly true that the work done by P equals P × arc AA'. Nevertheless, the theory is quite correct as applied to the lever considered statically, that is, as in a state of rest and equilibrium, because the finite arcs of displacement, when it really is displaced, are exactly proportional to the infinitely small arcs, known as virtual velocities, through which it would be displaced, if instead of being at rest, it suffered an infinitely small displacement.
It is curious, moreover, that, when we take the theory of the lever treated according to the principle of virtual velocities, we get equations exactly similar in form to those of the theory of value as established above. The general principle of virtual velocities is to the effect that, if any number of forces be in equilibrium at one or more points of a rigid body, and if this body receive an infinitely small displacement, the algebraic sum of the products of each force into its displacement is equal to zero. In the case of a lever of the first order, this amounts to saying that one force multiplied into its displacement will be neutralised by the other force multiplied into its negative displacement. But inasmuch as the displacements are exactly proportional to the lengths of the arms of the lever, we obtain as a derivative equation, that the forces multiplied each by its own arm are equal to each other. No doubt in the quotation given above, P × AC = W × BC is an equation between finite quantities; but the real equation derived immediately from the principle of virtual velocities, is P × AA' = W × BB', in which P and W are finite, but AA' and BB' are in strictness infinitely small displacements. Let us write this equation in the form
then as we also have
we can substitute; hence
I dwell upon this matter at some length because we here have exactly the forms of the equations of exchange. As we have seen, the original equation is of the general form
where fx and yy represent finite expressions for the degrees of utility of the commodities Y and X, as regards some individual, and dy and dx are infinitesimal quantities of those commodities exchanged. But these infinitesimals may in this case at least be eliminated, because, in virtue of the Law of Indifference, they are exactly proportional to the whole finite quantities exchanged. Hence for 
we substitute 
. We may write the equations one below the other, so as to make the analogy visible—thus
To put this analogy of the theories of exchange and of the lever in the clearest possible light, I give below a diagram, in which the several economic qualities are represented by the parts of the diagram to which they correspond or are proportional.
Now in statical problems no such process as integration is applicable. The equation lies actually between imaginary infinitesimal quantities, and there is no effect to be summed up. Yet there is no statical problem which is not subject to the principle of virtual velocities, and Poisson, in his Traité de Mécanique,
which commences with statical theorems, asserts explicitly,1 "Dans cet ouvrage, j'emploierai exclusivement la méthode des infiniment petits."
[Back to Table of Contents]Impediments to Exchange.
We have hitherto treated the theory of exchange as if the action of exchange could be carried on without trouble or cost. In reality, the cost of conveyance is almost always of importance, and it is sometimes the principal element in the question. To the cost of mere transport must be added a variety of charges of brokers, agents, packers, dock, harbour, light dues, etc., together with any customs duties imposed either on the importation or exportation of commodities. All these charges, whether necessary or arbitrary, are so many impediments to commerce, and tend to reduce its advantages. The effect of any one such charge, or of the aggregate of the costs of exchange, can be represented in our formulæ in a very simple manner.
In whatever mode the charges are payable, they may be conceived as paid by the surrender on importation of a certain fraction of the commodity received; for the amount of the charges will usually be proportional to the quantity of goods, and, if expressed in money, can be considered as turned into commodity.
Thus, if A gives x in exchange, this is not the quantity received by B; a part of x is previously subtracted, so that B receives say mx, which is less than x, and the terms of exchange must be adjusted on his part so as to agree with this condition. Hence the second equation will be
Again, A, though giving x, will not receive the whole of y; but say ny, so that his equation similarly will be
The result is, that there is not one ratio of exchange, but two ratios; and the more these differ, the less advantage will there be in exchange. It is obvious that A has either to remain satisfied with less of the second commodity than before, or has to give more of his own in purchasing it. By an obvious transfer of the factors m and n we may state the equations of impeded exchange in the concise form—
[Back to Table of Contents] Illustrations of the Theory of Exchange.
As stated above, the Theory of Exchange may seem to be of a somewhat abstract and perplexing character; but it is not difficult to find practical illustrations which will show how it is verified in the actual working of a great market. The ordinary laws of supply and demand, when properly stated, are the practical manifestation of the theory. Considerable discussion has taken place concerning these laws, in consequence of Mr. W. T. Thornton's writings upon the subject in the Fortnightly Review, and in his work on the Claims of Labour. Mill, although he had previously declared the Theory of Value to be complete and perfect (see p. 76), was led by Mr. Thornton's arguments to allow that modification was required.
For my own part, I think that most of Mr. Thornton's arguments are beside the question. He suggests that there are no regular laws of supply and demand, because he adduces certain cases in which no regular variation can take place. Those cases might be indefinitely multiplied, and yet the laws in question would not be touched. Of course, laws which assume a continuity of variation are inapplicable where continuous variation is impossible. Economists can never be free from difficulties unless they will distinguish between a theory and the application of a theory. Because, in retail trade, in English or Dutch auction, or other particular modes of traffic, we cannot at once observe the operation of the laws of supply and demand, it is not in the least to be supposed that those laws are false. In fact, Mr. Thornton seems to allow that, if prospective demand and supply are taken into account, they become substantially true. But, in the actual working of any market, the influence of future events should never be neglected, neither by a merchant nor an economist.
Though Mr. Thornton's objections are mostly beside the question, his remarks have served to show that the action of the laws of supply and demand was inadequately explained by previous economists. What constitutes the demand and the supply was not carefully enough investigated. As Mr. Thornton points out, there may be a number of persons willing to buy; but if their highest offer is ever so little short of the lowest price which the seller is willing to take, their influence is nil. If in an auction there are ten people willing to buy a horse at £20, but not higher, their demand instantly ceases when any one person offers £21. I am inclined not only to accept such a view, but to carry it further. Any change in the price of an article will be determined not with regard to the large numbers who might or might not buy it at other prices, but by the few who will or will not buy it according as a change is made close to the existing price.
The theory consists in carrying out this view to the point of asserting that it is only comparatively insignificant quantities of supply and demand which are at any moment operative on the ratio of exchange. This is practically verified by what takes place in any very large market—say that of the Consolidated Three Per Cent Annuities. As the whole amount of the English funds is nearly eight hundred millions sterling, the quantity bought or sold by any ordinary purchaser is inconsiderably small in comparison. Even £1000 worth of stock may be taken as an infinitesimally small increment, because it does not appreciably affect the total existing supply. Now the theory consists in asserting that the market price of the funds is affected from hour to hour not by the enormous amounts which might be bought or sold at extreme prices, but by the comparatively insignificant amounts which are being sold or bought at the existing prices. A change of price is always occasioned by the overbalancing of the inclinations of those who will or will not sell just about the point at which prices stand. When Consols are at 93½, and business is in a tranquil state, it matters not how many buyers there are at 93, or sellers at 94. They are really off the market. Those only are operative who may be made to buy or sell by a rise or fall of an eighth. The question is, whether the price shall remain at 93½, or rise to 
, or fall to 
. This is determined by the sale or purchase of comparatively very small amounts. It is the purchasers who find a little stock more profitable to them than the corresponding sum of money who make the price rise by 
. When the price of the funds is very steady and the market quiescent, it means that the stocks are distributed among holders in such a way that the exchange of more or less at the prevailing price is a matter of indifference.
In practice, no market ever long fulfils the theoretical conditions of equilibrium, because, from the various accidents of life and business, there are sure to be people every day compelled to sell, or having sudden inducements to buy. There is nearly always, again, the influence of prospective supply or demand, depending upon the political intelligence of the moment. Speculation complicates the action of the laws of supply and demand in a high degree, but does not in the least degree arrest their action or alter their nature. We shall never have a Science of Economics unless we learn to discern the operation of law even among the most perplexing complications and apparent interruptions.
[Back to Table of Contents]Problems in the Theory of Exchange.
We have hitherto considered only one simple case of the Theory of Exchange. In all other cases where the commodities are capable of indefinite subdivision, the principles will be exactly the same, but the particular conditions may be subject to variation.
We may, firstly, express the conditions of a great market where vast quantities of some stock are available, so that any one small trader will not appreciably affect the ratio of exchange. This ratio is, then, approximately a fixed number, and each trader exchanges at that ratio just so much as suits him. These circumstances may be represented by supposing A to be a trading body possessing two very large stocks of commodities, a and b. Let C be a person who possesses a comparatively small quantity c of the second commodity, and gives a portion of it, y, which is very small compared with b, in exchange for a portion x of a, which is very small compared with a. Then, after exchange, we shall find A in possession of the quantities a - x and b + y, and C in possession of x and c - y. The equations will become
Since a - x and b + y, by supposition, do not appreciably differ from a and b, we may substitute the latter quantities, and we have, for the first equation, approximately,
The ratio of exchange being an approximately fixed ratio determined by the conditions of the trading body A, there is, in reality, only one undetermined quantity, x, the quantity of commodity which C finds it advantageous to purchase by expending part of c. This will now be determined by the equation
This equation will represent the condition in regard to any one distinct commodity of a very small country trading with a much larger one. It might represent, to some extent, the circumstances of trade between the Channel Islands and the great markets of England, though, of course, it is never absolutely verified, because the smallest purchasers do affect the market in some degree. The equation still more accurately represents the position of an individual consumer with regard to the aggregate trade of a large community, since he must buy at the current prices, which he cannot in an appreciable degree affect.
A still simpler formula, however, is needed to represent the conditions of a large part of our purchases. In many cases we want so little of a commodity, that an individual need not give more than a very small fraction of his possessions to obtain it. We may suppose, then, that y in the last problem is a very small part of c, so that y2 (c - y) does not differ appreciably from y2c. Taking m as before to be the existing ratio of exchange, we have only one equation—
This means that C will buy of the commodity until its degree of utility falls below that of the commodity he gives. A person's expenditure on salt is in this country an inconsiderable item of expense; what he thus spends does not make him appreciably poorer; yet, if the established price or ratio is one penny for each pound of salt, he buys in any time, say one year, so many pounds of salt that an additional pound would not have so much utility to him as a penny. In the above equation m. y2c represents the utility to him of a penny, which being an inconsiderable fraction of his possessions, is approximately invariable in utility, and he buys salt until f2x, which is approximately the utility of the next pound, is equal to, or it may be somewhat less than that of the penny. But this case must not be confused with that of purchases which appreciably affect the possessions of the purchaser. Thus, if a poor family purchase much butchers'-meat, they will probably have to go without something else. The more they buy, the lower the final degree of utility of the meat, and the higher the final degree of utility of something else; and thus these purchases will be the more narrowly limited.
[Back to Table of Contents]Complex Cases of the Theory.
We have hitherto considered the Theory of Exchange as applying only to two trading bodies possessing and dealing in two commodities. Exactly the same principles hold true, however numerous and complicated may be the conditions. The main point to be remembered in tracing out the results of the theory is, that the same pair of commodities in the same market can have only one ratio of exchange, which must therefore prevail between each body and each other, the costs of conveyance being considered as nil. The equations become rapidly more numerous as additional bodies or commodities are considered; but we may exhibit them as they apply to the case of three trading bodies and three commodities.
Thus, suppose that
A possesses the stock a of cotton, and gives x1 of it to B, x2 to C.
B possesses the stock b of silk, and gives y1 to A, y2 to C.
C possesses the stock c of wool, and gives z1 to A, z2 to B.
We have here altogether six unknown quantities—x1, x2, y1, y2, z1, z2; but we have also sufficient means of determining them. They are exchanged as follows—
A gives x1 for y1, and x2 for z1.
B gives 'y1 for x1, and y2 for z2.
C gives z1 for x2, and z2 for y2.
These may be treated as independent exchanges; each body must be satisfied in regard to each of its exchanges, and we must therefore take into account the functions of utility or the final degrees of utility of each commodity in respect of each body. Let us express these functions as follows—
| f1, y1, c1 are the respective functions of utility for | A. |
|---|---|
| f2, y2, c2 are the respective functions of utility for | B. |
| f3, y3, c3 are the respective functions of utility for | C. |
Now A, after the exchange, will hold a - x1 - x2 of cotton and y1 of silk; and B will hold x1 of cotton and b - y1 - y2 of silk: their ratio of exchange, y1 for x1, will therefore be governed by the following pair of equations:—
The exchange of A with C will be similarly determined by the ratio of the degrees of utility of wool and cotton on each side subsequent to the exchange; hence we have
There will also be interchange between B and C which will be independently regulated on similar principles, so that we have another pair of equations to complete the conditions, namely—
We might proceed in the same way to lay down the conditions of exchange between more numerous bodies, but the principles would be exactly the same. For every quantity of commodity which is given in exchange something must be received; and if portions of the same kind of commodity be received from several distinct parties, then we may conceive the quantity which is given for that commodity to be broken up into as many distinct portions. The exchanges in the most complicated case may thus always be decomposed into simple exchanges, and every exchange will give rise to two equations sufficient to determine the quantities involved. The same can also be done when there are two or more commodities in the possession of each trading body.
[Back to Table of Contents]Competition in Exchange.
One case of the Theory of Exchange is of considerable importance, and arises when two parties compete together in supplying a third party with a certain commodity. Thus, suppose that A, with the quantity of one commodity denoted by a, purchases another kind of commodity both from B and from C, who respectively possess b and c of it. All the quantities concerned are as follows—
A gives x1 of a to B and x2 to C,
B gives y1 of b to A,
C gives y2 of c to A.
As each commodity may be supposed to be perfectly homogeneous, the ratio of exchange must be the same in one case as in the other, so that we have one equation thus furnished—
Now, provided that A gets the right commodity in the proper quantity, he does not care whence it comes, so that we need not, in his equation, distinguish the source or destination of the quantities; he simply gives x1 + x2, and receives in exchange y1 + y2. Observing, then, that by (1)
we have the usual equation of exchange—
But B and C must both be separately satisfied with their shares in the transaction. Thus
There are altogether four unknown quantities—x1, x2, y1, y2; and we have four equations by which to determine them. Various suppositions might be made as to the comparative magnitudes of the quantities b and c, or the character of the functions concerned; and conclusions could then be drawn as to the effect upon the trade. The general result would be, that the smaller holder must more or less conform to the prices of the larger holder.
[Back to Table of Contents]Failure of the Equations of Exchange.
Cases constantly occur in which equations of the kind set forth in the preceding pages fail to hold true, or lead to impossible results. Such failure may indicate that no exchange at all takes place, but it may also have a different meaning.
In the first case, it may happen that the commodity possessed by A has a high degree of utility to A, and a low degree to B, and that vice versâ B's commodity has a high degree of utility to B and less to A. This difference of utility might exist to such an extent, that though B were to receive very little of A's commodity, yet the final degree of utility to him would be less than that of his own commodity, of which he enjoys much more. In such a case no benefit can arise from exchange, and no exchange will consequently take place. This failure of exchange will be indicated by a failure of the equations.
It may also happen that the whole quantities of commodity possessed are exchanged, and yet the equations fail. A may have so low a desire for consuming his own commodity, that the very last increment of it has less degree of utility to him than a small addition to the commodity received in exchange. The same state of things might happen to exist with B as regards his commodity: under these circumstances the whole possessions of one might be exchanged for the whole of the other, and the ratio of exchange would of course be defined by the ratio of these quantities. Yet each party might desire the last increment of the commodity received more than he desires the last increment of that given, so that the equations would fail to be true. This case will hardly occur practically in international trade, since two nations usually trade in many commodities, a fact which would alter the conditions.
Again, the equations of exchange will fail to be possible when the commodity or useful article possessed on one or both sides is indivisible. We have always assumed hitherto that more or less of a commodity may be had, down to infinitely small quantities. This is approximately true of all ordinary trade, especially international trade between great industrial nations. Any one sack of corn or any one bar of iron is practically infinitesimal compared with the quantities exchanged by America and England; and even one cargo or parcel of corn or iron is a small fraction of the whole. But, in exceptional cases, even international trade might involve indivisible articles. We might conceive the British Government giving the Koh-i-noor diamond to the Khedive of Egypt in exchange for Pompey's Pillar, in which case it would certainly not answer the purpose to break up one article or the other.1 When an island or portion of territory is transferred from one possessor to another, it is often necessary to take the whole, or none. America, in purchasing Alaska from Russia, would hardly have consented to purchase less than the whole. In every sale of a house, factory, or other building, it is usually impracticable to make any division without greatly lessening the utility of the whole. In all such cases our equations must fail to exist, because we cannot contemplate the existence of an increment or a decrement to an indivisible article.
Suppose, for example, that A and B each possess a book: they cannot break up the books, and must therefore exchange them entire, if at all. Under what conditions will they do so? Plainly on the condition that each makes a gain of utility by so doing. Here we deal not with the final degree of utility depending on an infinitesimal quantity, but on the whole utility of the complete article. Now let us assign the symbols as follows:—
| u1 = the | utility of | A's book to A, |
| u2 = the | utility of | A's book to B, |
| v1 = the | utility of | B's book to A, |
| v2 = the | utility of | B's book to B. |
Then the conditions of exchange are simply
v1> u1,
u2> v2.
We might indeed theoretically contemplate the case where the utilities were exactly equal on one side; thus
v1> u1,
u2 = v2;
B would then be wholly indifferent to the exchange, and I do not see any means of deciding whether he would or would not consent to it. But we need hardly consider the case, as it could seldom practically occur. Were the utilities exactly equal on both sides in respect to both objects, there would obviously be no motive to exchange. Again, the slightest loss of utility on either side would be a complete bar to the transaction, because we are not supposing, at present, that any other commodities are in possession so as to allow of separate inducements, or that any other motives than such as arise out of simple desire of one's own convenience enter into the question.
A much more difficult problem arises when we suppose an indivisible article exchanged for a divisible commodity. When Russia sold Alaska this was a practically indivisible thing; but it was bought with money of which more or less might be given to indefinitely small quantities. A bargain of this kind is exceedingly common; indeed it occurs in the case of every house, mansion, estate, factory, ship, or other complete whole, which is sold for money. Our former equations of exchange certainly fail, for they involve increments of commodity on both sides. The theory seems to give a very unsatisfactory answer, for the problem proves to be, within certain limits, indeterminate.
Let X be the indivisible article; u1 its utility to its possessor A, and u2 its utility to B. Let y be the quantity of commodity given for it, a commodity which is supposed to be divisible ad infinitum; let v1 be the total utility of y to A, and v2 its total utility to B. Then it is quite evident that, in order to give rise to exchange, v1 must be greater than u1, and u2 must be greater than v2; that is, there must, as before, be a gain of utility on each side. The quantity y must not be so great then as to deprive B of gain, nor so small as to deprive A of gain. The following is an extract from Mr. Thornton's work which exactly expresses the problem:—
"There are two opposite extremes—one above which the price of a commodity cannot rise, the other below which it cannot fall. The upper of these limits is marked by the utility, real or supposed, of the commodity to the customer; the lower, of its utility to the dealer. No one will give for a commodity a quantity of money or money's worth, which, in his opinion, would be of more use to him than the commodity itself. No one will take for a commodity a quantity of money or of anything else which he thinks would be of less use to himself than the commodity. The price eventually given and taken may be either at one of the opposite extremes, or may be anywhere intermediate between them."1
Three distinct cases might occur, which can best be illustrated by a concrete example. Suppose we can read the thoughts of the parties in the sale of a house. If A says £1200 is the least price which will satisfy him, and B holds that £800 is the highest price which it will be profitable for him to give, no exchange can possibly take place. If A should find £1000 to be his lowest limit, while B happens to name the same sum for his highest limit, the transaction can be closed, and the price will be exactly defined. But supposing, finally, that A is really willing to sell at £900, and B is prepared to buy at £1100, in what manner can we theoretically determine the price? I see no mode of solving the question. Any price between £900 and £1100 will leave a profit on each side, and both parties will lose if they do not come to terms. I conceive that such a transaction must be settled upon other than strictly economical grounds. The result of the bargain will greatly depend upon the comparative amount of knowledge of each other's positions and needs which either bargainer may possess or manage to obtain in the course of the transaction. Thus the power of reading another man's thoughts is of high importance in business, and the art of bargaining mainly consists in the buyer ascertaining the lowest price at which the seller is willing to part with his object, without disclosing if possible the highest price which he, the seller, is willing to give. The disposition and force of character of the parties, their comparative persistency, their adroitness and experience in business, or it may be feelings of justice or of kindliness, will also influence the decision. These are motives more or less extraneous to a theory of Economics, and yet they appear necessary considerations in this problem. It may be that indeterminate bargains of this kind are best arranged by an arbitrator or third party.
The equations of exchange may fail again when commodities are divisible, but not to infinitely small quantities. There is always, in retail trade, a convenient unit below which we do not descend in purchases. Paper may be bought in quires, or even in packets, which it may not be desirable to break up. Wine cannot be bought from the wine merchant in less than a bottle at a time. In all such cases exchange cannot, theoretically speaking, be perfectly adjusted, because it will be infinitely improbable that an integral number of units will precisely verify the equations of exchange. In a large proportion of cases, indeed, the unit may be so small compared with the whole quantities exchanged as practically to be infinitely small. But suppose that a person be buying ink which is only to be had, under the circumstances, in one shilling bottles. If one bottle be not quite enough, how will he decide whether to take a second or not? Clearly by estimating the aggregate utility of the bottle of ink compared with the shilling. If there be an excess, he will certainly purchase it, and proceed to consider whether a third be desirable or not.
This case might be illustrated by Fig. VI., in which the spaces o q1, p1q2, p2q3, etc., represent the total utilities of successive bottles of ink; while the equal spaces o r1, p1r2, etc., represent the total utilities of successive shillings, which we may assume to be practically invariable. There is no doubt that three bottles will be
purchased, but the fourth will not be purchased unless the mixtilinear figure p3q3q4p4 exceed in area the rectangle p3r3r4p4.
Cases of this kind are similar to those treated in pp. 120-124, where the things exchanged are indivisible, except that the question of exchange or no exchange occurs over and over again with respect to each successive unit, and is decided in respect to each by the excess of the total utility of the unit to be received over the total utility of that to be given. There is indeed perfect harmony between the cases where equations can and where they cannot be established; for we have only to imagine the indivisible units of commodity to be indefinitely lessened in size to enable us to pass gradually down to the case where equality of the increments of utility is ultimately established.
[Back to Table of Contents]Negative and Zero Value.
Only a few economists, notably Mr. H. D. Macleod in several of his publications, have noticed the fact that there may be such a thing as negative value. Yet there cannot be the least doubt that people often labour, or pay money to other labourers, in order to get rid of things, and they would not do this unless such things were hurtful, that is, had the opposite quality to utility—disutility. Water, when it gets into a mine, is a costly thing to get out again, and many people have been ruined by wet mines. Quarries and mines usually produce great quantities of valueless rock or earth, variously called duff, spoil, waste, rubbish, and no inconsiderable part of the cost of working arises from the need of raising and carrying this profitless mass of matter and then finding land on which to deposit it. Every furnace yields cinders, dross, or slag, which can seldom be sold for any money, and every household is at the expense of getting rid, in one way or another, of sewage, ashes, swill, and other rejectanea. Reflection soon shows, in short, that no inconsiderable part of the values with which we deal in practical economics must be negative values.
It will hardly be needful to show at full length that this negative value may be regarded as varying continuously in the same way as positive value. If after a long drought rain begins to fall heavily, it is at first hailed as a great benefit; the rain-water may be so valuable as to produce a crop, when otherwise successful agriculture would have been impossible. Rain may thus avert famine; but after the rain has fallen for a certain length of time, the farmer begins to think he has had enough of it; more rain will retard his operations, or injure the growing plants. As the rain continues to fall he fears further injury; water begins to flood his land, and there is even danger of the soil and crops being all washed away together. But the rain unfortunately pours down more and more heavily, until at length perhaps the crops, soil, house, stock,—nay, the farmer himself, are all swept bodily away. That same water, then, which in moderate quantity would have been of the greatest possible benefit, has only to be supplied in greater and greater quantities to become injurious, until it ends with occasioning the ruin, and even the death, of the individual. Those acquainted with the floods and droughts of Australia know that this is no fancy sketch.1
In many other cases it might be shown similarly that matter, we can hardly call it commodity, acquires a higher and higher degree of disutility the greater the quantity which has to be disposed of. Such is the case with the sewage of great towns, the foul or poisoned water from mines, dye-works, etc. Any obstacle, however, may be regarded as so much discommodity, whether it be a mountain which has to be bored through to make a railway, or a hollow which has to be filled up with an expensive embankment. If a building site requires a certain expenditure in levelling and draining before it can be made use of, the cost of this work is, of course, subtracted from the value which the land would otherwise possess. As every advantage in property gives rise to value, so every disadvantage must be set against that value.
We now come to the question how negative value is to be represented in our equations. Let us suppose a person possessing a of some commodity to find it insufficient: then it has positive degree of utility for him, that is to say f(a) is positive. Suppose x to be added to a and gradually increased: f(a + x) will gradually decrease. Let us assume that for a certain value of x it becomes zero; then, if the further increase of x turns utility into disutility, f(a + x) will become a negative quantity. How will this negative sign affect the validity of the equations which we have been employing in preceding pages, and in which each member has appeared to be both formally and intrinsically positive? It is plain that we cannot equate a positive to a negative quantity; but it will be found that if, at the same time that we introduce negative utility, we also assign to each increment of commodity the positive or negative sign, according as it is added to or subtracted from the exchanger's possessions, that is to say, received or given in exchange, no such difficulty arises.
Suppose A and B respectively to hold a and b, and to exchange dx and dy of the commodities X and Y. Then it will be apparent from the general character of the argument on pp. 98-100, that the fundamental equation there adopted will be included in the more general form—
In this equation either factor of either term may be intrinsically negative, while the alternative signs before x and y allow for every possible case of giving and receiving in exchange.
Four possible cases will arise. In the first case, both commodities have utility for each person, that is to say, f and y are both positive functions; but A gives some of X in return for some of Y. This means that dx is negative, and dy positive, while the quantities in possession after exchange are a - x, and b+y. Thus the equation becomes
We should have merely to transpose the negative term to the other side of the equation, and to assume b = 0, to obtain the equation on p. 99.
As the second case, suppose that Y possesses disutility for A, so that the function y becomes for him negative; in order to get rid of y, he must also pay x with it, and both these quantities as well as dy and dx receive the negative sign. Then the equation takes the shape
The third case is the counterpart of the last, and represents B's position, who receives both x and y, on the ground that one of these quantities is discommodity to him. But putting the matter as the case of A, we may assume f to be positive, y negative, and giving the positive sign to all of x,y,dx, and dy, we obtain the equation—
It is possible to conceive yet a fourth case in which people should be exchanging two discommodities; that is to say, getting rid of one hurtful substance by accepting in place of it what is felt to be less hurtful, though still possessing disutility. In this case we have both f and y negative, as well as one of the quantities exchanged; taking x and dx as positive, and y and dy as negative, the equation assumes the form
It might be difficult to discover any distinct cases of this last kind of exchange. Generally speaking, when a person receives assistance in getting rid of some inconvenient possession, he pays in money or other commodity for the service of him who helps to remove the burden. It must naturally be a very rare case that the remover has some burden which it would suit the other party to receive in exchange. Yet the contingency may, and no doubt does, sometimes occur. Two adjacent landowners, for instance. might reasonably agree that, if A allows B to throw the spoil of his mine on A's land, then A shall be allowed to drain his mine into B's mine. It might happen that B was comparatively more embarrassed by the great quantity of his spoil than by water, and that A had room for the spoil, but could not get rid of the water in other ways without great difficulty. An exchange of inconveniences would then be plainly beneficial.
Looking at the equations obtained in the four cases as stated above, it is apparent that the general equation of exchange consists in equating to zero the sum of one positive and one negative term, so that the signs, both of the utility functions and of the increments, may be disregarded. Thus the fundamental equation may be written in the general form
We may express the result of this theory in general terms by saying that the algebraic sum of the utility or disutility received or parted with, as regards the last increments concerned in an act of traffic, will always be zero. It also follows that, without regard to sign, the increments are in magnitude inversely as their degrees of utility or disutility. The reader will not fail to notice the remarkable analogy between this theory and that of the equilibrium of two forces regarded according to the principle of virtual velocities. A rigid lever will remain in equilibrium under the action of two forces, provided that the algebraic sum of the forces, each multiplied by its infinitely small displacement, be zero. Substitute for force degree of utility, positive or negative, and for infinitely small displacements infinitely small quantities of commodity exchanged, and the principles are identical.
It still remains to consider the imaginary case in which substances possess or are supposed to possess neither utility nor disutility, and are yet exchanged in finite quantities. Substituting the ratio of y and x for that of dy and dx, the general equation
will give the value
both the functions of utility being zero. This means that the quantities exchanged will be indeterminate so far as the theory of utility goes. If one substance possesses utility, and the other does not, the ratio of exchange becomes either 
, infinity or zero, indicating that there can be no comparison in our theory between things which do and those which do not possess utility. Practically speaking, such cases do not occur except in an approximate manner. Such things as cinders, shavings, night soil, etc., have either low degrees of utility or disutility. If the dustman takes them away for nothing, they must have utility for him sufficient to pay the cost of removal. When the dust is riddled, one part is usually found to have utility just sufficient to balance the disutility of the remainder, giving us an instance of the second or third form of the equation of exchange according as we regard the matter from the householder's or the dustman's point of view.
Equivalence of Commodities.
Much confusion is thrown into the statistical investigation of questions of supply and demand by the circumstance that one commodity can often replace another, and serve the same purposes more or less perfectly. The same, or nearly the same, substance is often obtained from two or three sources. The constituents of wheat, barley, oats, and rye are closely similar, if not identical. Vegetable structures are composed mainly of the same chemical compound in nearly all cases. Animal meat, again, is of nearly the same composition from whatever animal derived. There are endless differences of flavour and quality, but these are often insufficient to prevent one kind from serving in place of another.
Whenever different commodities are thus applicable to the same purposes, their conditions of demand and exchange are not independent. Their mutual ratio of exchange cannot vary much, for it will be closely defined by the ratio of their utilities. Beef and mutton, for instance, differ so slightly, that people eat them almost indifferently. But the whole-sale price of mutton, on an average, exceeds that of beef in the ratio of 9 to 8, and we must therefore conclude that people generally esteem mutton more than beef in this proportion, otherwise they would not buy the dearer meat. It follows that the final degrees of utility of these meats are in this ratio, or that if fx be the degree of utility of mutton, and yy that of beef, we have
8. fx = 9. yy.
This equation would doubtless not hold true in extreme circumstances; if mutton became comparatively scarce, there would probably be some persons willing to pay a higher price, merely because it would then be considered a delicacy. But this is certain, that, so long as the equation of utilities holds true, the ratio of exchange between mutton and beef will not diverge from that of 8 to 9. If the supply of beef falls off to a small extent, people will not pay a higher price for it, but will eat more mutton; and if the supply of mutton falls off, they will eat more beef. The conditions of supply will have no effect upon the ratio of exchange; we must, in fact, treat beef and mutton as one commodity of two different strengths, just as gold at eighteen and gold at twenty carats are hardly considered as two but rather as one commodity, of which twenty parts of one are equivalent to eighteen of the other.
It is upon this principle that we must explain, in harmony with Cairnes' views, the extraordinary permanence of the ratio of exchange of gold and silver, which from the commencement of the eighteenth century up to recent years never diverged much from 15 to 1. That this fixedness of ratio did not depend entirely upon the amount or cost of production is proved by the very slight effect of the Australian and Californian gold discoveries, which never raised the gold price of silver more than about 4 2/3 per cent, and failed to have a permanent effect of more than 1½ per cent. This permanence of relative values may have been partially due to the fact, that gold and silver can be employed for exactly the same purposes, but that the superior brilliancy of gold occasions it to be preferred, unless it be about 15 or 15½ times as costly as silver. Much more probably, however, the explanation of the fact is to be found in the fixed ratio of 15½ to 1, according to which these metals are exchanged in the currency of France and some other continental countries. The French Currency Law of the Year XI. established an artificial equation—
Utility of gold = 15½ × Utility of silver;
and it is probably not without some reason that Wolowski and other recent French economists attributed to this law of replacement an important effect in preventing disturbance in the relations of gold and silver.
Since the first edition of this work was published, the views of Wolowski have received striking verification in the unprecedented fall in the value of silver which has occurred in the last three or four years. The ratio of equivalent weights of silver and gold, which had never before risen much above 16 to 1, commenced to rise in 1874, and was at one time (July 1876) as high as 22·5 to 1 in the London market. Though it has since fallen, the ratio continues to be subject to frequent considerable oscillations. The great production of silver in Nevada may contribute somewhat to this extraordinary result, but the principal cause must be the suspension of the French Law of the Double Standard, and the demonetisation of silver in Germany, Scandinavia, and elsewhere. As I have treated the subject of the value of silver and the Double Standard elsewhere,1 I need not pursue it here.
[Back to Table of Contents]Acquired Utility of Commodities.
The Theory of Exchange, as explained above, rests entirely on the consideration of quantities of utility, and no reference to labour or cost of production has been made. The value of a divisible commodity, if I may for a moment use the dangerous term, is measured, not, indeed, by its total utility, but by its final degree of utility, that is by the intensity of the need we have for more of it. But the power of exchanging one commodity for another greatly extends the range of utility. We are no longer limited to considering the degree of utility of a commodity as regards the wants of its immediate possessor; for it may have a higher usefulness to some other person, and can be transferred to that person in exchange for some commodity of a higher degree of utility to the purchaser. The general result of exchange is, that all commodities sink, as it were, to the same level of utility in respect of the last portions consumed.
In the Theory of Exchange we find that the possessor of any divisible commodity will exchange such a portion of it, that the next increment would have exactly equal utility with the increment of other produce which he would receive for it. This will hold good however various may be the kinds of commodity he requires. Suppose that a person possesses one single kind of commodity, which we may consider to be money, or income, and that p,q,r,s,t, etc., are quantities of other commodities which he purchases with portions of his income. Let x be the uncertain quantity of money which he will desire not to exchange; what relation will exist between these quantities x,p,q,r, etc.? This relation will partly depend upon the ratio of exchange, partly on the final degree of utility of these commodities. Let us assume, for a moment, that all the ratios of exchange are equalities, or that a unit of one is always to be purchased with a unit of another. Then, plainly, we must have the degrees of utility equal, otherwise there would be advantage in acquiring more of that possessing the higher degree of utility. Let the sign f denote the function of utility, which will be different in each case; then we have simply the equations—
f1x = f2p = f3q = f4r = f5s = etc.
But, as a matter of fact, the ratio of exchange is seldom or never that of unit for unit; and when the quantities exchanged are unequal, the degrees of utility will not be equal. If for one pound of silk I can have three of cotton, then the degree of utility of cotton must be a third that of silk, otherwise I should gain by exchange. Thus the general result of the facility of exchange prevailing in a civilised country is, that a person procures such quantities of commodities that the final degrees of utility of any pair of commodities are inversely as the ratios of exchange of the commodities.
Let x1, x2, x3, x4, etc., be the portions of his income given for p,q,r,s, etc., respectively, then we must have
and so on. The theory thus represents the fact, that a person distributes his income in such a way as to equalise the utility of the final increments of all commodities consumed. As water runs into hollows until it fills them up to the same level, so wealth runs into all the branches of expenditure. This distribution will vary greatly with different individuals, but it is self-evident that the want which an individual feels most acutely at the moment will be that upon which he will expend the next increment of his income. It obviously follows that in expending a person's income to the greatest advantage, the algebraic sum of the quantities of commodity received or parted with, each multiplied by its final degree of utility, will be zero.
We can now conceive, in an accurate manner, the utility of money, or of that supply of commodity which forms a person's income. Its final degree of utility is measured by that of any of the other commodities which he consumes. What, for instance, is the utility of one penny to a poor family earning fifty pounds a year? As a penny is an inconsiderable portion of their income, it may represent one of the infinitely small increments, and its utility is equal to the utility of the quantity of bread, tea, sugar, or other articles which they could purchase with it, this utility depending upon the extent to which they were already provided with those articles. To a family possessing one thousand pounds a year, the utility of a penny may be measured in an exactly similar manner; but it will be much less, because their want of any given commodity will be satiated or satisfied to a much greater extent, so that the urgency of need for a pennyworth more of any article is much reduced.
The general result of exchange is thus to produce a certain equality of utility between different commodities, as regards the same individual; but between different individuals no such equality will tend to be produced. In Economics we regard only commercial transactions, and no equalisation of wealth from charitable motives is considered. The degree of utility of wealth to a very rich man will be governed by its degree of utility in that branch of expenditure in which he continues to feel the most need of further possessions. His primary wants will long since have been fully satisfied; he could find food, if requisite, for a thousand persons, and so, of course, he will have supplied himself with as much as he in the least desires. But so far as is consistent with the inequality of wealth in every community, all commodities are distributed by exchange so as to produce the maximum of benefit. Every person whose wish for a certain thing exceeds his wish for other things, acquires what he wants provided he can make a sufficient sacrifice in other respects. No one is ever required to give what he more desires for what he less desires, so that perfect freedom of exchange must be to the advantage of all.
[Back to Table of Contents]The Gain by Exchange.
It is a most important result of this theory that the ratio of exchange gives no indication of the real benefit derived from the action of exchange. So many trades are occupied in buying and selling, and make their profits by buying low and selling high, that there arises a fallacious tendency to believe that the whole benefit of trade depends upon the differences of prices. It is implied that to pay a high price is worse than doing without the article, and the whole financial system of a great nation may be distorted in the effort to carry out a false theory.
This is the result to which some of J. S. Mill's remarks, in his Theory of International Trade, would lead. That theory is always ingenious, and as it seems to me, nearly always true; but he draws from it the following conclusion:1 —"The countries which carry on their foreign trade on the most advantageous terms are those whose commodities are most in demand by foreign countries, and which have themselves the least demand for foreign commodities. From which, among other consequences, it follows that the richest countries, cœteris paribus, gain the least by a given amount of foreign commerce: since, having a greater demand for commodities generally, they are likely to have a greater demand for foreign commodities, and thus modify the terms of interchange to their own disadvantage. Their aggregate gains by foreign trade, doubtless, are generally greater than those of poorer countries, since they carry on a greater amount of such trade, and gain the benefit of cheapness on a larger consumption: but their gain is less on each individual article consumed."
In the absence of any explanation to the contrary, this passage must be taken to mean that the advantage of foreign trade depends upon the terms of exchange, and that international trade is less advantageous to a rich than to a poor country. But such a conclusion involves confusion between two distinct things—the price of a commodity and its total utility. A country is not merely like a great mercantile firm buying and selling goods, and making a profit out of the difference of price; it buys goods in order to consume them. But, in estimating the benefit which a consumer derives from a commodity, it is the total utility which must be taken as the measure, not the final degree of utility on which the terms of exchange depend.
To illustrate this truth we may employ the curves in Fig. VII. to represent the functions of utility of two commodities. Let the wool of Australia be represented by the line ob, and its total utility to Australia by the area of the curvilinear figure obrp. Let the utility of a second commodity, say cotton goods, to Australia be similarly represented in the lower curve, so that the quantity of commodity measured by o'b' gives a total utility represented by the figure o'p'r'b'. Then, if Australia gives half its wool, ab, for the quantity of cotton goods represented by o'a', it loses the utility aqrb, but gains that represented by the larger area o'p'q'a'. There is accordingly a considerable net gain of utility, which is the real object of exchange. Even had Australia sold its wool at a lower price, obtaining cotton goods
only to the amount of o'c, the utility of this amount, op'sc, would have exceeded that of the wool given for it.
So far is Mill's statement from being fundamentally correct, that I believe the truth lies in the opposite direction. As a general rule, the greatness of the price which a country is willing and able to pay for the productions of other countries, measures, or at least manifests, the greatness of the benefit which it derives from such imports. He who pays a high price must either have a very great need of that which he buys, or very little need of that which he pays for it; on either supposition there is gain by exchange. In questions of this sort there is but one rule which can be safely laid down, namely, that no one will buy a thing unless he expects advantage from the purchase; and perfect freedom of exchange, therefore, tends to the maximising of utility.
One advantage of the Theory of Economics, carefully studied, will be to make us very careful in our conclusions when the matter is not of the simplest possible nature. The fact that we can most imperfectly estimate the total utility of any one commodity should prevent us, for instance, from attempting to measure the benefit of any trade. Accordingly, when Mill proceeds from his theory of international trade to that of taxation, and arrives at the conclusion that one nation may, by means of taxes on commodities imported, "appropriate to itself, at the expense of foreigners, a larger share than would otherwise belong to it of the increase in the general productiveness of the labour and capital of the world,"1 I venture to question the truth of his results. I conceive that his arguments involve a confusion between the ratio of exchange and the total utility of a commodity, and a far more accurate knowledge of economical laws than any one yet possesses would be required to estimate the true effect of a tax. Customs duties may be requisite as a means of raising revenue, but the time is past when any economist should give the slightest countenance to their employment for manipulating trade, or for interfering with the natural tendency of exchange to increase utility.
[Back to Table of Contents]Numerical Determination of the Laws of Utility.
The future progress of Economics as a strict science must greatly depend upon our acquiring more accurate notions of the variable quantities concerned in the theory. We cannot really tell the effect of any change in trade or manufacture until we can with some approach to truth express the laws of the variation of utility numerically. To do this we need accurate statistics of the quantities of commodities purchased by the whole population at various prices. The price of a commodity is the only test we have of the utility of the commodity to the purchaser; and if we could tell exactly how much people reduce their consumption of each important article when the price rises, we could determine, at least approximately, the variation of the final degree of utility—the all-important element in Economics.
In such calculations we may at first make use of the simpler equation given on p. 113. For the first approximation we may assume that the general utility of a person's income is not affected by the changes of price of the commodity; so that, if in the equation
f x = m. y c
we may have many different corresponding values for x and m, we may treat yc, the utility of money, as a constant, and determine the general character of the function fx, the final degree of utility. This function would doubtless be a purely empirical one—a mere aggregate of terms devised so that their sum shall vary in accordance with statistical facts. The subject is too complex to allow of our expecting any simple precise law like that of gravity. Nor, when we have got the laws, shall we be able to give any exact explanation of them. They will be of the same character as the empirical formulæ used in many of the physical sciences—mere aggregates of mathematical symbols intended to replace a tabular statement.1 Nevertheless, their determination will render Economics a science as exact as many of the physical sciences; as exact, for instance, as Meteorology is likely to be for a very long time to come.
The method of determining the function of utility explained above will hardly apply, however, to the main elements of expenditure. The price of bread, for instance, cannot be properly brought under the equation in question, because, when the price of bread rises much, the resources of poor persons are strained, money becomes scarcer with them, and yc, the utility of money, rises. The natural result is, the lessening of expenditure in other directions; that is to say, all the wants of a poor person are supplied to a less degree of satisfaction when food is dear than when it is cheap. When in the long course of scientific progress a sufficient supply of suitable statistics has been at length obtained, it will become a mathematical problem of no great difficulty how to disentangle the functions expressing the degrees of utility of various commodities. One of the first steps, no doubt, will be to ascertain what proportion of the expenditure of poor people goes to provide food, at various prices of that food. But great difficulty is thrown in the way of all such inquiries by the vast differences in the condition of persons; and still greater difficulties are created by the complicated ways in which one commodity replaces or serves instead of another.
[Back to Table of Contents]Opinions as to the Variation of Price.
There is no difficulty in finding in works of Economists remarks upon the relation between a change in the supply of a commodity and the consequent rise of price. The general principles of the variation of utility have been familiar to many writers.
As a general rule the variation of price is much more marked in the case of necessaries of life than in the case of luxuries. This result would follow from the fact observed by Adam Smith, that "The desire for food is limited in every man by the narrow capacity of the human stomach; but the desire of the conveniences and ornaments of building, dress, equipage, and household furniture, seems to have no limit or certain boundary." As I assert that value depends upon desire for more, it follows that any excessive supply of food will lower its price very much more than in the case of articles of luxury. Reciprocally, a deficiency of food will raise its price much more than would happen in the case of less necessary articles. This conclusion is in harmony with facts; for Chalmers says:1 "The necessaries of life are far more powerfully affected in the price of them by a variation in their quantity than are the luxuries of life. Let the crop of grain be deficient by one-third in its usual amount, or rather, let the supply of grain in the market, whether from the home produce or by importation, be curtailed to the same extent, and this will create a much greater addition than of one-third to the price of it. It is not an unlikely prediction that its cost would be more than doubled by the shortcoming of one-third or one-fourth in the supply."
He goes on to explain, at considerable length, that the same would not happen with such an article as rum. A deficiency in the supply of rum from the West Indies would occasion a rise of price, but not to any great extent, because there would be a substitution of other kinds of spirits, or else a reduction in the amount consumed. Men can live without luxuries, but not without necessaries. "A failure in the general supply of esculents to the extent of one-half would more than quadruple the price of the first necessaries of life, and would fall with very aggravated pressure on the lower orders. A failure to the same extent in all the vineyards of the world would most assuredly not raise the price of wine to anything near this proportion. Rather than pay four times the wonted price for Burgundy, there would be a general descent to claret, or from that to port, or from that to the home-made wines of our own country, or from that to its spirituous, or from that to its fermented liquors."1 He points to sugar especially as an article which would be extensively thrown out of consumption by any great rise in price,1 because it is a luxury, and at the same time forms a considerable element in expenditure. But he thinks that, if an article occasions a total expenditure of very small amount, variations of price will not much affect its consumption.
Speaking of nutmeg, he says: "There is not sixpence a year consumed of it for each family in Great Britain; and perhaps not one family that spends more than a guinea on this article alone. Let the price then be doubled or trebled; this will have no perceptible effect on the demand; and the price will far rather be paid than that the wonted indulgence should in any degree be foregone.... The same holds true of cloves, and cinnamon, and Cayenne pepper, and all the precious spiceries of the East; and it is thus that while, in the general, the price of necessaries differs so widely from that of luxuries, in regard to the extent of oscillation, there is a remarkable approximation in this matter between the very commonest of these necessaries and the very rarest of these luxuries."1
In these interesting observations Chalmers correctly distinguishes between the effect of desire for the commodity in question and that for other çommodities. The cost of nutmeg does not appreciably affect the general expenditure on other things, and the equation on p. 113 therefore applies. But if sugar becomes scarce, to consume as before would necessitate a reduction of consumption in other directions; and as the degree of utility of more necessary articles rises much more rapidly than that of sugar, it is the latter article which is thrown out of use by preference. This is a far more complex case, which includes also the case of corn and all large articles of consumption.
Chalmers' remarks on the price of sugar are strongly supported by facts concerning the course of the sugar markets in 1855-6. In the year 1855, as is stated in Tooke's History of Prices,1 attention was suddenly drawn to a considerable reduction which had taken place in the stocks of sugar. The price rapidly advanced, but before it had reached the highest point the demand became almost wholly suspended. Not only did retail dealers avoid replenishing their stocks, but there was an immediate and sometimes entire cessation of consumption among extensive classes. There were instances among the retail grocers of their not selling a single pound of sugar until prices receded to what the public was satisfied was a reasonable rate.
[Back to Table of Contents]Variation of the Price of Corn.
As to Chalmers' ingenious remarks upon the consumption of nutmeg, he seems to be at least partially correct. To a certain extent he brings into view the principle explained above, that when only a small quantity of income is required to purchase a certain kind of commodity in sufficient abundance, the degree of utility of income will not be appreciably affected by the price paid, that is to say (p. 113) yc remains approximately constant. It follows that 
is constant, or in other words the final degree of utility of the small commodity purchased must be directly proportional to the price. If then the price rise much, either the consumer must relinquish the use of that commodity almost entirely, or else he must feel such need of it, that a small decrease of consumption is irksome to him; that is to say, looking to our curves of utility, either we must recede to a part of the curve very close to the axis of y, or else the curve must be one which rises rapidly as we move towards the origin. Now Chalmers assumes that with nutmeg the latter is the case. People accustomed to use it in his time were so fond of it that they would pay a much higher price rather than decrease their consumption considerably. This means that it possessed a high degree of utility to them, which could only be overbalanced by some serious increase in the value of yc, which would ultimately mean the need of the necessaries of life.
It is very curious that in this subject, which reaches to the very foundations of Political Economy, we owe more to early than later writers. Before our science could be said to exist at all, writers on Political Arithmetic had got about as far as we have got at present. In a pamphlet of 1737,1 it is remarked that "People who understand trade will readily agree with me, that the tenth part of a commodity in a market, more than there is a brisk demand for, is apt to lower the market, perhaps, twenty or thirty per cent, and that a deficiency of a tenth part will cause as exorbitant an advance." Sir J. Dalrymple,1 again, says: "Merchants observe, that if the commodity in market is diminished one-third beneath its mean quantity, it will be nearly doubled in value; and that if it is augmented one-third above its mean quantity, it will sink near one-half in its value; or that, by further diminishing or augmenting the quantity, these disproportions between the quantity and prices vastly increase." These remarks bear little signs of accuracy, indeed, for the writers have spoken of commodities in general as if they all varied in price in a similar degree. It is probable that they were thinking of corn or other kinds of the more necessary food. In the Spectator we find a conjecture,1 that the production of one-tenth part more of grain than is usually consumed would diminish the value of the grain one-half. I know nothing more strange and discreditable to statists and economists than that in so important a point as the relations of price and supply of the main article of food, we owe our most accurate estimates to writers who lived from one to two centuries ago.
There is a celebrated estimate of the variation of the price of corn which I have found quoted in innumerable works on Economics. It is commonly attributed to Gregory King, whose name should be held in honour as one of the fathers of statistical science in England. Born at Lichfield in 1648, King devoted himself much to mathematical studies, and was often occupied in surveying. His principal public appointments were those of Lancaster Herald and Secretary to the Commissioners of Public Accounts; but he is known to fame by the remarkable statistical tables concerning the population and trade of England, which he completed in the year 1696. His treatise was entitled Natural and Political Observations and Conclusions upon the State and Condition of England, 1696. It was never printed in the author's lifetime, but the contents were communicated in a most liberal manner to Dr. Davenant, who, making suitable acknowledgments as to the source of his information, founded thereupon his Essay upon the Probable Methods of making a People gainers in the Balance of Trade.1 Our knowledge of Gregory King's conclusions was derived from this and other essays of Davenant, until George Chalmers printed the whole treatise at the end of the third edition of his well-known Estimate of the Comparative Strength of Great Britain.
The estimate of which I am about to speak is given by Davenant in the following words:1 "We take it, that a defect in the harvest may raise the price of corn in the following proportions:—
So that when corn rises to treble the common rate, it may be presumed that we want above 
of the common produce; and if we should want 
, or half the common produce, the price would rise to near five times the common rate."
Though this estimate has always been attributed to Gregory King, I cannot find it in his published treatise; nor does Davenant, who elsewhere makes full acknowledgments of what he owes to King, here attribute it to his friend. It is therefore, perhaps, due to Davenant.
We may re-state this estimate in the following manner, taking the average harvest and the average price of corn as unity:—
| Quantity of Corn | 1.0 | .9 | .8 | .7 | .6 | .5 |
| Price | 1.0 | 1.3 | 1.8 | 2.6 | 3.8 | 5.5 |
Many writers have commented on this estimate. Thornton1 observes that it is probably exceedingly inaccurate, and that it is not clear whether the total stock, or only the harvest of a single year, is to be taken as deficient. Tooke,2 however, than whom on such a point there is no higher authority, believes that King's estimate "is not very wide of the truth, judging from the repeated occurrence of the fact that the price of corn in this country has risen from one hundred to two hundred per cent and upwards when the utmost computed deficiency of the crops has not been more than between one-sixth and one-third of an average."
I have endeavoured to ascertain the law to which Davenant's figures conform, and the mathematical function obtained does not greatly differ from what we might have expected. It is probable that the price of corn should never sink to zero, as, if abundant, it could be used for feeding horses, poultry, and cattle, or for other purposes for which it is too costly at present. It is said that in America corn, no doubt Indian corn, has been occasionally used as fuel. On the other hand, when the quantity is much diminished, the price should rise rapidly, and should become infinite before the quantity is zero, because famine would then be impending. The substitution of potatoes and other kinds of food renders the famine point very uncertain; but I think that a total deficiency of corn could not be made up by other food. Now a function of the form 
fulfils these conditions; for it becomes infinite when x is reduced to b, but for greater values of x always decreases as x increases. An inspection of the numerical data shows that n is about equal to 2, and, assuming it to be exactly 2, I find that the most probable values of a and b are a = .824 and b = .12. The formula thus becomes
The following numbers show the degree of approximation between the first of these formulæ and the data of Davenant:—
| Harvest | 1.0 | .9 | .8 | .7 | .6 | .5 |
| Price (Davenant) | 1.0 | 1.3 | 1.8 | 2.6 | 3.8 | 5.5 |
| Price calculated | 1.06 | 1.36 | 1.78 | 2.45 | 3.58 | 5.71 |
I cannot undertake to say how nearly Davenant's estimate agrees with experience; but, considering the close approximation in the above numbers, we may safely substitute the empirical formula for his numbers; and there are other reasons already stated for supposing that this formula is not far from the truth. Roughly speaking, the price of corn may be said to vary inversely as the square of the supply, provided that this supply be not unusually small. I find that this is nearly the same conclusion as Whewell drew from the same numbers. He says:1 "If the above numbers were to be made the basis of a mathematical rule, it would be found that the price varies inversely as the square of the supply, or rather in a higher ratio."
There is further reason for believing that the price of corn varies more rapidly than in the inverse ratio of the quantity. Tooke estimates1 that in 1795 and 1796 the farmers of England gained seven millions sterling in each year by a deficiency of one-eighth part in the wheat crop, not including the considerable profit on the rise of price of other agricultural produce. In each of the years 1799 and 1800, again, farmers probably gained eleven millions sterling by deficiency. If the price of wheat varied in the simple inverse proportion of the quantity, they would neither gain nor lose, and the fact that they gained considerably agrees with our formula as given above.
The variation of utility has not been overlooked by mathematicians, who had observed, as long ago as the early part of last century—before, in fact, there was any science of Political Economy at all—that the theory of probabilities could not be applied to commerce or gaming without taking notice of the very different utility of the same sum of money to different persons. Suppose that an even and fair bet is made between two persons, one of whom has £10,000 a year, the other £100 a year; let it be an equal chance whether they gain or lose £50. The rich person will, in neither case, feel much difference; but the poor person will receive far more harm by losing £50 than he can be benefited by gaining it. The utility of money to a poor person varies rapidly with the amount; to a rich person less so. Daniel Bernoulli, accordingly, distinguished in any question of probabilities between the moral expectation and the mathematical expectation, the latter being the simple chance of obtaining some possession, the former the chance as measured by its utility to the person. Having no means of ascertaining numerically the variation of utility, Bernoulli had to make assumptions of an arbitrary kind, and was then able to obtain reasonable answers to many important questions. It is almost self-evident that the utility of money decreases as a person's total wealth increases; if this be granted, it follows at once that gaming is, in the long run, a sure way to lose utility; that every person should, when possible, divide risks, that is, prefer two equal chances of £50 to one similar chance of £100; and the advantage of insurance of all kinds is proved from the same theory. Laplace drew a similar distinction between the fortune physique, or the actual amount of a person's income, and the fortune morale, or its benefit to him."1
In answer to the objections of an ingenious correspondent, it may be remarked that when we say gaming is a sure way to lose utility, we take no account of the utility—that is, the pleasure attaching to the pursuit of gaming itself; we regard only the commercial loss or gain. If a person with a certain income prefers to run the risk of losing a portion of it at play, rather than spending it in any other way, it must no doubt be conceded that the political economist, as such, can make no conclusive objection. If the gamester is so devoid of other tastes that to spend money over the gaming-table is the best use he can discover for it, economically speaking, there is nothing further to be said. The question then becomes a moral, legislative, or political one. A source of amusement which, like gaming, betting, dram-drinking, or opium-eating, is not in itself always pernicious, may come to be regarded as immoral, if in a considerable proportion of cases it leads to excessive and disastrous results. But this question evidently leads us into a class of subjects which could not be appropriately discussed in this work treating of pure economic theory.
[Back to Table of Contents]The Origin of Value.
The preceding pages contain, if I am not mistaken, an explanation of the nature of value which will, for the most part, harmonise with previous views upon the subject. Ricardo has stated, like most other economists, that utility is absolutely essential to value; but that "possessing utility, commodities derive their exchangeable value from two sources: from their scarcity, and from the quantity of labour required to obtain them."1 Senior, again, has admirably defined wealth, or objects possessing value, as "those things, and those things only, which are transferable, are limited in supply, and are directly or indirectly productive of pleasure or preventive of pain." Speaking only of things which are transferable, or capable of being passed from hand to hand, we find that two of the clearest definitions of value recognise utility and scarcity as the essential qualities. But the moment that we distinguish between the total utility of a mass of commodity and the degree of utility of different portions, we may say that it is scarcity which prevents the fall in the final degree of utility. Bread has the almost infinite utility of maintaining life, and when it becomes a question of life or death, a small quantity of food exceeds in value all other things. But when we enjoy our ordinary supplies of food, a loaf of bread has little value, because the utility of an additional loaf is small, our appetites being satiated by our customary meals.
I have pointed out the excessive ambiguity of the word Value, and the apparent impossibility of using it safely. When intended to express the mere fact of certain articles exchanging in a particular ratio, I have proposed to substitute the unequivocal expression—ratio of exchange. But I am inclined to believe that a ratio is not the meaning which most persons attach to the word Value. There is a certain sense of esteem or desirableness, which we may have with regard to a thing apart from any distinct consciousness of the ratio in which it would exchange for other things. I may suggest that this distinct feeling of value is probably identical with the final degree of utility. While Adam Smith's often-quoted value in use is the total utility of a commodity to us, the value in exchange is defined by the terminal utility, the remaining desire which we or others have for possessing more.
There remains the question of labour as an element of value. Economists have not been wanting who put forward labour as the cause of value, asserting that all objects derive their value from the fact that labour has been expended on them; and it is thus implied, if not stated, that value will be proportional to labour. This is a doctrine which cannot stand for a moment, being directly opposed to facts. Ricardo disposes of such an opinion when he says:1 "There are some commodities, the value of which is determined by their scarcity alone. No labour can increase the quantity of such goods, and therefore their value cannot be lowered by an increased supply. Some rare statues and pictures, scarce books and coins, wines of a peculiar quality, which can be made only from grapes grown on a particular soil, of which there is a very limited quantity, are all of this description. Their value is wholly independent of the quantity of labour originally necessary to produce them, and varies with the varying wealth and inclinations of those who are desirous to possess them."
The mere fact that there are many things, such as rare ancient books, coins, antiquities, etc., which have high values, and which are absolutely incapable of production now, disperses the notion that value depends on labour. Even those things which are producible in any quantity by labour seldom exchange exactly at the corresponding values.1 The market price of corn, cotton, iron, and most other things is, in the prevalent theories of value, allowed to fluctuate above or below its natural or cost value. There may, again, be any discrepancy between the quantity of labour spent upon an object and the value ultimately attaching to it. A great undertaking like the Great Western Railway, or the Thames Tunnel, may embody a vast amount of labour, but its value depends entirely upon the number of persons who find it useful. If no use could be found for the Great Eastern steamship, its value would be nil, except for the utility of some of its materials. On the other hand, a successful undertaking, which happens to possess great utility, may have a value, for a time at least, far exceeding what has been spent upon it, as in the case of the Atlantic cable. The fact is, that labour once spent has no influence on the future value of any article: it is gone and lost for ever. In commerce bygones are for ever bygones; and we are always starting clear at each moment, judging the values of things with a view to future utility. Industry is essentially prospective, not retrospective; and seldom does the result of any undertaking exactly coincide with the first intentions of its promoters.
But though labour is never the cause of value, it is in a large proportion of cases the determining circumstance, and in the following way:—Value depends solely on the final degree of utility. How can we vary this degree of utility?—By having more or less of the commodity to consume. And how shall we get more or less of it?—By spending more or less labour in obtaining a supply. According to this view, then, there are two steps between labour and value. Labour affects supply, and supply affects the degree of utility, which governs value, or the ratio of exchange. In order that there may be no possible mistake about this all-important series of relations. I will re-state it in a tabular form, as follows:—
Cost of production determines supply.
Supply determines final degree of utility.
Final degree of utility determines value.
But it is easy to go too far in considering labour as the regulator of value; it is equally to be remembered that labour is itself of unequal value. Ricardo, by a violent assumption, founded his theory of value on quantities of labour considered as one uniform thing. He was aware that labour differs infinitely in quality and efficiency, so that each kind is more or less scarce, and is consequently paid at a higher or lower rate of wages. He regarded these differences as disturbing circumstances which would have to be allowed for; but his theory rests on the assumed equality of labour. This theory rests on a wholly different ground. I hold labour to be essentially variable, so that its value must be determined by the value of the produce, not the value of the produce by that of the labour. I hold it to be impossible to compare à priori the productive powers of a navvy, a carpenter, an iron-puddler, a schoolmaster, and a barrister. Accordingly, it will be found that not one of my equations represents a comparison between one man's labour and another's. The equation, if there is one at all, is between the same person in two or more different occupations. The subject is one in which complicated action and reaction takes place, and which we must defer until after we have described, in the next chapter, the Theory of Labour.
[Back to Table of Contents]CHAPTER V
THEORY OF LABOUR
[Back to Table of Contents]Definition of Labour.
ADAM SMITH said, "The real price of everything, what everything really costs to the man who wants to acquire it, is the toil and trouble of acquiring it.... Labour was the first price, the original purchase-money, that was paid for all things."1 If subjected to a very searching analysis, this celebrated passage might not prove to be so entirely true as it would at first sight seem to most readers to be. Yet it is substantially true, and luminously expresses the fact that labour is the beginning of the processes treated by economists, as consumption is the end and purpose. Labour is the painful exertion which we undergo to ward off pains of greater amount, or to procure pleasures which leave a balance in our favour. Courcelle-Seneuil2 and Hearn have stated the problem of Economics with the utmost truth and brevity in saying, that it is to satisfy our wants with the least possible sum of labour.
In defining labour for the purposes of the economist we have a choice between two courses. In the first place, we may, if we like, include in it all exertion of body or mind. A game of cricket would, in this case, be labour; but if it be undertaken solely for the sake of the enjoyment attaching to it, the question arises whether we need take it under our notice. All exertion not directed to a distant and distinct end must be repaid simultaneously. There is no account of good or evil to be balanced at a future time. We are not prevented in any way from including such cases in our Theory of Economics; in fact, our Theory of Labour will, of necessity, apply to them. But we need not occupy our attention by cases which demand no calculus. When we exert ourselves for the sole amusement of the moment, there is but one rule needed, namely, to stop when we feel inclined—when the pleasure no longer equals the pain.
It will probably be better, therefore, to take the second course and concentrate our attention on such exertion as is not completely repaid by the immediate result. This would give us a definition nearly the same as that of Say, who defined labour as "Action suivée, dirigée vers un but." Labour, I should say, is any painful exertion of mind or body undergone partly or wholly with a view to future good.1 It is true that labour may be both agreeable at the time and conducive to future good; but it is only agreeable in a limited amount, and most men are compelled by their wants to exert themselves longer and more severely than they would otherwise do. When a labourer is inclined to stop, he clearly feels something that is irksome, and our theory will only involve the point where the exertion has become so painful as to nearly balance all other considerations. Whatever there is that is wholesome or agreeable about labour before it reaches this point may be taken as a net profit of good to the labourer; but it does not enter into the problem. It is only when labour becomes effort that we take account of it, and, as Hearn truly says,1 "such effort, as the very term seems to imply, is more or less troublesome." In fact, we must, as will shortly appear, measure labour by the amount of pain which attaches to it.
[Back to Table of Contents]Quantitative Notions of Labour.
Let us endeavour to form a clear notion of what we mean by amount of labour. It is plain that duration will be one element of it; for a person labouring uniformly during two months must be allowed to labour twice as much as during one month. But labour may vary also in intensity. In the same time a man may walk a greater or less distance; may saw a greater or less amount of timber; may pump a greater or less quantity of water; in short, may exert more or less muscular and nervous force. Hence amount of labour will be a quantity of two dimensions, the product of intensity and time when the intensity is uniform, or the sum represented by the area of a curve when the intensity is variable.
But intensity of labour may have more than one meaning; it may mean the quantity of work done, or the painfulness of the effort of doing it. These two things must be carefully distinguished, and both are of great importance for the theory. The one is the reward, the other the penalty, of labour. Or rather, as the produce is only of interest to us so far as it possesses utility, we may say that there are three quantities involved in the theory of labour—the amount of painful exertion, the amount of produce, and the amount of utility gained. The variation of utility, as depending on the quantity of commodity possessed, has already been considered; the variation of the amount of produce will be treated in the next chapter; we will here give attention to the variation of the painfulness of labour.
Experience shows that as labour is prolonged the effort becomes as a general rule more and more painful. A few hours' work per day may be considered agreeable rather than otherwise; but so soon as the overflowing energy of the body is drained off, it becomes irksome to remain at work. As exhaustion approaches, continued effort becomes more and more intolerable. Jennings has so clearly stated this law of the variation of labour, that I must quote his words.1 "Between these two points, the point of incipient effort and the point of painful suffering, it is quite evident that the degree of toilsome sensations endured does not vary directly as the quantity of work performed, but increases much more rapidly, like the resistance offered by an opposing medium to the velocity of a moving body.
"When this observation comes to be applied to the toilsome sensations endured by the working classes, it will be found convenient to fix on a middle point, the average amount of toilsome sensation attending the average amount of labour, and to measure from this point the degrees of variation. If, for the sake of illustration, this average amount be assumed to be of ten hours' duration, it would follow that, if at any period the amount were to be supposed to be reduced to five hours, the sensations of labour would be found, at least by the majority of mankind, to be almost merged in the pleasures of occupation and exercise, whilst the amount of work performed would only be diminished by one-half; if, on the contrary, the amount were to be supposed to be increased to twenty hours, the quantity of work produced would only be doubled, whilst the amount of toilsome suffering would become insupportable. Thus, if the quantity produced, greater or less than the average quantity, were to be divided into any number of parts of equal magnitude, the amount of toilsome sensation attending each succeeding increment would be found greater than that which would attend the increment preceding; and the amount of toilsome sensation attending each succeeding decrement would be found less than that which would attend the decrement preceding."
There can be no question of the general truth of the above statement, although we may not have the data for assigning the exact law of the variation. We may imagine the painfulness of labour in proportion to produce to be represented by some such curve as abcd in Fig. VIII. In this diagram the height of points above the line ox denotes pleasure, and depth below it pain. At the moment of commencing labour it is usually more irksome than when the mind and body are well bent to the work. Thus, at first, the pain is measured by oa. At b there is neither pain nor pleasure. Between b and c an excess of pleasure is represented as due to the exertion itself. But after c the energy begins to be rapidly exhausted, and the resulting pain is shown by the downward tendency of the line cd.
We may at the same time represent the degree of utility of the produce by some such curve as pq, the amount of produce being measured along the line ox. Agreeably to the theory of utility, already given, the curve shows that, the larger the wages earned, the less is the pleasure derived from a further increment.
There will, of necessity, be some point m such that qm = dm, that is to say, such that the pleasure gained is exactly equal to the labour endured. Now, if we pass the least beyond this point, a balance of pain will result: there will be an ever-decreasing motive in favour of labour, and an ever-increasing motive against it. The labourer will evidently cease, then, at the point m. It would be inconsistent with human nature for a man to work when the pain of work exceeds the desire of possession, including all the motives for exertion.
We must consider the duration of labour as measured by the number of hours' work per day. The alternation of day and night on the earth has rendered man essentially periodic in his habits and actions. In a natural and wholesome condition a man should return each twenty-four hours to exactly the same state; at any rate, the cycle should be closed within the seven days of the week. Thus the labourer must not be supposed to be either increasing or diminishing his normal strength. But the theory might also be made to apply to cases where special exertion is undergone for many days or weeks in succession, in order to complete work, as in collecting the harvest. Adequate motives may lead to and warrant overwork, but, if long continued, excessive labour reduces the strength and becomes insupportable; and the longer it continues the worse it is, the law being somewhat similar to that of periodic labour.
[Back to Table of Contents]Symbolic Statement of the Theory.
In attempting to represent these conditions of labour with accuracy, we shall find that there are no less than four quantities concerned; let us denote them as follows:—
t = time, or duration of labour.
l = amount of labour, as meaning the aggregate balance of pain accompanying it, irrespective of the produce.
x = amount of commodity produced.
v = total utility of that commodity.
The amount of commodity produced will be very different in different cases. In any one case the rate of production will be determined by dividing the whole quantity produced by the time of production, provided that the rate of production has been uniform; it will then be 
. But if the rate of production be variable, it can only be determined at any moment by comparing a small quantity of produce with the small portion of time occupied in its production. More strictly speaking, we must ascertain the ratio of an infinitely small quantity of produce to the corresponding infinitely small portion of time. Thus the rate of production is properly denoted by 
or at the limit by 
.
Again, the degree of painfulness of labour would be 
if it remained invariable; but as it is highly variable, we must again compare small increments, and 
or, at the limit, 
correctly represents the degree of painfulness of labour. But we must also take into account the fact that the utility of commodity is not constant. If a man works regularly twelve hours a day, he will produce more commodity than in ten hours; therefore the final degree of utility of his commodity, whether he consume it himself or whether he exchange it, will not be quite so high as when he produced less. This degree of utility is denoted, as before, by 
the ratio of the increment of utility to the increment of commodity.
The amount of reward of labour can now be expressed; for it is
that is to say, it is the product of the ratio of the commodity produced to the time, multiplied by the ratio of the utility to the amount of produce. Thus, the last two hours of work in the day generally gives less reward, both because less produce is then created in proportion to the time spent, and because that produce is less necessary and useful to one who makes enough to support himself in the other ten hours.
We can now ascertain the length of time which should be selected as the most advantageous term of labour. A free labourer endures the irksomeness of work because the pleasure he expects to receive, or the pain he expects to ward off, by means of the produce, exceeds the pain of exertion. When labour itself is a worse evil than that which it saves him from, there can be no motive for further exertion, and he ceases. Therefore he will cease to labour just at the point when the pain becomes equal to the corresponding pleasure gained; and we thus have t defined by the equation
In this, as in the other questions of Economics, all depends upon the final increments, and we have expressed in the above formula the final equivalence of labour and utility. A man must be regarded as earning all through his hours of labour an excess of utility; what he produces must be considered not merely the exact equivalent of the labour he gives for it, for it would be, in that case, a matter of indifference whether he laboured or not. As long as he gains, he labours, and when he ceases to gain, he ceases to labour.
In some cases, as in some kinds of machine labour, the rate of production is uniform, or nearly so, and by choice of suitable units may be made equal to unity; the result may then be put more simply in this way. Labour may be considered as expended in successive small quantities, Dl, each lasting, for instance, for a quarter of an hour; the corresponding benefit derived from the labour will then be denoted by Du. Now, so long as Du exceeds in amount of pleasure the negative quantity or pain of Dl, the difference of sign being disregarded, there will be gain inducing to continued labour. Were Du to fall below Dl, there would be more harm than good in labouring; therefore, the boundary between labour and inactivity will be defined by the equality of Du and Dl, and at the limit we have the equation
[Back to Table of Contents] Dimensions of Labour.
If I have correctly laid down, in preceding chapters, the Theory of Dimensions of Utility and Value, there ought not to be much difficulty in stating the similar theory as regards Labour. We might in fact treat labour as simply one case of disutility or negative utility, that is as pain, or at any rate as a generally painful balance of pleasure and pain, endured in the action of acquiring commodity. Thus its dimensions might be described as identical with those of utility; U would then denote intensity of labour, or degree of labour, just as it was used to denote degree of utility. If we measure labour with respect to the quantity of commodity produced, that is, if we make commodity the variable, then total amount of labour will be the integral of U dM, and the dimensions of amount of labour will be MU, identical with those of total utility.
If for any reasons of convenience we prefer to substitute a new symbol, specially appropriated to express the dimensions of labour, and say that intensity of labour is represented by E (Endurance), and total quantity of labour incurred in the production of certain commodity by ME, it must be remembered that the change is one of convenience only; U and E are essentially quantities of the same nature, and the difference, so far as there is any, arises from the fact that quantities symbolised by E will usually be negative as compared with those symbolised by U. Labour, however, is often measured and bought and sold by time, instead of by piecework or commodity produced; in this case, while E continues to express intensity of labour, ET will express the dimensions of amount of labour.
Rate of production will obviously possess the same dimensions as rate of consumption (p. 64), namely, MT-1, and this quantity forms a link between labour as measured by time and by produce; for ET × MT-1 = ME. It would be possible to invent various other economic quantities, such as acceleration of production, with the dimensions MT-2; but, until it is apparent how such quantities enter into economic theorems, it seems needless to consider them further.
[Back to Table of Contents]Balance between Need and Labour.
In considering this Theory of Labour an interesting question presents itself. Supposing that circumstances alter the relation of produce to labour, what effect will this have upon the amount of labour which will be exerted? There are two effects to be considered. When labour produces more commodity, there is more reward, and therefore more inducement to labour. If a workman can earn ninepence an hour instead of sixpence, may he not be induced to extend his hours of labour by this increased result? This would doubtless be the case were it not that the very fact of getting half as much more than he did before, lowers the utility to him of any further addition. By the produce of the same number of hours he can satisfy his desires more completely; and if the irksomeness of labour has reached at all a high point, he may gain more pleasure by relaxing that labour than by consuming more products. The question thus depends upon the direction in which the balance between the utility of further commodity and the painfulness of prolonged labour turns.
In our ignorance of the exact form of the functions either of utility or of labour, it will be impossible to decide this question in an à priori manner; but there are a few facts which indicate in which direction the balance does usually turn. Statements are given by Porter, in his Progress of the Nation,1 which show that when a sudden rise took place in the prices of provisions in the early part of this century, workmen increased their hours of labour, or, as it is said, worked double time, if they could obtain adequate employment. Now, a rise in the price of food is really the same as a decrease of the produce of labour, since less of the necessaries of life can be acquired in exchange for the same money wages. We may conclude, then, that English labourers enjoying little more than the necessaries of life, will work harder the less the produce; or, which comes to the same thing, will work less hard as the produce increases.
Evidence to the like effect is found in the general tendency to reduce the hours of labour at the present day, owing to the improved real wages now enjoyed by those employed in mills and factories. Artisans, mill-hands, and others, seem generally to prefer greater ease to greater wealth, thus proving that the painfulness of labour varies so rapidly as easily to overbalance the gain of utility. The same rule seems to hold throughout the mercantile employments. The richer a man becomes, the less does he devote himself to business. A successful merchant is generally willing to give a considerable share of his profits to a partner, or to a staff of managers and clerks, rather than bear the constant labour of superintendence himself. There is also a general tendency to reduce the hours of labour in mercantile offices, due to increased comfort and opulence.
It is obvious, however, that there are many intricacies in a matter of this sort. It is not always possible to graduate work to the worker's liking; in some businesses a man who insisted on working only a few hours a day would soon have no work to do. In the professions of law, medicine, and the like, it is the reputation of enjoying a large practice which attracts new clients. Thus a successful barrister or physician generally labours more severely as his success increases. This result partly depends upon the fact that the work is not easily capable of being performed by deputy. A successful barrister, too, soon begins to look forward to the extrinsic rewards of a high judicial or parliamentary position. But the case of an eminent solicitor, architect, or engineer is one where the work is to a great extent done by employees, and done without reference to social or political rewards, and where yet the most successful man endures the most labour, or rather is most constantly at work. This indicates that the irksomeness of the labour does not increase so as to over-balance the utility of the increment of reward. In some characters and in some occupations, in short, success of labour only excites to new exertions, the work itself being of an interesting and stimulating nature. But the general rule is to the contrary effect, namely, that a certain success disinclines a man to increased labour. It may be added that in the highest kinds of labour, such as those of the philosopher, scientific discoverer, artist, etc., it is questionable how far great success is compatible with ease; the mental powers must be kept in perfect training by constant exertion, just as a racehorse or an oarsman needs to be constantly exercised.
It is evident that questions of this kind depend greatly upon the character of the race. Persons of an energetic disposition feel labour less painfully than their fellowmen, and, if they happen to be endowed with various and acute sensibilities, their desire of further acquisition never ceases. A man of lower race, a negro for instance, enjoys possession less, and loathes labour more; his exertions, therefore, soon stop. A poor savage would be content to gather the almost gratuitous fruits of nature, if they were sufficient to give sustenance; it is only physical want which drives him to exertion. The rich man in modern society is supplied apparently with all he can desire, and yet he often labours unceasingly for more. Bishop Berkeley, in his Querist,1 has very well asked, "Whether the creating of wants be not the likeliest way to produce industry in a people? And whether, if our (Irish) peasants were accustomed to eat beef and wear shoes, they would not be more industrious?"
[Back to Table of Contents]Distribution of Labour.
We now come to consider the conditions which regulate the comparative amounts of different commodities produced in a country. Theoretically speaking, we might regard each person as capable of producing various commodities, and dividing his labour according to certain rules between the different employments; it would not be impossible, too, to mention cases where such division does take place. But the result of commerce and the division of labour is usually to make a man find his advantage in performing one trade only; and I give the formulæ as they would apply to an individual, only because they are identical in general character with those which apply to a whole nation.
Suppose that an individual is capeble of producing two kinds of commodity. His sole object, of course, is to produce the greatest amount of utility; but this will depend partly upon the comparative degrees of utility of the commodities, and partly on his comparative facilities for producing them. Let x and y be the respective quantities of the commodities already produced, and suppose that he is about to apply more labour; on which commodity shall he spend the next increment of labour?—Plainly, on that which will yield most utility. Now, if an increment of labour, Dl, will yield either of the increments of commodity Dx and Dy, the ratios of produce to labour, namely,
will form one element in the problem. But to obtain the comparative utilities of these commodities, we must multiply respectively by
For instance,
expresses the amount of utility which can be obtained by producing a little more of the first commodity; if this be greater than the same expression for the other commodity, it would evidently be best to make more of the first commodity until it ceased to yield any excess of utility. When the labour is finally distributed, we must have the increments of utility from the several employments equal, and at the limit we have the equation—
When this equation holds, there can be no motive for altering or regretting the distribution of labour, and the utility produced is at its maximum.
There are in this problem two unknown quantities, namely, the two portions of labour appropriated to the two commodities. To determine them, we require one other equation in addition to the above. If we put
l = l1 + l2,
we have still an unknown quantity to determine, namely, l; but the principles of labour (pp. 172-177) now give us an equation. Labour will be carried on until the increment of utility from any of the employments just balances the increment of pain. This amounts to saying that du, the increment of utility derived from the first employment of labour, is equal in amount of feeling to dl1, the increment of labour by which it is obtained. This gives us then the further equation—
If we pay regard to sign, indeed, we must remember that dl is, when measured in the same scale as du, intrinsically negative, but inasmuch as it is given in exchange for du, which is received, it will in this respect be taken negatively, and thus the above equation holds true.1
[Back to Table of Contents]Relation of the Theories of Labour and Exchange.
It may tend to give the reader confidence in the preceding theories when he finds that they lead directly to the well-known law, as stated in the ordinary language of economists, that value is proportional to the cost of production. As I prefer to state the same law, it is to the effect that the ratio of exchange of commodities will conform in the long run to the ratio of productiveness, which is the reciprocal of the ratio of the costs of production. The somewhat perplexing relations of these quantities will be fully explained in the next section, but we may now proceed to prove the above result symbolically.
To simplify our expressions, let us substitute for the rate of production
the symbol 
. Then 
express the relative quantities of two different commodities produced by an increment of labour, and we have the following equation, identical with that on page 184.
Let us suppose that the person to whom it applies is in a position to exchange with other persons. The conditions of production will now, in all probability, be modified. For x the quantity of our commodity may perhaps be increased to x + x1, and y diminished to y - y1, by an exchange of the quantities x1 and y1. If this be so, we shall, as shown in the Theory of Exchange, have the equation
Our equation of production will now be modified, and become
But this equation has its first member identical with the first member of the equation of exchange given above, so that we may at once deduce the all-important equation
The reader will remember that
expresses the ratio of produce to labour; thus we have proved that commodities will exchange in any market in the ratio of the quantities produced by the same quantity of labour. But as the increment of labour considered is always the final one, our equation also expresses the truth, that articles will exchange in quantities inversely as the costs of production of the most costly portions, i.e. the last portions added. This result will prove of great importance in the theory of Rent.
Let it be observed that, in uniting the theories of exchange and production, a complicated double adjustment takes place in the quantities of commodity involved. Each party adjusts not only its consumption of articles in accordance with their ratio of exchange, but it also adjusts its production of them. The ratio of exchange governs the production as much as the production governs the ratio of exchange. For instance, since the Corn Laws have been abolished in England, the effect has been, not to destroy the culture of wheat, but to lessen it. The land less suitable to the growth of wheat has been turned to grazing or other purposes more profitable comparatively speaking. Similarly the importation of hops or eggs or any other article of food does not even reduce the quantity raised here, but prevents the necessity for resorting to more expensive modes of increasing the supply. It is not easy to express in words how the ratios of exchange are finally determined. They depend upon a general balance of producing power and of demand as measured by the final degree of utility. Every additional supply tends to lower the degree of utility; but whether that supply will be forthcoming from any country depends upon its comparative powers of producing different commodities.
Any very small tract of country cannot appreciably affect the comparative supply of commodities: it must therefore adjust its productions in accordance with the general state of the market. The county of Bedford, for instance, would not appreciably affect the markets for corn, cheese, or cattle, whether it devoted every acre to corn or to grazing. Therefore the agriculture of Bedfordshire will have to be adapted to circumstances, and each field will be employed for arable or grazing land according as prevailing prices render one employment or the other more profitable. But any large country will affect the markets as well as be affected. If the whole habitable surface of Australia, instead of producing wool, could be turned to the cultivation of wine, the wool market would rise, and the wine market fall. If the Southern States of America abandoned cotton in favour of sugar, there would be a revolution in these markets. It would be inevitable for Australia to return to wool and the American States to cotton. These are illustrations of the reciprocal relation of exchange and production.
[Back to Table of Contents]Relations of Economic Quantities.
I hope that I may sometime be able, in a future and much larger work, to explain in detail the results which can be derived from the mathematical theory expounded in the previous pages. This essay gives them only in an implicit manner. But, before leaving the subject of exchange, it may be well without delay to point out how the results so far set forth connect themselves with the recognised doctrines of political economy. For the sake of accuracy I have avoided the use of the word value; the expression cost of production, so continually recurring in most economical treatises, is also here conspicuous by its absence. The reader then, unless he be very careful, may be thrown into some perplexity, when he proceeds to compare my results with those familiar to him elsewhere. I will therefore proceed to trace out the connections between the several quantitative expressions, which most commonly occur in discussions concerning value, exchange, and production.
In the first place, the ratio of exchange is the actual numerical ratio of the quantities given and received. Let X and Y be the names of the commodities: x and y the quantities of them respectively exchanged. Then the ratio of exchange is that of y to x. But the value of a commodity in exchange is greater as the quantity received is less, so that the ratio of the quantities dealt with must be the reciprocal of the ratio of the values of the substances, meaning by value the value per unit of the commodity. Thus we may say
Value is of course very frequently estimated by price, that is, by the quantity of legal money for which the commodity may be exchanged. Price is indeed ambiguous in the same way as value; it means either the price of the whole quantity, or the price per unit of the quantity. Let p1 be the price per unit of X, and p2 the similar price of Y. Then it is apparent that y × p2 will be the whole price of y, and x × p1 will be the whole price of x. These two must be equal to each other, so that we get
Thus we find that, when price means price per unit, the quantities exchanged are reciprocally as the prices. When price means price of the whole quantity, the quantities given and received are always of equal price.
Turning now to the production of commodity, it is sufficiently obvious that the cost of production, so far as this expression can be accurately interpreted, varies as the reciprocal of the degree of productiveness. The rate of wages remaining constant, the cost per unit of commodity must of course be lower as the quantity produced in return for a certain amount of wages is greater. Thus we may lay down the equation
Now, it was shown in pp. 186, 187 that the quantities exchanged are directly proportional to the degrees of productiveness, or
But the ratio of the values is the reciprocal of 
and the ratio of the costs of production is the reciprocal of the other member of the above equation. Thus it follows that
or, in other words, value is proportional to cost of production. As, moreover, the final degrees of utility of commodities are inversely as the quantities exchanged, it follows that the values per unit are directly proportional to the final degrees of utility.
As it is quite indispensable that the student of political economy should keep the relations of these quantities before his mind with perfect clearness, I repeat the results in several forms of statement. Thus we may group the ratios together—
We may state the matter more briefly in the following words:—The quantities of commodity given or received in exchange are directly proportional to the degrees of productiveness of labour applied to their production, and inversely proportional to the values and prices of those commodities and to their costs of production per unit, as well as to their final degrees of utility. I will even repeat the same statements once more in the form of a diagram—
| Quantities of Commodity exchanged vary | |
|---|---|
| directly as the quantities | inversely as their |
| produced by the same labour. | (1) Values. |
| (2) Prices. | |
| (3) Costs of production. | |
| (4) Final degrees of utility. | |
Various Cases of the Theory.
As we have now reached the principal question in Economics, it will be well to consider the meaning and results of our equations in some detail.
It will, in the first place, be apparent that the absolute facility of producing commodities will not determine the character and amount of trade. The ratio of exchange 
is not determined by 
nor by 
separately, but by their comparative magnitudes. If the producing power of a country were doubled, no direct effect would be produced upon the terms of its commerce provided that the increase were equal in all branches of production. This is a point of great importance, which was correctly conceived by Ricardo, and has been fully explained by J. S. Mill.
But though there is no such direct effect, it may happen that there will be an indirect effect through the variation in the degree of utility of different articles. When an increased amount of every commodity can be produced, it is not likely that the increase will be equally desired in each branch of consumption. Hence the degree of utility will fall in some cases more than in others. An alteration of the ratios of exchange must result, and the production of the less needed commodities will not be extended so much as in the case of the more needed ones. We might find in such instances new proofs that value depends not upon labour but upon the degree of utility.
It will also be apparent that nations possessing exactly similar powers of production cannot gain by mutual commerce, and consequently will not have any such commerce, however free from artificial restrictions. We get this result as follows:—Taking 
as before, to be the final ratios of productiveness in one country, and 
in a second, then, if the conditions of production are exactly similar, we have
But when a country does not trade at all, its labour and consumption is distributed according to the condition
Now, from these equations, it follows necessarily that
that is to say, the production and consumption already conform to the conditions of production of the second country, and will not undergo any alteration when trade with this country becomes possible.
This is the doctrine usually stated in works on Political Economy, and for which there are good grounds. But I do not think the statement will hold true if the conditions of consumption be very different in two countries. There might be two countries exactly similar in regard to their powers of producing beef and corn, and if their habits of consumption were also exactly similar, there would be no trade in these articles. But suppose that the first country consumed proportionally more beef, and the second more corn; then, if there were no trade, the powers of the soil would be differently taxed, and different ratios of exchange would prevail. Freedom of trade would cause an interchange of corn for beef. Thus I conclude that it is only where the habits of consumption, as well as the powers of production, are alike, that trade brings no advantage.
The general effect of foreign commerce is to disturb, to the advantage of a country, the mode in which it distributes its labour. Excluding from view the cost of carriage, and the other expenses of commerce, we must always have true
If, then, 
was originally less in proportion to 
than is in accordance with these equations, some labour will be transferred from the production of y to that of x until, by the increased magnitude of and the lessened magnitude of w equality is brought about.
As in the theory of exchange, so in the theory of production, any of the equations may fail, and the meaning is capable of interpretation. Thus, if the equation
cannot be established, it is impossible that the production of both commodities, y and x, can go on. One of them will be produced at an expenditure of labour constantly out of proportion to that at which it may be had by exchange. If we could not, for instance, import oranges from abroad, part of the labour of the country would probably be diverted from its present employment to raise them; but the cost of production would be always above that of getting them indirectly by exchange, so that free trade necessarily destroys such a wasteful branch of industry It is on this principle that we import the whole of our wines, teas, sugar, coffee, spices, and many other articles from abroad.
The ratio of exchange of any two commodities will be determined by a kind of struggle between the conditions of consumption and production; but here again failure of the equations may take place. In the all-important equations
expresses the ease with which we may make additions to y. If we find any means, by machinery or otherwise, of increasing y without limit, and with the same ease as before, we must, in all probability, alter the ratio of exchange 
in a corresponding degree. But if we could imagine the existence of a large population, within reach of the supposed country, whose desire to consume the quantity y1 never decreased, however large was the quantity available, then we should never have 
equal to 
and the producers of y would make large gains of the nature of rent.
Joint Production.
In one of the most interesting chapters of his Principles of Political Economy, Book III., chap. xvi., John Stuart Mill has treated of what he calls "Some peculiar Cases of Value." Under this title he refers to those commodities which are not produced by separate processes, but are the concurrent or joint results of the same operations. "It sometimes happens," he says, "that two different commodities have what may be termed a joint cost of production. They are both products of the same operation, or set of operations, and the outlay is incurred for the sake of both together, not part for one and part for the other. The same outlay would have to be incurred for either of the two, if the other were not wanted or used at all. There are not a few instances of commodities thus associated in their production. For example, coke and coal-gas are both produced from the same material, and by the same operation. In a more partial sense, mutton and wool are an example; beef, hides, and tallow; calves and dairy produce; chickens and eggs. Cost of production can have nothing to do with deciding the values of the associated commodities relatively to each other. It only decides their joint value.... A principle is wanting to apportion the expenses of production between the two." He goes on to explain that, since the cost of production principle fails us, we must revert to a law of value anterior to cost of production, and more fundamental, namely, the law of supply and demand.
On some other occasion I may perhaps more fully point out the fallacy involved in Mill's idea that he is reverting to an anterior law of value, the law of supply and demand, the fact being that in introducing the cost of production principle, he had never quitted the laws of supply and demand at all. The cost of production is only one circumstance which governs supply, and thus indirectly influences values.
Again, I shall point out that these cases of joint production, far from being "some peculiar cases," form the general rule, to which it is difficult to point out any clear or important exceptions. All the great staple commodities at any rate are produced jointly with minor commodities. In the case of corn, for instance, there are the straw, the chaff, the bran, and the different qualities of flour or meal, which are products of the same operations. In the case of cotton, there are the seed, the oil, the cotton waste, the refuse, in addition to the cotton itself. When beer is brewed the grains regularly return a certain price. Trees felled for timber yield not only the timber, but the loppings, the bark, the outside cuts, the chips, etc. No doubt the secondary products are often nearly valueless, as in the case of cinders, slag from blast furnaces, etc. But even these cases go to show all the more impressively that it is not cost of production which rules values, but the demand and supply of the products.
The great importance of these cases of joint production renders it necessary for us to consider how they can be brought under our theory. Let us suppose that there are two commodities, X and Y, yielded by one same operation, which always produces them in the same ratio, say of m of X to n of Y. It might seem at first sight as if this ratio would correspond to the ratio of the degrees of productiveness, as shown a few pages above, that we might say
and thus arrive at the conclusion that things jointly produced would always exchange in the ratio of productiveness. But this would be entirely false, because that equation can only be established when there is freedom of producing one or the other, at each application of a new increment of labour. It is the freedom of varying the quantities of each that allows of the produce being accommodated to the need of it, so that the ratio of the degrees of utility, of the degrees of productiveness, and of the quantities exchanged are brought to equality. But in cases of joint production there is no such freedom; the one substance cannot be made without making a certain fixed proportion of the other, which may have little or no utility.
It will easily be seen, however, that such cases are brought under our theory by simply aggregating together the utilities of the increments of the joint products. If dx cannot be produced without dy, these being the products of the same increment of labour, dl, then the ratio of produce to labour cannot be written otherwise than as
It is impossible to divide up the labour and say that so much is expended on producing X, and so much on Y. But we must estimate separately the utilities of dx and dy, by multiplying by their degrees of utility 
and 
and we then have the aggregate ratio of utility to labour as
It is plain that we have no equation arising out of these conditions of production, so that the ratio of exchange of X and Y will be governed only by the degrees of utility. But if we compare X and Y with a third commodity Z, as regards its production, we shall arrive at the equation
In other words, the increment of utility obtained by applying an increment of labour to the production of Z, must equal the sum of the increments of utility which would be obtained if the same increment of labour were applied to the joint production of X and Y. It is evident that the above equation taken alone gives us no information as to the ratios existing between the quantities dx,dy, and dz. Before we can obtain any ratios of exchange we must have the further equation between the degrees of utility of X and Y, namely,
As a general rule, however, any two processes of production will both yield joint products, so that the equation of productiveness will take the form of a sum of increments of utility on both sides, which we may thus write briefly—
Such an equation becomes then a kind of equation of condition of which the influence may be very slight regarding the ratio of exchange of any two of the commodities concerned. And if in some cases the terms on one side of such an equation are reduced to one or two, it is probably because the other increments of produce are nearly or quite devoid of utility. As in the cases of cinders, chips, sawdust, spent dyes, potato stalks, chaff, etc. etc., almost every process of industry yields refuse results, of which the utility is zero or nearly so. To solve the subject fully, however, we should have to admit negative utilities, as elsewhere explained, so that the increment of utility from any increment dl of labour would really take the form
du1 ± du2 ± du3 ±...
The waste products of a chemical works, for instance, will sometimes have a low value; at other times it will be difficult to get rid of them without fouling the rivers and injuring the neighbouring estates; in this case they are discommodities and take the negative sign in the equations.
[Back to Table of Contents]Over-production.
The theory of the distribution of labour enables us to perceive clearly the meaning of over-production in trade. Early writers on Economics were always in fear of a supposed glut, arising from the powers of production surpassing the needs of consumers, so that industry would be stopped, employment fail, and all but the rich would be starved by the superfluity of commodities. The doctrine is evidently absurd and self-contradictory. As the acquirement of suitable commodities is the whole purpose of industry and trade, the greater the supplies obtained the more perfectly industry fulfils its purpose. To bring about a universal glut would be to accomplish completely the aim of the economist, which is to maximise the products of labour. But the supplies must be suitable—that is, they must be in proportion to the needs of the population. Over-production is not possible in all branches of industry at once, but it is possible in some as compared with others. If, by miscalculation, too much labour is spent in producing one commodity, say silk goods, our equations will not hold true. People will be more satiated with silk goods than cotton, woollen, or other goods. They will refuse, therefore, to purchase them at ratios of exchange corresponding to the labour expended. The producers will thus receive in exchange goods of less utility than they might have acquired by a better distribution of their labour.
In extending industry, therefore, we must be careful to extend it proportionally to all the requirements of the population. The more we can lower the degree of utility of all goods by satiating the desires of the purchasers the better; but we must lower the degrees of utility of different goods in a corresponding manner, otherwise there is an apparent glut and a real loss of labour.
[Back to Table of Contents]Limits to the Intensity of Labour.
I have mentioned (p. 170) that labour may vary either in duration or intensity, but have yet paid little attention to the latter circumstance. We may approximately measure the intensity of labour by the amount of physical force undergone in a certain time, although it is the pain attending that exertion of force which is the all-important element in Economics. Interesting laws have been or may be detected connecting the amount of work done with the intensity of labour. Even where these laws have not been ascertained, long experience has led men, by a sort of unconscious process of experimentation and inductive reasoning, to select that rate of work which is most advantageous.
Let us take such a simple kind of work as digging. A spade may be made of any size, and if the same number of strokes be made in the hour, the requisite exertion will vary nearly as the cube of the length of the blade. If the spade be small the fatigue will be slight, but the work done will also be slight. A very large spade, on the other hand, will do a great quantity of work at each stroke, but the fatigue will be so great that the labourer cannot long continue at his work. Accordingly, a certain medium-sized spade is adopted, which does not overtax a labourer and prevent him doing a full day's work, but enables him to accomplish as much as possible. The size of a spade should depend partly upon the tenacity and weight of the material, and partly upon the strength of the labourer. It may be observed that, in excavating stiff clay, navvies use a small strong spade; for ordinary garden purposes a larger spade is employed; for shovelling loose sand or coals a broad capacious shovel is used; and a still larger instrument is employed for removing corn, malt, or any loose light powder.
In most cases of muscular exertion the weight of the body or of some limb is of great importance. If a man be employed to carry a single letter, he really moves a weight of say a hundred and sixty pounds for the purpose of conveying a letter weighing perhaps half an ounce. There will be no appreciable increase of labour if he carries twenty letters, so that his efficiency will be multiplied twenty times. A hundred letters would probably prove a slight burden, but there would still be a vast gain in the work done. It is obvious, however, that we might go on loading a postman with letters until the fatigue became excessive; the maximum useful result would be obtained with the largest load which does not severely fatigue the man, and trial soon decides the weight with considerable accuracy.
The most favourable load for a porter was investigated by Coulomb, and he found that most work could be done by a man walking upstairs without any load, and raising his burden by means of his own weight in descending. A man could thus raise four times as much in a day as by carrying bags on his back with the most favourable load. This great difference doubtless arises from the muscles being perfectly adapted to raising the human body, whereas any additional weight throws irregular or undue stress upon them. Charles Babbage, also, in his admirable Economy of Manufactures, has remarked on this subject, and has pointed out that the weight of some limb of the body is an element in all calculations of human labour.
"The fatigue produced on the muscles of the human frame," says Babbage, "does not altogether depend on the actual force employed in each effort, but partly on the frequency with which it is exerted. The exertion necessary to accomplish every operation consists of two parts: one of these is the expenditure of force which is necessary to drive the tool or instrument; and the other is the effort required for the motion of some limb of the animal producing the action. In driving a nail into a piece of wood, one of these is lifting the hammer, and propelling its head against the nail; the other is raising the arm itself, and moving it in order to use the hammer. If the weight of the hammer is considerable, the former part will cause the greatest portion of the exertion. If the hammer is light, the exertion of raising the arm will produce the greatest part of the fatigue. It does therefore happen that operations requiring very trifling force, if frequently repeated, will tire more effectually than more laborious work. There is also a degree of rapidity beyond which the action of the muscles cannot be pressed."1
It occurred to me, some time since, that this was a subject admitting of interesting inquiry, and I tried to determine, by several series of experiments, the relation between the amount of work done by certain muscles and the rate of fatigue. One series consisted in holding weights varying from one pound to eighteen pounds in the hand while the arm was stretched out at its full length. The trials were two hundred and thirty-eight in number, and were made at intervals of at least one hour, so that the fatigue of one trial should not derange the next. The average number of seconds during which each weight could be sustained was found to be as follows:—
| Weight in pounds . . | 18 | 14 | 10 | 7 | 4 | 2 | 1 |
| Time in seconds... | 15 | 32 | 60 | 87 | 148 | 219 | 321. |
If the arm had been thus employed in any kind of useful work, we should have estimated the useful effect by the product of the weight sustained and the time. The results would be as follows, in pounds- seconds:—
| Weight... | 18 | 14 | 10 | 7 | 4 | 2 | 1 |
| Useful effect... | 266 | 455 | 603 | 612 | 592 | 438 | 321. |
The maximum of useful effect would here appear to be about seven pounds, which is about the weight usually chosen for dumb-bells and other gymnastic instruments. Details of the other series of experiments are described in an article in Nature (30th June 1870, vol. ii. p. 158).
I undertook these experiments as a mere illustration of the mode in which some of the laws forming the physical basis of Economics might be ascertained. I was unaware that Professor S. Haughton had already, by experiment, arrived at a theory of muscular action, communicated to the Royal Society in 1862. I was gratified to find that my entirely independent results proved to be in striking agreement with his principles, as was pointed out by Professor Haughton in two articles in Nature.1
I am not aware that any exact experiments upon walking or marching have been made, but, as Professor Haughton has remarked to me, they might easily be carried out in the movements of an army. It would only be necessary, on each march which is carried up to the limits of endurance, to register the time and distance passed over. Had we a determination of the exact relations of time, space, and fatigue, it would be possible to solve many interesting problems. For instance, if one person has to overtake another, what should be their comparative rates of walking? Assuming the fatigue to increase as the square of the velocity multiplied by the time, we easily obtain an exact solution, showing that the total fatigue will be least when one person walks twice as quickly as he whom he wishes to overtake.
In different cases of muscular exertion we shall find different problems to solve. The most advantageous rate of marching will greatly depend upon whether the loss of time or the fatigue is the most important. To march at the rate of four miles an hour would soon occasion enormous fatigue, and could only be resorted to under circumstances of great urgency. The distance passed over would bear a much higher ratio to the fatigue at the rate of three, or even two and a half miles an hour. But, if the speed were still further reduced, a loss of strength would again arise, owing to that expended in merely sustaining the body, as distinguished from that of moving it forward.
The Economics of Labour will constantly involve questions of this kind. When a work has to be completed in a brief space of time, workmen may be incited by unusual reward to do far more than their usual amount of work; but so high a rate would not be profitable in other circumstances. The fatigue always rapidly increases when the speed of work passes a certain point, so that the extra result is far more costly in reality. In a regular and constant employment the greatest result will always be gained by such a rate as allows a workman each day, or each week at the most, to recover all fatigue and recommence with an undiminished store of energy.
[Back to Table of Contents]CHAPTER VI
THEORY OF RENT
[Back to Table of Contents]Accepted Opinions concerning Rent.
THE general correctness of the views put forth in preceding chapters derives great probability from their close resemblance to the Theory of Rent, as it has been accepted by English writers for nearly a century. It has not been usual to state this theory in mathematical symbols, and clumsy arithmetical illustrations have been employed instead; but it is easy to show that the fluxional calculus is the branch of mathematics which most correctly applies to the subject.
The Theory of Rent was first discovered and clearly stated by James Anderson in a tract published in 1777, and called An Inquiry into the Nature of the Corn Laws, with a view to the Corn Bill proposed for Scotland. An extract from this work may be found in MacCulloch's edition of the Wealth of Nations, p. 453, giving a most clear explanation of the effect of the various fertility of land, and showing that it is not the rent of land which determines the price of its produce, but the price of the produce which determines the rent of the land. The following passage must be given in Anderson's own words:—1
"... In every country there is a variety of soils, differing considerably from one another in point of fertility. These we shall at present suppose arranged into different classes, which we shall denote by the letters A, B, C, D, E, F, etc., the class A comprehending the soils of the greatest fertility, and the other letters expressing different classes of soils, gradually decreasing in fertility as you recede from the first. Now, as the expense of cultivating the least fertile soil is as great or greater than that of the most fertile field, it necessarily follows that if an equal quantity of corn, the produce of each field, can be sold at the same price, the profit on cultivating the most fertile soil must be much greater than that of cultivating the others; and as this continues to decrease as the sterility increases, it must at length happen that the expense of cultivating some of the inferior soils will equal the value of the whole produce."
The theory really rests upon the principle, which I have called the Law of Indifference, that for the same commodity in the same market there can only be one price or ratio of exchange. Hence, if different qualities of land yield different amounts of produce to the same labour, there must be an excess of profit in some over others. There will be some land which will not yield the ordinary wages of labour, and which will, therefore, not be taken into cultivation, or if, by mistake, it is cultivated, will be abandoned. Some land will just pay the ordinary wages; better land will yield an excess, so that the possession of such land will become a matter of competition, and the owner will be able to exact as rent from the cultivators the whole excess above what is sufficient to pay the ordinary wages of labour.
There is a secondary origin for rent in the fact, that if more or less labour and capital be applied to the same portion of land, the produce will not increase proportionally to the amount of labour. It is quite impossible that we could go on constantly increasing the yield of one farm without limit, otherwise we might feed the whole country upon a single farm. Yet there is no definite limit; for, by better and better culture, we may always seem able to raise a little more. But the last increment of produce will come to bear a smaller and smaller ratio to the labour required to produce it, so that it soon becomes, in the case of all land, undesirable to apply more labour.
MacCulloch has given, in his edition of the Wealth of Nations,1 a supplementary note, in which he explains, with the utmost clearness and scientific accuracy, the nature of the theory. This note contains by far the best statement of the theory, as it seems to me, and I will therefore quote his recapitulation of the principles which he establishes.
"1. That if the produce of land could always be increased in proportion to the outlay on it, there would be no such thing as rent.
"2. That the produce of land cannot, at an average, be increased in proportion to the outlay, but may be indefinitely increased in a less proportion.
"3. That the least productive portion of the outlay, which, speaking generally, is the last, must yield the ordinary profits of stock. And
"4. That all which the other portions yield more than this, being above ordinary profits, is rent."
A most satisfactory account of the theory is also given in James Mill's Elements of Political Economy, a work which I never read without admiring its brief, clear, and powerful style. James Mill constantly uses the expression dose of capital. "The time comes," he says, "at which it is necessary either to have recourse to land of the second quality, or to apply a second dose of capital less productively upon land of the first quality." He evidently means by a dose of capital a little more capital, and though the name is peculiar, the meaning is simply that of an increment of capital. The number of doses or increments mentioned is only three, but this is clearly to avoid prolixity of explanation. There is no reason why we should not consider the whole capital divided into many more doses. The same general law which makes the second dose less productive than the first, will make a hundredth dose, speaking generally, less productive than the preceding ninety-ninth dose. Theoretically speaking, there is no need or possibility of stopping at any limit. A mathematical law is in theory always continuous, so that the doses considered are indefinitely small and indefinitely numerous. I consider, then, that James Mill's mode of expression is exactly equivalent to that which I have adopted in earlier parts of this book. As mathematicians have invented a precise and fully recognised mode of expressing doses or increments, I know not why we should exclude language from Economics which is found convenient in all other sciences. It is mere pedantry to insist upon calling that a dose in Economics, which in all the other sciences is called by the perfectly established and expressive term increment.
The following are James Mill's general conclusions as to the nature of Rent.1 "In applying capital, either to lands of various degrees of fertility, or in successive doses to the same land, some portions of the capital so employed are attended with a greater produce, some with a less. That which yields the least yields all that is necessary for reimbursing and rewarding the capitalist. The capitalist will receive no more than this remuneration for any portion of the capital which he employs, because the competition of others will prevent him. All that is yielded above this remuneration the landlord will be able to appropriate. Rent, therefore, is the difference between the return yielded to that portion of the capital which is employed upon the land with the least effect, and that which is yielded to all the other portions employed upon it with a greater effect."
[Back to Table of Contents]Symbolic Statement of the Theory.
The accepted Theory of Rent, as given above, needs little or no alteration to adapt it to expression in mathematical symbols. For doses or increments of capital I shall substitute increments of labour, partly because the functions of capital remain to be considered in the next chapter, and partly because James Mill, J. S. Mill, and MacCulloch hold the application of capital to be synonymous with the application of labour. This assumption is implied in James Mill's statement (p. 13); it is expressly stated in J. S. Mill's First Fundamental Proposition concerning the Nature of Capital;1 and MacCulloch adds a footnote2 to make it clear, that as all capital was originally produced by labour, the application of additional capital is the application of additional labour. "Either the one phrase or the other may be used indiscriminately." This doctrine is in itself altogether erroneous, but it will not be erroneous to assume as a mode of simplifying the problem that the increments of labour applied are equally assisted by capital. It is a separate and subsequent problem to determine how rent or interest arises when the same labour is assisted by different quantities of capital.
I shall suppose that a certain labourer, or, what comes to exactly the same thing, a body of labourers, expend labour on several different pieces of ground. On what principle will they distribute their labour between the several pieces? Let us imagine that a certain amount has been spent upon each, and that another small portion, Dl, is going to be applied. Let there be two pieces of land, and let Dx1, Dx2, be the increments of produce to be expected from the pieces respectively. They will naturally apply the labour to the land which yields the greatest result. So long as there is any advantage in one use of labour over another, the most advantageous will certainly be adopted. Therefore, when they are perfectly satisfied with the distribution made, the increment of produce to the same labour will be equal in each case; or we have 
To attain scientific accuracy, we must decrease the increments infinitely, and then we obtain the equation—
Now 
represents the ratio of produce, or the productiveness of labour, as regards the last increment of labour applied. We may say, then, that whenever a labourer or body of labourers distribute their labour over pieces of land with perfect economy, the final ratios of produce to labour will be equal.
We may now take into account the general law, that when more and more labour is applied to the same piece of land, the produce ultimately does not increase proportionately to the labour. This means that the function dx/dl diminishes without limit towards zero after x has passed a certain quantity. The whole produce of a piece of land is x, the whole labour spent upon it is l; and x varies in some way as l varies, never decreasing when l increases. We may say, then, that x is a function of l; let us call it Pl. When a little more labour is expended, the increment of produce dx is dPl, and 
is the final rate of production, the same as was previously denoted by 
.
In the Theory of Labour it was shown that no increment of labour would be expended unless there was sufficient recompense in the produce, but that labour would be expended up to the point at which the increment of utility exactly equals the increment of pain incurred in acquiring it. Here we find an exact definition of the amount of labour which will be profitably applied.
It was also shown that the last increment of labour is the most painful, so that if a person is recompensed for the last increment of labour which he applies to land by the rate of production 
, it follows that all the labour he applies might be recompensed sufficiently at the same rate. The whole labour is l, so that if the recompense were equal over the whole, the result would be 
. Consequently, he obtains more than the necessary return to labour by the amount
or, as we may write it,
Pl-l · P'l,
in which P'l is the differential coefficient of Pl, or the final rate of production. This expression represents the advantage he derives from the possession of land in affording him more profit than other methods of employing his labour. It is therefore the rent which he would ask before yielding it up to another person, or equally the rent which he would be able and willing to pay if hiring it from another.
The same considerations apply to every piece of land cultivated. When the same person or body of labourers cultivates several pieces, P'l will be of the same magnitude in each case, but the quantities of labour, and possibly the functions of labour, will be different. Thus with two pieces of land the rent may be represented as
P1l1 + P2l2 - (l1 + l2) P1'l1;
or, speaking generally of any number of pieces, it is the sum of the quantities of the form Pl, minus the sum of the quantities of the form l.P'l.
[Back to Table of Contents]Illustrations of the Theory.
It is very easy to illustrate the Theory of Rent by diagrams. For, let distances along the line ox denote quantities of labour, and let the curve apc represent the variation of the rate of production, so that the area of the curve will be the measure of the produce. Thus when labour has been applied to the amount om, the produce will correspond to the area apmo. Let a small new increment of labour, mm', be applied, and
suppose the rate of production equal over the whole of the increment. Then the small parallelogram, pp'm'm, will be the produce. This will be proportional in quantity to pm, so that the height of any point of the curve perpendicularly above a point of the line ox represents the rate of production at that point in the application of labour.
If we further suppose that the labourer considers his labour, mm', repaid by the produce pm', there is no reason why any other part of his labour should not be repaid at the same rate. Drawing, then, a horizontal line, rpq, through the point p, his whole labour, om, will be repaid by the produce represented by the area orpm. Consequently, the overlying area, rap, is the excess of produce which can be exacted from him as rent, if he be not himself the owner of the land.
Imagining the same person to cultivate another piece of land, we might take the curve, bqc, to represent its productiveness. The same rate of production will repay the labourer in this case as in the last, so that the intersection of the same horizontal line, rpq, with the curve, will determine the final point of labour, n. The area, rn, will be the measure of the sufficient recompense to the whole labour, on, spent upon the land; and the excess of produce or rent will be the area, rbq. In a similar manner, any number of pieces of land might be considered. The figure might have been drawn so that the curves would rise on leaving the initial line oy, indicating that a very little labour will have a poor rate of production; and that a certain amount of labour is requisite to develop the fertility of the soil. This may often or always be the case, as a considerable quantity of labour is generally requisite in first bringing land into cultivation, or merely keeping it in a fit state for use. The laws of rent depend on the undoubted principle, that the curves always ultimately decline towards the base line ox, that is, the final rate of production always ultimately sinks towards zero.
[Back to Table of Contents]CHAPTER VII
THEORY OF CAPITAL
[Back to Table of Contents]The Function of Capital.
IN considering the nature and principles of Capital, we enter a distinct branch of our subject. There is no close or necessary connection between the employment of capital and the processes of exchange. Both by the use of capital and by exchange we are enabled vastly to increase the sum of utility which we enjoy; but it is conceivable that we might have the advantages of capital without those of exchange. An isolated man like Alexander Selkirk might feel the benefit of a stock of provisions, tools, and other means of facilitating industry, although cut off from traffic with other men. Economics, then, is not solely the science of Exchange or Value: it is also the science of Capitalisation.
The views which I shall endeavour to establish on this subject are in fundamental agreement with those adopted by Ricardo; but I shall try to put the Theory of Capital in a more simple and consistent manner than has been the case with some later economists. We are told, with perfect truth, that capital consists of wealth employed to facilitate production; but when economists proceed to enumerate the articles of wealth constituting capital, they obscure the subject. "The capital of a country," says Mac-Culloch,1 "consists of those portions of the produce of industry existing in it which may be directly employed either to support human beings, or to facilitate production." Professor Fawcett again says:2 "Capital is not confined to the food which feeds the labourers, but includes machinery, buildings, and, in fact, every product due to man's labour which can be applied to assist his industry; but capital which is in the form of food does not perform its functions in the same way as capital that is in the form of machinery: the one is termed circulating capital, the other fixed capital."
The notion of capital assumes a new degree of simplicity as soon as we recognise that what has been called a part is really the whole. Capital, as I regard it, consists merely in the aggregate of those commodities which are required for sustaining labourers of any kind or class engaged in work. A stock of food is the main element of capital; but supplies of clothes, furniture, and all the other articles in common daily use are also necessary parts of capital. The current means of sustenance constitute capital in its free or uninvested form. The single and all-important function of capital is to enable the labourer to await the result of any long-lasting work,—to put an interval between the beginning and the end of an enterprise.
Not only can we, by the aid of capital, erect large works which would otherwise have been impossible, but the production of articles which would have been very costly in labour may be rendered far more easy. Capital enables us to make a great outlay in providing tools, machines, or other preliminary works, which have for their sole object the production of some important commodity, and which will greatly facilitate production when we enter upon it.
[Back to Table of Contents]Capital is concerned with Time.
Several economists have clearly perceived that the time elapsing between the beginning and end of a work is the difficulty which capital assists us to surmount. Thus James Mill has said: "If the man who subsists on animals cannot make sure of his prey in less than a day, he cannot make sure of his prey in less than a day, he cannot have less than a whole day's subsistence in advance. If hunting excursions are undertaken which occupy a week or a month, subsistence for several days may be required. It is evident, when men come to live upon those productions which their labour raises from the soil, and which can be brought to maturity only once in the year, that subsistence for a whole year must be laid up in advance."1
Much more recently, Professor Hearn has said, in his admirable work entitled Plutology:1 "The first and most obvious mode in which capital directly operates as an auxiliary of industry is to render possible the performance of work which requires for its completion some considerable time. In the simplest agricultural operations there is the seed-time and the harvest. A vineyard is unproductive for at least three years before it is thoroughly fit for use. In gold mining there is often a long delay, sometimes even of five or six years, before the gold is reached. Such mines could not be worked by poor men unless the storekeepers gave the miners credit, or, in other words, supplied capital for the adventure. But, in addition to this great result, capital also implies other consequences which are hardly less momentous. One of these is the steadiness and continuity that labour thus acquires. A man, when aided by capital, can afford to remain at his work until it is finished, and is not compelled to leave it incomplete while he searches for the necessary means of subsistence. If there were no accumulated fund upon which the labourer could rely, no man could remain for a single day exclusively engaged in any other occupation than those which relate to the supply of his primary wants. Besides these wants, he should also from time to time search for the materials on which he was to work."
These passages imply, as it seems to me, a clear insight into the nature and purposes of capital, except that the writers have not with sufficient boldness followed out the consequences of their notion. If we take a comprehensive view of the subject, it will be seen that not only the chief but the sole purpose of capital is as above described. Capital simply allows us to expend labour in advance. Thus, to raise corn we need to turn over the surface of the soil. If we proceed straight to the work, and use the implements with which nature has furnished us—our fingers—we should spend an enormous amount of painful labour with very little result. It is far better, therefore, to spend the first part of our labour in making a spade or other implement to assist the rest of our labour. This spade represents so much labour which has been invested, and so far spent; but if it lasts three years, its cost may be considered as repaid gradually during those three years. This labour, like that of digging, has for its object the raising of corn, and the only essential difference is that it has to precede the production of corn by a longer interval. The average interval of time for which labour will remain invested in the spade is half of the three years. Similarly, if we possess a larger capital, and expend it in making a plough, which will last for twenty years, we invest at the beginning a great deal of labour which is only gradually repaid during those twenty years, and which is therefore, on the average, invested for about ten years.
It is true that in modern industry we should seldom or never find the same man making the spade or plough, and afterwards using the implement. The division of labour enables me, with much advantage, to expend a portion of my capital in purchasing the implement from some one who devotes his attention to the manufacture, and probably expends capital previously in facilitating the work. But this does not alter the principles of the matter. What capital I give for the spade merely replaces what the manufacturer had already invested in the expectation that the spade would be needed. Exactly the same considerations may be applied to much more complicated applications of capital. The ultimate object of all industry engaged with cotton is the production of cotton goods. But the complete process of producing those goods is divided into many parts; and it is necessary to begin the spending of labour a long time before any goods can be finished.
In the first place, labour will be required to till the land which is to bear the cotton plants, and probably two years at least will elapse between the time when the ground is first broken and the time when the cotton reaches the mills. A cotton mill, again, must be a very strong and durable structure, and must contain machinery of a very costly character, which can only repay its owner by a long course of use. We might spin and weave cotton goods as in former times, or as it is done in Cashmere, with a very small use of capital; but then the labour required would be enormously greater in proportion to the produce. It is far more economical in the end to spend a vast amount of labour and capital in building a substantial mill and filling it with the best machinery, which will then go on working with unimpaired efficiency for thirty years or more. This means that, in addition to the labour spent in superintending the machines at the moment when goods are produced, a great quantity of labour has been spent from one to thirty years in advance, or, on the average, fifteen years in advance. This expenditure is repaid by an annuity of profit extending over those thirty years.
The interval elapsing between the first exertion of labour and the enjoyment of the result is further increased by any time during which the raw material may lie in warehouses before reaching the machines; and by the time employed in distributing the goods to retail dealers, and through them to the consumers. It may even happen that the consumer finds it desirable to keep a certain stock on hand, so that the time when the real object of the goods is fulfilled becomes still further deferred. During this time, also, capital seems to me to be invested, and only as actual utilisation takes place is expenditure repaid by corresponding utility enjoyed.
I would say, then, in the most general manner, that whatever improvements in the supply of commodities lengthen the average interval between the moment when labour is exerted and its ultimate result or purpose accomplished, such improvements depend upon the use of capital. And I would add that this is the sole use of capital. Whenever we overlook the irrelevant complications introduced by the division of labour and the frequency of exchange, all employments of capital resolve themselves into the fact of time elapsing between the beginning and the end of industry.
[Back to Table of Contents]Quantitative Notions concerning Capital.
One main point which has to be clearly brought before the mind in this subject is the difference between the amount of capital invested and the amount of investment of capital. The first is a quantity of one dimension only—the quantity of capital; the second is a quantity of two dimensions, namely, the quantity of capital, and the length of time during which it remains invested. If one day's labour remains invested for two years, the capital is only that equivalent to one day; but it is locked up twice as long as if it were invested for only one year. Now all questions in which we consider the most advantageous employment of capital turn upon the length of investment quite as much as upon the amount. The same capital will serve for twice as much industry if it be absorbed or invested for only half the time.
The amount of investment of capital will evidently be determined by multiplying each portion of capital invested at any moment by the length of time for which it remains invested. One pound invested for five years gives the same result as five pounds invested for one year, the product being five pound-years. Most commonly, however, investment proceeds continuously or at intervals, and we must form clear notions on the subject. Thus, if a workman be employed during one year on any work, the result of which is complete, and enjoyed at the end of that time, the absorption of capital will be found by multiplying each day's wages by the days remaining till the end of the year, and adding all the results together. If the daily wages be four shillings, then we have
We may also represent the investment by a diagram such as Fig. X. The length along the line ox indicates the duration of investment, and the height
attained at any point, a, is the amount of capital invested. But it is the whole area of the rectangles up to any point, a, which measures the amount of investment during the time oa.
The whole result of continued labour is not often consumed and enjoyed in a moment; the result generally lasts for a certain length of time. We must then conceive the capital as being progressively uninvested. Let us, for sake of simple illustration, imagine the labour of producing the harvest to be continuously and equally expended between the first of September in one year and the same day in the next. Let the harvest be then completely gathered, and its consumption begin immediately and continue equally during the succeeding twelve months. Then the amount of investment of capital will be represented by the area of an isosceles triangle, as in Fig. XI., the base of which corresponds to two years
of duration. Now the area of a triangle is equal to the height multiplied by half the base; and as the height represents the greatest amount invested, that upon the first of September, when the harvest is gathered; half the base, or one year, is the average time of investment of the whole amount.
In the 37th proposition of the first book of Euclid it is proved that all triangles upon the same base and between the same parallels are equal in area. Hence we may draw the conclusion that, provided capital be invested and uninvested continuously and in simple proportion to the time, we need only regard the greatest amount invested and the greatest time of investment. Whether it be all invested suddenly, and then gradually withdrawn; or gradually invested and suddenly withdrawn; or gradually invested and gradually withdrawn; the amount of investment will be in every case the greatest amount of capital multiplied by half the time elapsing from the beginning to the end of the investment.
[Back to Table of Contents]Expression for Amount of Investment.
To render our notions of the subject still more exact and general, let us resort once more to mathematical symbols.
Let Dp = amount of capital supposed to be invested in the time Dt; let t = time elapsing before its result is enjoyed, the enjoyment taking place in an interval of time Dt, which may be disregarded in comparison with t. Then t · Dp is the amount of investment; and if the investment is repeated, the sum of the quantities of the nature of t · Dp, or, in the customary mode of expression, St · Dp is the total amount of investment. But it will seldom be possible to assign each portion of result to an exactly corresponding portion of labour. Cotton goods are due to the aggregate industry of those who tilled the ground, grew the cotton, plucked, transported, cleaned, spun, wove, and dyed it; we cannot distinguish the moment when each labourer's work is separately repaid. To avoid this difficulty, we must fix on some moment of time when the whole transaction is closed, all labour upon the ground repaid, the mill and machinery worn out and sold, and the cotton goods consumed. Let t now denote the time elapsing from any moment up to this final moment of closing the accounts. Let Dp be as before an increment of capital invested, and let Dq be an increment of capital uninvested by the sale of the products and their enjoyment by the consumer. Thus it will be pretty obvious that the sum of the quantities t · Dp, less by the sum of the quantities t · Dq will be the total investment of capital, or expressed in symbols 
Dimensions of Capital, Credit and Debit.
As the subject presents itself to me at present, I apprehend that capital is to be regarded simply as commodity. If so, the dimension of capital will be represented by M, and the amount of investment of capital, possessing the additional dimension of time, will have the symbol MT. How then are we to determine the quantitative nature of what Senior called Abstinence, that temporary sacrifice of enjoyment which is essential to the existence of capital? Senior thus explicitly defined what he meant by the word:1 "By the word Abstinence, we wish to express that agent, distinct from labour and the agency of nature, the concurrence of which is necessary to the existence of capital, and which stands in the same relation to profit as labour does to wages." He goes on to explain that abstinence, though usually accompanying labour, is distinct from it. A careful consideration of Senior's remarks shows that in reality abstinence is the endurance of want, the abstaining from the enjoyment of utility which might be enjoyed. Now the degree or intensity of want is measured by the degree of utility of commodity if it were consumed. Great degree of utility simply means great want, so that one dimension of abstinence must be U, and time being also obviously an element of abstinence, the required symbolic statement of its dimensions will be UT. This result satisfactorily corresponds with Senior's definition, for he says that abstinence is to profit as labour is to wages. Now profit or interest is clearly symbolised by M, and wages also by M, both consisting simply of quantities of commodity. Thus UT bears just the same relation to M that ET does to M, for E signifies the degree of painfulness of labour, and can barely be distinguished from U, except in sign.
The relation of abstinence, UT, to total utility, MU, also confirms our result. For if we convert abstinence into satisfaction, by giving a supply of commodity for consumption, this action is symbolically represented by multiplying UT into MT-1, which yields MU, or utility.
It will need no argument to show that the dimension of debit and credit, having regard only to what is borrowed and owed, will be the dimension of commodity simply, or M. According to the practice of commerce, a contract of debt is a contract to return a certain physically defined quantity of a specified substance, such as an ounce of gold, a ton of pig-iron, a hogshead of palm oil. No attempt is made to define quantities of utility, so that the debt when repaid shall yield utility equal to what it possessed when lent. The borrower and lender either take their chance about this, or provide for it in the rate of interest to be paid. It is equally obvious that in another sense the amount of credit or debit will be proportional to the duration of the operation, and will have the dimensions MT.
[Back to Table of Contents]Effect of the Duration of Work.
Perhaps the most interesting point in the Theory of Capital is the advantage arising from the rapid performance of work, if it is capable of being done with convenience and with the same ultimate result. To investigate this point, suppose that 
= the whole amount of wages which it is requisite to pay in building a house, and that this does not alter when we vary, within certain limits, the time employed in the work, denoted by t. If the work goes on continuously, we shall, during each unit of time, have an amount invested equal to the tth part of ****w. The whole amount of investment of capital will therefore be represented by the area of a triangle whose base is t and height w; that is, the investment is ½ tw. Thus when the whole expenditure is ultimately the same, the amount of investment is simply proportional to the time. The result would be more serious if the accumulation of compound interest during the time were taken into account; but the consideration of compound interest would render the formulæ very complex, and is not requisite for the purpose in view.
We must clearly distinguish the case treated above, in which the amount of labour is the same, but spread over a longer time, from other cases where the labour increases in proportion to the time. The investment of capital, then, grows in an exceedingly rapid manner. Neglecting the first cost of tools, materials, and other preparations, let the first day's labour cost a; during the second day this remains invested, and the amount of capital a is added; on each following day a like addition is made. The amount of capital invested is evidently
| At beginning | of second | day | a, |
| At beginning | of third | day | a + a, |
| At beginning | of fourth | day | a + a + a; |
and so on. If the work lasts during n + 1 days, the total amount of investment of capital will be
a + 2 a + 3 a + 4 a +... n a.
The sum of the series is
which increases by a term involving the square of the time. The employment of capital thus grows in proportion to the triangular numbers
1, 3, 6, 10, 15, 21, etc.
If we regard the investment as taking place continuously, the whole absorption of capital is represented
by the area of a right-angled triangle (Fig. XII.), in which ob1, b1, b2, b2b3, etc., are the successive units of time. The heights of the lines a1b1, a2b2 represent the amounts invested at the ends of the times. The daily investment being a, the total amount of investment will be
, increasing as the square of the time.
Cases of this kind continually occur, as in sinking a deep mine, of which the requisite depth cannot be previously known with accuracy. Any large work, such as a breakwater, an embankment, the foundations of a great bridge, a dock, a long tunnel, the dredging of a channel, involves a problem of a similar nature; for it is seldom known what amount of labour and capital will be required; and if the work lasts much longer than was expected, the result is usually a financial disaster.
[Back to Table of Contents]Illustrations of the Investment of Capital.
The time during which capital remains invested, and the circumstances of its investment and reproduction, are exceedingly various in different employments. If a person plants cabbages, they will be ready in the course of a few months, and the labour of planting and tending them, together with a part of the labour of preparing and manuring the soil, yields its results with very little delay. In planting a forest tree, however, a certain amount of labour is expended, and no result obtained until after the lapse of thirty, forty, or fifty years. The first cost of enclosing, preparing, and planting a plantation is considerable; and though, after a time, the loppings and thinnings of the trees repay the cost of superintendence and repairs, yet the absorption of capital is great, and we may thus account for the small amount of planting which goes on. The ageing of wine is a somewhat similar case. A certain amount of labour is expended without result for ten or fifteen years, and the cost of storage is incurred during the whole time. To estimate the real cost of the articles at the end of the time, we must, in all such cases, add compound interest, and this grows in a rapid manner. Every pound invested at the commencement of a business becomes 1·63 pounds at the end of ten years, 11·47 pounds at the end of fifty years, and no less than 131·50 pounds at the end of a century, the rate of interest being taken at five per cent. Thus it cannot be profitable to store wine for fifty years, unless it become about twelve times as valuable as it was when new. It cannot pay to plant an oak and let it live a century, unless the timber then repays the cost of planting 132 times.
If an annual charge, however small, has to be incurred (for instance, the cost of storage and superintendence), the expense mounts up in a still more alarming manner. Thus, if the cost of any investment is one pound per annum, the amount invested, with compound interest at five per cent, becomes 12·58 pounds at the end of ten years, 209·35 pounds at the end of fifty years, and the enormous amount of 2610·03 at the end of a century. We shall almost always have to take into account both the original and continuous cost of an investment. Thus if a stock of wine worth £100 be laid by for fifty years, and the cost of storage be £1 per annum, the total cost at the end of the time will be £1147·0 on account of original cost, and £209·35 for storage, or in all £1356·35.
It is to be feared that the rapid accumulation of compound interest is often overlooked in estimating the cost of public works and other undertakings of considerable duration. A great fort, breakwater, or canal (the Caledonian Canal, for instance) is often not completed for twenty years after its commencement, and in the meantime it may be of little or no use. Suppose that its cost has been £10,000 each year; then the aggregate cost would seem to be £200,000, but allowing for interest at five per cent it is really £330,000. The French engineer and economist, Minard,1 fully understood this point of finance, and showed that in the case of some public works, such as the great digue of Cherbourg harbour, and canals, the execution of which is allowed sometimes to drag on for half a century before any adequate result is returned, the real cost is incomparably greater than it is represented to be by merely stating the sums of money expended. In some cases, such as the first canal of Saint Quentin, a work, after being long prosecuted, is abandoned, and the loss by first cost and interest becomes enormous. The Guernsey Harbour is a case in point, and the English dockyards would supply abundance of similar facts.
An interesting example of the investment of capital occurs in the case of gold and silver, a large stock of which is maintained either in the form of money, or plate and jewellery. Labour is spent in the digging or mining of the metals, which is gradually repaid by the use or satisfaction arising from the possession of the metals during the whole time for which they continue in use. Hence the investment of capital extends over the average duration of the metals. Now, if the stock of gold requires one per cent of its amount to maintain it undiminished, it will be apparent that each particle of gold remains in use 100 years on the average; if ½ per cent is sufficient, the average duration will be 200 years. We may state the result thus:
| Loss of gold or silver annually. | Average duration of each particle in use. |
|---|---|
| 1 per cent | 100 years |
| ½ per cent | 200 years |
| ¼ per cent | 400 years |
| 1/10 per cent | 1000 years |
The wear and loss of the precious metals in a civilised country is probably not more than 
part annually, including plate, jewellery, and money in the estimate, so that the average investment will be for 200 years. It is curious that, if we regard a quantity of gold as wearing away annually by a fixed percentage of what remains, the duration of some part is infinite, and yet the average duration is finite. Some of the gold possessed by the Romans is doubtless mixed with what we now possess; and some small part of it will be handed down as long as the human race exists.
Fixed and Circulating Capital.
Economists have long been accustomed to distinguish capital into the two kinds, fixed and circulating. Adam Smith called that circulating which passes from hand to hand, and yields a revenue by being parted with. The fact of being frequently exchanged is, however, an accidental circumstance which leads to no results of importance. Ricardo altered the use of the terms, applying the name circulating to that which is frequently destroyed and has to be reproduced. He says unequivocally:1 "In proportion as fixed capital is less durable, it approaches to the nature of circulating capital. It will be consumed, and its value reproduced in a shorter time, in order to preserve the capital of the manufacturer." Accepting this doctrine, and carrying it out to the full extent, we must say that no precise line can be drawn between the two kinds. The difference is one of amount and degree. The duration of capital may vary from a day to several hundred years; the most circulating is the least durable; the most fixed the most durable.
[Back to Table of Contents]Free and Invested Capital.
I believe that the clear explanation of the doctrine of capital requires the use of a term free capital, which has not been hitherto recognised by economists. By free capital I mean the wages of labour, either in its transitory form of money, or its real form of food and other necessaries of life. The ordinary sustenance requisite to support labourers of all ranks when engaged upon their work is really the true form of capital. It is quite in agreement with the ordinary language of commercial men to say, not that a factory, or dock, or railway, or ship, is capital, but that it represents so much capital sunk in the enterprise. To invest capital is to spend money, or the food and maintenance which money purchases, upon the completion of some work. The capital remains invested or sunk until the work has returned profit, equivalent to the first cost, with interest.
Much clearness would result from making the language of Economics more nearly coincident with that of commerce. Accordingly, I would not say that a railway is fixed capital, but that capital is fixed in the railway. The capital is not the railway, but the food of those who made the railway. Abundance of free capital in a country means that there are copious stocks of food, clothing, and every article which people insist upon having—that, in short, everything is so arranged that abundant subsistence and conveniences of every kind are forth-coming without the labour of the country being much taxed to provide them. In such circumstances it is possible that a part of the labourers of the country can be employed on works of which the utility is distant, and yet no one will feel scarcity in the present.
[Back to Table of Contents]Uniformity of the Rate of Interest.
A most important principle of this subject is, that free capital can be indifferently employed in any branch or kind of industry. Free capital, as we have just seen, consists of a suitable assortment of all kinds of food, clothing, utensils, furniture, and other articles which a community requires for its ordinary sustenance. Men and families consume much the same kind of commodities, whatever may be the branch of manufacture or trade by which they earn a living. Hence there is nothing in the nature of free capital to determine its employment to one kind of industry rather than another. The very same wages, whether we regard the money wages, or the real wages purchased with the money, will support a man whether he be a mechanic, a weaver, a coal miner, a carpenter, a mason, or any other kind of labourer.
The necessary result is, that the rate of interest for free capital will tend to and closely attain uniformity in all employments. The market for capital is like all other markets: there can be but one price for one article at one time. It is a case of the Law of Indifference (p. 90). Now the article in question is the same, so that its price must be the same. Accordingly, as is well known, the rate of interest, when freed from considerations of risk, trouble, and other interfering causes, is the same in all trades; and every trade will employ capital up to the point at which it just yields the current interest. If any manufacturer or trader employs so much capital in supporting a certain amount of labour that the return is less than in other trades, he will lose; for he might have obtained the current rate by lending it to other traders.
[Back to Table of Contents]General Expression for the Rate of Interest.
We may obtain a general expression for the rate of interest yielded by capital in any employment provided that we may suppose the produce for the same amount of labour to vary as some continuous function of the time elapsing between the expenditure of the labour and the enjoyment of the result. Let the time in question be t, and the produce for the same amount of labour the function of t denoted by Ft, which may be supposed always to increase with t. If we now extend the time to t + Dt, the produce will be F (t + Dt), and the increment of produce F (t + Dt) - Ft. The ratio which this increment bears to the increment of investment of capital will determine the rate of interest. Now, at the end of the time t, we might receive the product Ft, and this is the amount of capital which remains invested when we extend the time by Dt. Hence the amount of increased investment of capital is Dt · Ft; and, dividing the increment of produce by this last expression, we have
When we reduce the magnitude of Dt infinitely, the limit of the first factor of the above expression is the differential coefficient of Ft, so that we find the rate of interest to be represented by
The interest of capital is, in other words, the rate of increase of the produce divided by the whole produce; but this is a quantity which must rapidly approach to zero, unless means can be found of continually maintaining the rate of increase. Unless a body moves with a rapidly increasing speed, the space it moves over in any unit of time must ultimately become inconsiderable compared with the whole space passed over from the commencement. There is no reason to suppose that industry, generally speaking, is capable of returning any such vastly increasing produce from the greater application of capital. Every new machine or other great invention will usually require a fixation of capital for a certain average time, and may be capable of paying interest upon it; but when this average time is reached, it fails to afford a return to more prolonged investments.
To take an instance, let us suppose that the produce of labour in some case is proportional to the interval of abstinence t; then we have say Ft = a · t, in which a is an unknown constant. The differential coefficient F't is now a; and the rate of interest
or
or
; or the rate of interest varies inversely as the time of investment.
[Back to Table of Contents]Dimension of Interest.
The formula which we obtained in the preceding section has been subjected to close criticism by an eminent mathematician, who proposed several alternative formulæ, but finally accepted my solution of the question as correct. As Professor Adamson, however, has also raised some objections to the formula, it seems desirable to explain its meaning and mode of derivation more fully than was done in the first edition.
In the first place, as regards the theory of dimensions the formula is clearly correct. The rate of interest expresses the ratio which the annual sum paid per annum for the loan of capital bears to the capital. The interest and the capital are quantities of the same nature, their ratio being an abstract number. Dividing by length of time rate of interest will have the dimension T -1.
Or we may put it in this way—Interest is paid per annum, or per month, or per other unit of time, and the less the magnitude of this unit, the less must be the numerical expression of the rate of interest. Simple interest at five per cent per annum is 0.416... per cent per month, and so on. Hence time enters negatively, and the dimension of the rate of interest will be T -1. Or, again, we may state it thus symbolically—The capital advanced may be taken as having the dimension M; the annual return has the dimensions MT. Dividing the former by the latter we obtain
Now the formula
clearly agrees with this result; for the denominator is a certain unknown function of the time of advance of the capital t. We may assume that it can be expressed in a finite series of the powers of t, and the numerator, being the differential coefficient of the same function, will be of one degree of power less than Ft. Hence the dimensions of the formula will be
It must be carefully remembered that it is the rate of interest which has the dimension T -1, not interest itself, which, being simply commodity of some kind, has the dimension of commodity, namely M, of the same nature, and having the same dimensions.
The function of capital is simply this, that labour which would produce certain commodity m1, if that commodity were needed immediately for the satisfaction of wants, is applied so as to produce m2 after the lapse of the time t. The reason for this deferment is that m2 usually exceeds m1, and the difference or interest m2 - m1 is commodity having the same dimensions as m1. Hence the rate of interest, apart from the question of time, would be m2 - m1 divided by m1, and the quantities being of the same nature, the ratio will be an abstract number devoid of dimensions. But the time for which the results of labour are foregone is as important a matter as the quantity of commodity. The amount of deferment is m1t, so that the rate of interest is m2 - m1 divided by m1t, which will have the dimension T -1.
Exactly the same result would be obtained, however, if we regarded the use of capital from a different point of view. Capital and deferment of consumption are not needed only in order to increase production, that is to say, the manufacture of goods; they are needed also to equalise consumption, and to allow commodity to be consumed when its utility is at the highest point. Now, when certain commodity is consumed within an interval of time, the utility produced will, as we have seen, possess the dimensions MUT -1 T, or MU. Suppose that instead of being consumed within that interval, the commodity is held in hand for a time before being consumed at all. Then the amount of deferment of utility will be proportional both to the interval of time over which it is deferred, and to the utility which is deferred. Thus the amount of deferment will have the dimensions MUT. The increase of utility due to deferment will clearly have the same dimensions as were previously determined, namely MU. Hence the ratio of this increase to the amount of deferment will have the dimensions 
or T -1, and this result corresponds with the dimension of the rate of interest as otherwise reached.
Peacock on the Dimensions of Interest.
The need of some care in forming our conceptions of these quantities is strikingly illustrated by the fact that not quite fifty years ago so profound and philosophic a mathematician as the late Dean Peacock completely misapprehended the matter. In the first edition of his celebrated and invaluable Treatise on Algebra, published in 1830, he gives (§111, p. 91) the interest of money as an example of a quantity of three dimensions, and one which may be represented by a solid. He says: "If p represent the principal or sum of money lent or forborne, r the rate of interest (of £1 for one year), and t the number of years, then the interest accumulated or due will be represented by prt; for if r be the interest of £1 for one year, pr will be the interest of a sum of money denoted by p for one year, and therefore prt will be the amount of this interest in t years, no interest being reckoned upon interest due: such would be the result according to the principles of Arithmetical Algebra.
"If we now suppose prt represented respectively by lines which form the adjacent edges of a parallelopipedon, the solid thus formed will represent the interest accumulated or due: in other words, it will represent whatever is represented by the general formula prt when specific values and significations are given to its symbols: for in whatever manner we may suppose any one of the symbols of prt to vary, the solid will vary in the same proportion.
"The lines which we assume to represent units of p,r, and t, are perfectly arbitrary, whether they are made equal to each other or not: this is clearly the case with p and t, which are quantities of a different nature: and the third quantity is likewise different from the other two, being an abstract numerical quantity: for it expresses the relation between the interest of £1 and £1, or between the interest of £100 and £100, which is the quotient of the division of one quantity by another of the same nature: thus, if the interest be five per cent, then 
: if four per cent, then 
: and similarly in other cases: the line, therefore, which is assumed to represent the abstract unit to which r is referred, is independent of the lines which represent units of p and of t, and may therefore be assumed at pleasure, equally with those lines.
"The lines which represent p and t form a rectangular area, which is the geometrical representation of their product: the third quantity r, being merely numerical, may either be represented by a line, as in the case just considered, when a solid parallelopipedon is made the representative of prt: or we may consider the area pt as representing the product prt when r = 1, and that this product in any other case is represented by a rectangle which bears to the rectangle pt the ratio of r to 1: this may be effected by increasing or diminishing one of the sides of the rectangle in the required ratio: the product prt may therefore be correctly represented either by a solid or an area, when one of the factors is an abstract number."
The conclusion at which he arrives is a lame one, for he thinks that the same kind of quantity may be represented indifferently by a solid or an area. The fact is that Peacock confused a product of three factors with a quantity of three dimensions. He took these dimensions as if they were, say M = money, R = rate of interest, and T = time. If we simply multiply these together, as Peacock first does, we get a quantity apparently of three dimensions, MRT. If, according to Peacock's subsequent idea, we take R to be an abstract numerical quantity, then we have two dimensions left, namely, MT. He overlooks the fact that the rate of interest involves time negatively, although he describes r as "the rate of interest (of £1 for one year)." Correctly stated, the dimensions of prt, the quantity of interest are M × T -1 × T or M, that is simply the dimension of the money advanced.
If you say, for instance, that the simple interest of £300 at five per cent per annum for five years is £75, there remains no reference in this result to time: £75 is simply £75, and is of exactly the same nature as the £300 which bore the interest.
That Peacock subsequently discovered error, or at least difficulty, in this section, is rendered probable by the fact that he omitted the illustration altogether in his second edition; but he does not, so far as I have observed, give any explanation.
[Back to Table of Contents]Tendency of Profits to a Minimum.
It is one of the favourite doctrines of economists since the time of Adam Smith, that as society progresses and capital accumulates, the rate of profit, or more strictly speaking, the rate of interest, tends to fall. The rate will always ultimately sink so low, they think, that the inducements to further accumulation will cease. This doctrine is in striking agreement with the result of the somewhat abstract analytical investigation given above. Our formula for the rate of interest shows that unless there be constant progress in the arts, the rate must tend to sink towards zero, supposing accumulation of capital to go on. There are sufficient statistical facts, too, to confirm this conclusion historically. The only question that can arise is as to the actual cause of this tendency.
Adam Smith vaguely attributed it to the competition of capitalists, saying: "The increase of stock which raises wages, tends to lower profit. When the stocks of many rich merchants are turned into the same trade, their mutual competition naturally tends to lower its profit; and when there is a like increase of stock in all the different trades carried on in the same society, the same competition must produce the same effect in them all."1
Later economists have entertained different views. They attributed the fall of interest to the rise in the cost of labour. The produce of labour, they said, is divided between capitalists and labourers, and if it is necessary to give more to labour, there must be less left to capital, and the rate of profit will fall. I shall discuss the validity of this theory in the final chapter, and will only remark here, that it is not in agreement with the view which I have ventured to take concerning the origin of interest. I consider that interest is determined by the increment of produce which it enables a labourer to obtain, and is altogether independent of the total return which he receives for this labour. Our formula (p. 245) shows that the rate of interest will be greater as the whole produce Ft is less, if the advantage of more capital, measured by F't, remains unchanged. In many ill-governed countries, where the land is wretchedly tilled, the average produce is small, and yet the rate of interest is high, simply because the want of security prevents the due supply of capital: hence more capital is urgently needed, and its price is high. In America and the British Colonies the produce is often high, and yet interest is high, because there is not sufficient capital accumulated to meet all the demands. In England and other old countries the rate of interest is generally lower because there is an abundance of capital, and the urgent need of more is not actually felt.
I conceive that the returns to capital and labour are independent of each other. If the soil yields little, and capital will not make it yield more, then both wages and interest will be low, provided that the capital be not attracted away to more profitable employment. If the soil yields much, and capital will make it yield more, then both wages and interest will be high; if the soil yields much, and capital will not make it yield more, then wages will be high and interest low, unless the capital finds other investments. But the subject is much complicated by the interference of rent. When we speak of the soil yielding much, we must distinguish between the whole yield and the final rate of yield. In the Western States of America the land yields a large total, and all at a high final rate, so that the labourer enjoys the result. In England there is a large total yield, but a small final yield, so that the landowner receives a large rent and the labourer small wages. The more fertile land having here been long in cultivation, the wages of the labourer are measured by what he can earn by cultivating sterile land which it only just pays to take into cultivation.
[Back to Table of Contents]Advantage of Capital to Industry.
We must take great care not to confuse the rate of interest on capital with the whole advantage which it confers on industry. The rate of interest depends on the advantage of the last increment of capital, and the advantages of previous increments may be greater in almost any ratio. In considering the laws of utility, we found that an article possessing an immensely great total utility, for instance corn or water, might have a very low final degree of utility, because our need of it was almost entirely satisfied; yet the ratio of exchange always depends upon the final, not the previous degree of utility. The case is the same with capital. Some capital may be indispensable to a manufacture; hence the benefit conferred by the capital is indefinitely great, and were there no more capital to be had, the rate of interest which could be demanded, assuming the article manufactured to be necessary, would be almost unlimited. But as soon as ever a larger supply of capital becomes available, the prior benefit of capital is overlooked. As free capital is always the same in quality, the second portion may be made to replace the first if needful: hence capitalists can never exact from labourers the whole advantages which their capital confers—they can exact only a rate determined by the advantage of the last increment. A lender of capital cannot say to a borrower who wants £3000: "I know that £1000 is indispensable to your business, and therefore will charge you 100 per cent interest upon it; for the second £1000, which is less necessary, I will charge twenty per cent; and as upon the third £1000 you can only earn the common profit, I will only ask five percent." The answer would be, that there are many people only earning five per cent on their capital who would be glad to lend enough at a small advance of interest; and it is a matter of indifference who is the lender.
The general result of the tendency to uniformity of interest is, that employers of capital always get it at the lowest prevailing rate; they always borrow the capital which is least necessary to others, and
either the labourers themselves, or the public generally as consumers, gather all the excess of advantage. To illustrate this result, let distances along the line ox, in Fig. XIII., mark quantities of capital employing in any branch of industry a fixed number of labourers. Let the area of the curve denote the whole produce of labour and capital. Thus to the capital, on, results a produce measured by the area of the curvilinear figure between the upright lines oy and qn. But the amount of increased produce which would be due to an increment of capital would be measured by the line qn, so that this will represent F't (p. 245). The interest of the capital will be its amount, on, multiplied by the rate qn, or the area of the rectangle oq. The remainder of the produce, pqry, will belong to the labourer. But had less capital been available, say not more than om, its rate of interest would have been measured by pm, the amount of interest by the rectangle op, while the labourer must have remained contented with the smaller share, psy. I will not say that the above diagram represents with strict accuracy the relations of capital, produce, wages, rate of interest, and amount of interest; but it may serve roughly to illustrate their relations. I see no way of representing exactly the theory of capital in the form of a diagram.
[Back to Table of Contents]Are Articles in the Consumers' hands Capital?
The views of the nature of capital expressed in this chapter generally agree with those entertained by Ricardo and various other economists; but there is one point in which the theory leads me to a result at variance with the opinions of almost all writers. I feel quite unable to adopt the opinion that the moment goods pass into the possession of the consumer they cease altogether to have the attributes of capital. This doctrine descends to us from the time of Adam Smith, and has generally received the undoubting assent of his followers. The latter, indeed, have generally omitted all notice of such goods, treating them as if no longer under the view of the economist. Adam Smith, although he denied the possessions of a consumer the name of capital, took care to enumerate them as part of the stock of the community. He divides into three portions the general stock of a country, and while the second and third portions are fixed and circulating capital, the first is described as follows:—1
"The first is that portion which is reserved for immediate consumption, and of which the characteristic is, that it affords no revenue or profit. It consists in the stock of food, clothes, household furniture, etc., which have been purchased by their proper consumers, but which are not yet entirely consumed. The whole stock of mere dwelling-houses too subsisting at any one time in the country make a part of this first portion. The stock that is laid out in a house, if it is to be the dwelling-house of the proprietor, ceases from that moment to serve in the function of a capital, or to afford any revenue to its owner. A dwelling-house, as such, contributes nothing to the revenue of its inhabitant; and though it is, no doubt, extremely useful to him, it is as his clothes and household furniture are useful to him, which, however, make a part of his expense, and not of his revenue."
MacCulloch, indeed, in his edition of the Wealth of Nations, p. 121, has remarked upon this passage, that "the capital laid out in building houses for such persons is employed as much for the public advantage as if it were vested in the tools or instruments they make use of in their respective businesses." He appears, in fact, to reject the doctrine, and it is surprising that economists have generally acquiesced in Adam Smith's view, though it leads to manifest contradictions. It leads to the absurd conclusion that the very same thing fulfilling the very same purposes will be capital or not according to its accidental ownership. To procure good port wine it is necessary to keep it for a number of years, and Adam Smith would not deny that a stock of wine kept in the wine merchant's possession for this purpose is capital, because it yields him revenue. If a consumer buys it when new, and keeps it to improve, it will not be capital, although it is evident that he gains the same profit as the merchant by buying it at a lower price. If a coal merchant lays in a stock of coal when cheap, to sell when dear, it is capital; but if a consumer lays in a stock, it is not.
Adam Smith's views seem to be founded upon a notion that capital ought to give an annual revenue or increase of wealth like a field yields a crop of corn or grass. Speaking of a dwelling-house, he says: "If it is to be let to a tenant for rent, as the house itself can produce nothing, the tenant must always pay the rent out of some other revenue, which he derives either from labour, or stock, or land. Though a house, therefore, may yield a revenue to its proprietor, and thereby serve in the function of a capital to him, it cannot yield any to the public, nor serve in the function of a capital to it, and the revenue of the whole body of the people can never be in the smallest degree increased by it. Clothes and house-hold furniture, in the same manner, sometimes yield a revenue, and thereby serve in the function of a capital to particular persons. In countries where masquerades are common, it is a trade to let out mas-querade dresses for a night. Upholsterers frequently let furniture by the month or by the year. Undertakers let the furniture of funerals by the day and by the week. Many people let furnished houses, and get a rent, not only for the use of the house, but for that of the furniture. The revenue, however, which is derived from such things, must always be ultimately drawn from some other source of revenue."1
This notion that people live upon a kind of net revenue flowing in to them appears to be derived from the old French economists, and plays no part in modern Economics. Nothing is more requisite than a dwelling-house, and if a person cannot hire a house at the required spot, he must find capital to build it. I think that no economist would refuse to count among the fixed capital of the country that which is sunk in dwelling-houses. Capital is sunk in farming that we may have bread, in cotton mills that we may be clothed, and why not in houses that we may be lodged? If land yields an annual revenue of corn and wool, milk, beef, and other necessaries, houses yield a revenue of shelter and comfort. The sole end of all industry is to satisfy our wants; and if capital is requisite to supply shelter, and furniture and useful utensils, as it undoubtedly is, why refuse it the name which it bears in all other employments?
Can we deny that the property of a hotel-keeper is capital and yields a revenue to its owner? Yet it is invested in pots and pans, and beds, and all kinds of common furniture. In America it is not uncommon for people to live all their lives in hotels or boarding-houses; and we might readily conceive the system to advance until no one would undertake housekeeping except as a profession. Now if we allow to what is invested in hotels, hired furnished houses, lodgings, and the like, the nature of capital, I do not see how we can refuse it to common houses. We should thus be led into all kinds of absurdities.
For instance, if two people live in their own houses, these are not, according to present opinion, capital; if they find it convenient to exchange houses and pay rent each to the other, the houses are capital. At great watering-places like Brighton it is a regular business to lease houses, fill them with furniture, and then let them for short periods as furnished houses: surely it is capital which is embarked in the trade. If a private individual happens to own a furnished house which he does not at the time want, and lets it, can we refuse to regard his house and furniture as capital? Whenever one person provides the articles and another uses them and pays rent, there is capital. Surely, then, if the same person uses and owns them, the nature of the things is not fundamentally different. There is no need for a money payment to pass; but every person who keeps accurate accounts should debit those accounts with an annual charge for interest and depreciation on what he has invested in house and furniture. Housekeeping is an occupation involving wages, capital and interest, like any other business, except that the owner consumes the whole result.
By accepting this view of the subject, we shall avoid endless difficulties. What, for instance, shall we say to a theatre? Is it not the product of capital? Can it be erected without capital? Does it not return interest, if successful, like any cotton mill or steam vessel? If the economist agrees to this, he must allow, on similar grounds, that a very large part of the aggregate capital of the country is invested in theatres, hotels, schools, lecture rooms, and institutions of various kinds which do not belong to the industry of the country, taken in a narrow sense, but which none the less contribute to the wants of its inhabitants, which is the sole object of all industry.
I may add that even the food, clothes, and many other possessions of extensive classes are often indubitable capital; they are bought upon credit, and interest is undoubtedly paid for the capital sunk in them by the dealers. There is hardly, I suppose, a man of fashion in London who walks in his own clothes, and the tailors find in the practice a very profitable investment for capital. Except among the poorer classes, and often among them, food is seldom paid for until after it is consumed. Interest must be paid one way or another upon the capital thus absorbed. Whether or not these articles in the consumers' hands are capital, at any rate they have capital invested in them—that is, labour has been spent upon them of which the whole benefit is not enjoyed at once.
I might also point out at almost any length, that the stock of food, clothing, and other requisite articles of subsistence in the country are a main part of capital according to the statements of J. S. Mill, Professor Fawcett, and most other economists. Now what does it really matter if these articles happen to lie in the warehouses of traders or in private houses, so long as there is a stock? At present it is the practice for farmers and corn merchants to hold the produce of the harvest until the public buys and consumes it. Surely the stock of corn is capital. But if it were the practice of every housekeeper to buy up corn in the autumn and keep it in a private granary, would it not serve in exactly the same way to subsist the population? Would not everything go on exactly the same, except that every one would be his own capitalist in regard to corn in place of paying farmers and corn merchants for doing the business?
[Back to Table of Contents]CHAPTER VIII
CONCLUDING REMARKS
[Back to Table of Contents]The Doctrine of Population.
IT is no part of my purpose in this work to attempt to trace out, with any approach to completeness, the results of the theory given in the preceding chapters. When the views of the nature of Value, and the general method of treating the subject by the application of the fluxional calculus, have received some recognition and acceptance, it will be time to think of results. I shall therefore only occupy a few more pages in pointing out the branches of economic doctrine which have been passed over, and in indicating their connection with the theory.
The doctrine of population has been conspicuously absent, not because I doubt in the least its truth and vast importance, but because it forms no part of the direct problem of Economics. I do not remember to have seen it remarked that it is an inversion of the problem to treat labour as a varying quantity, when we originally start with labour as the first element of production, and aim at the most economical employment of that labour. The problem of Economics may, as it seems to me, be stated thus:—Given, a certain population, with various needs and powers of production, in possession of certain lands and other sources of material: required, the mode of employing their labour which will maximise the utility of the produce. It is what mathematicians would call a change of the variable, afterwards to treat that labour as variable which was originally a fixed quantity. It really amounts to altering the conditions of the problem so as to create at each change a new problem. The same results, however, would generally be obtained by supposing the other conditions to vary. Given, a certain population, we may imagine the land and capital at their disposal to be greater or less, and may then trace out the results which will, in many respects, be applicable respectively to a less or greater population with the original land and capital.
[Back to Table of Contents]Relation of Wages and Profit.
There is another inversion of the problem of Economics which is generally made in works upon the subject. Although labour is the starting-point in production, and the interests of the labourer the very subject of the science, yet economists do not progress far before they suddenly turn round and treat labour as a commodity which is bought up by capitalists. Labour becomes itself the object of the laws of supply and demand, instead of those laws acting in the distribution of the products of labour. Economists have invented, too, a very simple theory to determine the rate at which capital can buy up labour. The average rate of wages, they say, is found by dividing the whole amount of capital appropriated to the payment of wages by the number of the labourers paid; and they wish us to believe that this settles the question. But a little consideration shows that this proposition is simply a truism.The average rate of wages must be equal to what is appropriated to the purpose divided by the number who share it. The whole question will consist in determining how much is appropriated for the purpose; for it certainly need not be the whole existing amount of circulating capital. Mill distinctly says, that because industry is limited by capital, we are not to infer that it always reaches that limit;1 and, as a matter of fact, we often observe that there is abundance of capital to be had at low rates of interest, while there are also large numbers of artisans starving for want of employment. The wage-fund theory is therefore illusory as a real solution of the problem, though I do not deny that it may have a certain limited and truthful application, to be shortly considered.
Another part of the current doctrines of Economics determines the rate of profit of capitalists in a very simple manner. The whole produce of industry must be divided into the portions paid as rent, taxes, profits, and wages. We may exclude taxes as exceptional, and not very important. Rent also may be eliminated, for it is essentially variable, and is reduced to zero in the case of the poorest land cultivated. We thus arrive at the simple equation—
Produce = profit + wages.
A plain result also is drawn from the formula; for we are told that if wages rise profits must fall, and vice versâ. But such a doctrine is radically fallacious; it involves the attempt to determine two unknown quantities from one equation. I grant that if the produce be a fixed amount, then if wages rise profits must fall, and vice versâ. Something might perhaps be made of this doctrine if Ricardo's theory of a natural rate of wages, that which is just sufficient to support the labourer, held true. But I altogether question the existence of any such rate.
The wages of working men in this kingdom vary from perhaps ten shillings a week up to forty shillings or more; the minimum in one part of the country is not the minimum in another. It is utterly impossible, too, to define exactly what are the necessaries of life. I am inclined, therefore, to reject altogether the current doctrines as to the rate of wages; and even if the theory held true of any one class of labourers separately, there is the additional difficulty that we have to account for the very different rates which prevail in different trades. It is impossible that we should accept for ever Ricardo's sweeping simplification of the subject, involved in his assumption, that there is a natural ordinary rate of wages for common labour, and that all higher rates are merely exceptional instances, to be explained away on other grounds.
The view which I accept concerning the rate of wages is not more difficult to comprehend than the current one. It is that the wages of a working man are ultimately coincident with what he produces, after the deduction of rent, taxes, and the interest of capital. I think that in the equation
Produce = profit + wages,
the quantity of produce is essentially variable, and that profit is the part to be first determined. If we resolve profit into wages of superintendence, insurance against risk, and interest, the first part is really wages itself; the second equalises the result in different employments; and the interest is, I believe, determined as stated in the last chapter. The reader will observe the important qualification that wages are only ultimately thus determined—that is, in the long run, and on the average of any one branch of employment.
The fact that workmen are not their own capitalists introduces complexity into the problem. The capitalists, or entrepreneurs, enter as a distinct interest. It is they who project and manage a branch of production, and form estimates as to the expected produce. It is the amount of this produce which incites them to invest capital and buy up labour. They pay the lowest current rates for the kind of labour required; and if the produce exceeds the average, those who are first in the field make large profits. This soon induces competition on the part of other capitalists, who, in trying to obtain good workmen, will raise the rate of wages. Competition will proceed until the point is reached at which only the market rate of interest is obtained for the capital invested. At the same time wages will have been so raised that the workmen reap the whole excess of produce, unless indeed the price of the produce has fallen, and the public, as consumers, have the benefit. Whether this latter result will follow or not depends upon the number of labourers who are fitted for the work. Where much skill and education is required, extensive competition will be impossible, and a permanently high rate of wages will exist. But if only common labour is requisite, the price of the goods cannot be maintained, wages will fall to their former point, and the public will gain the advantage of cheaper supplies.
It will be observed that this account of the matter involves the temporary application of the wage-fund theory. It is the proper function of capitalists to sustain labour before the result is accomplished, and as many branches of industry require a large outlay long previous to any definite result being arrived at, it follows that capitalists must undertake the risk of any branch of industry where the ultimate profits are not accurately known. But we now have some clue as to the amount of capital which will be appropriated to the payment of wages in any trade. The amount of capital will depend upon the amount of anticipated profits, and the competition to obtain proper workmen will strongly tend to secure to the latter all their legitimate share in the ultimate produce.
For instance, let a number of schemes be set on foot for laying telegraphic cables. The ultimate profits are very uncertain, depending upon the utility of the cables as compared with their cost. If capitalists make a large estimate of those profits, they will apply much capital to the immediate manufacture of the cables. All workmen competent at the moment to be employed will be hired, and high wages paid if necessary. Every man who has peculiar skill, knowledge, or experience, rendering his assistance valuable, will be hired at any requisite cost. At this point it is the wage-fund theory that is in operation. But, after a certain number of years, the condition of affairs will be totally different. Capitalists will learn, by experience, exactly what the profits of cables may be; that amount of capital will be thrown into the work which finds the average amount of profits, and neither more nor less. The cost of transmitting messages will be reduced by competition, so that no excessive profits will be made by any of the parties concerned; the rate of wages, therefore, of every species of labour will be reduced to the average proper to labour of that degree of skill. But if there be required in any branch of the work a very special kind of skilled and experienced labour, it will not be affected by competition in the same way, and the wages or salary will remain high.
I think that it is in this way quite possible to reconcile theories which are at first sight so different. The wage-fund theory acts in a wholly temporary manner. Every labourer ultimately receives the due value of his produce after paying a proper fraction to the capitalist for the remuneration of abstinence and risk. At the same time workers of different degrees of skill receive very different shares according as they contribute a common or a scarce kind of labour to the result.
[Back to Table of Contents]Professor Hearn's Views.
I have the more pleasure and confidence in putting forward these somewhat heretical views concerning the general problem of Economics, inasmuch as they are nearly identical with those arrived at by Professor Hearn, of Melbourne University. It would be a somewhat long task to trace out exactly the coincidence of opinions between us, but he certainly adopts the notion that the capitalist merely buys up temporarily the prospects of the concern he manages and the labourers he employs. Thus he says: "In place of having a share in the undertaking, the co-operator sells for a stipulated price his labour or the use of his capital. The case therefore comes within the ordinary conditions of exchange; and the price of labour and the price of capital are determined in the same manner as all other questions of price are determined. Yet the general character of the partnership is not destroyed. Although each particular transaction amounts to a sale, yet for the continuance of the business a nearer connection arises. Although the whole loss of the undertaking, if the undertaking be unfortunate, falls upon the last proprietor, and the interests of the other parties have been previously secured, yet each such loss prevents a repetition of the transaction from which it arose. The capital which ought to have been replaced, and which if replaced would have afforded the means of employing labour and of defraying the interest upon other capital, has disappeared; and thus the market for labour and for capital is by so much diminished. Both the labourer and the intermediate capitalist are therefore directly concerned in the success of every enterprise towards which they have contributed. If it be successful, they feel the advantage; if it be not successful, they feel in like manner the loss. But this community of interest is no longer direct, but is indirect merely; and it arises not from the gains or the losses of partners, but from the increased ability, or the diminished demands, of customers."1
This passage really contains a statement of the views which I am inclined wholly to accept; but no passages which I can select will convey an adequate notion of the enlightened view which Professor Hearn takes of the industrial structure of society in his admirable work on Plutology.
[Back to Table of Contents]The Noxious Influence of Authority.
I have but a few lines more to add. I have ventured in the preceding pages to call in question not a few of the favourite doctrines of economists. To me it is far more pleasant to agree than to differ; but it is impossible that one who has any regard for truth can long avoid protesting against doctrines which seem to him to be erroneous. There is ever a tendency of the most hurtful kind to allow opinions to crystallise into creeds. Especially does this tendency manifest itself when some eminent author, enjoying power of clear and comprehensive exposition, becomes recognised as an authority. His works may perhaps be the best which are extant upon the subject in question; they may combine more truth with less error than we can elsewhere meet. But "to err is human," and the best works should ever be open to criticism. If, instead of welcoming inquiry and criticism, the admirers of a great author accept his writings as authoritative, both in their excellences and in their defects, the most serious injury is done to truth. In matters of philosophy and science authority has ever been the great opponent of truth. A despotic calm is usually the triumph of error. In the republic of the sciences sedition and even anarchy are beneficial in the long run to the greatest happiness of the greatest number.
In the physical sciences authority has greatly lost its noxious influence. Chemistry, in its brief existence of a century, has undergone three or four complete revolutions of theory. In the science of light, Newton's own authority was decisively set aside, though not until after it had retarded for nearly a century the progress of inquiry. Astronomers have not hesitated, within the last few years, to alter their estimates of all the dimensions of the planetary system, and of the universe, because good reasons have been shown for calling in question the real coincidence of previous measurements. In science and philosophy nothing must be held sacred. Truth indeed is sacred; but, as Pilate said, "What is truth?" Show us the undoubted infallible criterion of absolute truth, and we will hold it as a sacred inviolable thing. But in the absence of that infallible criterion, we have all an equal right to grope about in our search of it, and no body and no school nor clique must be allowed to set up a standard of orthodoxy which shall bar the freedom of scientific inquiry.
I have added these words because I think there is some fear of the too great influence of authoritative writers in Political Economy. I protest against deference for any man, whether John Stuart Mill, or Adam Smith, or Aristotle, being allowed to check inquiry. Our science has become far too much a stagnant one, in which opinions rather than experience and reason are appealed to.
There are valuable suggestions towards the improvement of the science contained in the works of such writers as Senior, Cairnes, Macleod, Cliffe-Leslie, Hearn, Shadwell, not to mention a long series of French economists from Baudeau and Le Trosne down to Bastiat and Courcelle-Seneuil; but they are neglected in England, because the excellence of their works was not comprehended by David Ricardo, the two Mills, Professor Fawcett, and others who have made the orthodox Ricardian school what it is. Under these circumstances it is a positive service to break the monotonous repetition of current questionable doctrines, even at the risk of new error. I trust that the theory now given may prove accurate; but, however this may be, it will not be useless if it cause inquiry to be directed into the true basis and form of a science which touches so directly the material welfare of the human race.
[Back to Table of Contents]APPENDIX I
List of Mathematico-Economic Books, Memoirs, and other published writings.
Remarks upon the purpose and some of the contents of this list will be found in the preface to the second edition of this book.
1711. CEVA (Joanne). De re nummaria quoad fieri potuit geometrice Nactata. Mantuae. 4to. 60 pp.
1717. MARIOTTE (Esme). Essaie de Logique. Second edition. In collected works. Leide. See Principe 97 and 11me Partie, Article III.
1720. HUTCHESON (Francis). An Inquiry into the Original of our Ideas of Beauty and Virtue. London. 8vo. (3d Edition, 1729, xxii, 304 pp.)
1728. HUTCHESON (Francis). An Essay on the Nature and Conduct of the Passions and Affections, with Illustrations on the Moral Sense. London. 8vo. xxiv, 333 pp.
[1754. FORBONNAIS. Element du Commerce, ch. ix, and passim.]
1765. BECCARIA (Cesare). Tentativo analitico sui contrabbandi. Estratto dal foglio periodico intitolato: Il Caffè (vol. i. Brescia). Custodi's Scrittori classici Italiani di Economia politica. Parte Moderna, vol. xii, pp. 235-241. Milano, 1804.
1771. ANONYMOUS. An Essay on the Theory of Money. London. 8vo. 161 pp. (attributed to Major-General Henry Lloyd).
1776. CONDILLAC (Etienne Bonnot de). Le Commerce et le Gouvernement. Paris.
1781. ANONYMOUS (A. N. Isnard). Traité des Richesses. Londres et Lausanne. 2 vols. 8vo. xxiv, 344, 327 pp.
1786. CONDORCET. Vie de Turgot, pp. 162-169.
1787. English Translation, pp. 403-409.
1792. S0ILIO (Guglielmo). Saggio sull' Influenza dell' Analisi nelle scienze politiche ed economiche. (In vol. v of the collection Nuova Raccolta d'opuscoli di Autori Siciliani. Palermo.)
1793. LANG. Historische Entwickelung der Deutschen Steuerverfassung. Riga.
1801. CANARD (Nicolas François). Principes d'Economie Politique: Ouvrage couronné par l'Institut. Paris. 8vo. 384 pp. Reviewed by Francis Horner, Edinburgh Review, No. II.
1801. CANARD (Nicolas François). Mémoire sur la question s'il est vrai que, dans un pays agricole, toute espèce d'impot retombe sur les propriétaires fonciers. Paris.
1802. BRISSON (B.) Essai sur la Navigation. Paris.
1802. KRÖNCKE (C.) Versuch einer Theorie des Fuhrwerks mit Anvendung auf dem Strassenbau. Giessen. 8vo.
[1803. SIMONELE (de Sismondi). De la Richesse Commerciale, vol. i, pp. 105-109, etc.]
1804. KRÖNCKE (C.) Das Steuerwesen nach seiner Natur und seinen Wirkungen untersucht. Giessen. 8vo.
1809. LANG. Ueber den obersten Grundsatz der Politischen Oeconomie. Riga. 8vo.
[1811. LANG (Joseph). Grundlinien der Politischen Arithmetik. xxii, 216 pp. 8vo. Clarkow.]
1815. BUQUOY (G. Graf von). Theorie der Nationalwirthschaft nach einem neuen Plane, und nach mehreren eigenen Ansichten dargestellt. Leipzig; hierzu 3 Nachräge, 1816-18. 4to. 524 pp.
1824. THOMPSON (T. Perronet). Westminster Review, No. I, vol. i, pp. 171-205. Article on the Instrument of Exchange. (Reprinted in 1830, 27 pp.)
1825. FUOCO (Francesco). Saggi Economici. Prima Serie. 2 tom, 8vo. Pisa, 1825-27.
1825. CAZAUT. Elémens d'économie privée et publique.
1826. THOMPSON (T. Perronet). On Rent.
1826. THÜNEN (Johann Heinrich von). Der isolirte Staat in Beziehung auf Landwirthschaft und Nationalökonomie, oder Untersuchungen über den Einfluss, den die Getreidepreise, der Reichthum des Bodens und die Abgaben auf den Ackerbau ausüben Hamburg. 8vo. viii, 290 pp.
1829. WHEWELL (William). Mathematical Exposition of some Doctrines of Political Economy. Cambridge Philosophical Transactions, vol. iii, pp. 191-230. Cambridge. 4to.
1830. Westminster Review. Postscript to Article on Instrument of Exchange. xii, 525-533.
1831. WALRAS (Auguste). De la Nature de la Richesse et de Porigine de la Valeur. Paris. 8vo. xxiv, 334 pp.
1831. WHEWELL (William). Mathematical Exposition of the Leading Doctrines in Mr. Ricardo's "Principles of Political Economy and Taxation." Cambridge Philosophical Transactions, vol. iv, pp. 155-198. Cambridge. 4to.
1832. LUBÉ (D. G.) Argument against the Gold Standard. London. 8vo. iv, 192 pp.
[1832. HERMANN (F. B. W.) Staatswirthschaftliche Untersuchungen.]
1838. COURNOT (Augustin). Recherches sur les Principes Mathématiques de la Théorie des Richesses. Paris. 8vo. xi, 198 pp.
1838. TOZER (John). Mathematical Investigation of the Effect of Machinery on the Wealth of a Community in which it is employed, and on the Fund for the Payment of Wages. Cambridge Philosophical Transactions, vol. vi, pp. 507-522. Cambridge. 4to.
1839. HAGEN (Karl Heinrich). Von der Staatslehre und von der Vorbereitung zum Dienste in der Staatsverwaltung. Aufsätze gerichtet an angehende Cameralisten, zunächst an seine Herren Zuhörer, von K. H. H. Koenigsberg. 8vo. 477 pp.
[1839. ELLET (Chas., Jr.) An Essay on the Laws of Trade in reference to the Works of Internal Improvement in the United States. viii, 248 pp. Plate. 8vo.]
1840. ANONYMOUS. On Currency. London (Charles Knight and Co.) 8vo. viii, 43, xxi pp. (Lubbock, J. W.)
1840. TOZER (John). On the Effect of the Non-Residence of Landlords, etc., on the Wealth of a Community. Cambridge Philosophical Transactions, vol. vii, pp. 189-196. Cambridge. 4to.
1842. THÜNEN (J. H. von). Der isolirte Staat, etc. Erster Theil. Rostock. 8vo. xv, 391 pp.
1842. THOMPSON (T. Perronet). Exercises, Political and others. Vol. iii, pp. 295-343. On the Instrument of Exchange. See 1824, Thompson.
1844. DUPUIT (Etienne Juvenal). De la Mesure de l'Utilité des Travaux Publics. Annales des Ponts et Chaussées. 2e série. Tome viii, pp. 332-375. Paris. 8vo.
1844. HAGEN (K. H.) Die Nothwendigkeit der Handelsfreiheit für das Nationaleinkommen, mathematisch nachgewiesen. Koenigsberg. 8vo. 32 pp.
1844. HAGEN (K. H.) System of Political Economy. Translated from the German by John Prince Smith. London. 8vo. viii, 88 pp.
1844. DE QUINCEY (Thomas). Logic of Political Economy. Edinburgh, London. 8vo. 260 pp.
1847. BORDAS. De la Mesure de l'Utilité des Travaux Publics. Annales des Ponts et Chaussées, 1847, 1er semestre, 2me série, tome xiii, p. 249. Paris. 8vo.
1848. MILL (John Stuart). Principles of Political Economy, with some of their applications to Social Philosophy. London. 2 vols. 8vo. (Book iii, chapters xvii, xviii. See 3d Edition, 1852, vol. ii, pp. 143, 144.)
1849. ESMENARD DU MAZET (Camille). Nouveaux Principes d'Economie Politique. Paris. 8vo. ix, 456 pp.
1849. DUPUIT (E. J.) De l'Influence des Péages sur l'Utilité des Voies de Communication. Annales des Ponts et Chaussées. No. 207. 2e série, 1849, 1er semestre. Paris. 8vo. Pp. 170-248.)
1850. MINARD. De l'Usage Gratuit des Constructions établies aux Frais de l'Etat. Annales des Ponts et Chaussées, 2e série, 1er semestre. Paris. 8vo. (P. 27.)
1850. LARDNER (Dionysius). Railway Economy. London. 8vo. (Chapter xiii.)
1850. THÜNEN (J. H. von). Der isolirte Staat, etc. Zweited Theil. Erste Abtheilung. Der naturgemässe Arbeitslohn und dessen Verhältniss zum Zinsfuss und zur Landrente. Rostock. 8vo. vi, 285 pp.
1850. WHEWELL (William). Mathematical Exposition of Certain Doctrines of Political Economy. Second and Third Memoirs, Cambridge Philosophical Transactions. Vol. ix, pp. 128-149, and Part II, pp. [1-7]. Cambridge. 4to.
1851. ESMENARD DU MAZET. De la Valeur: Lettre à M. J. Garnier. Paris. 8vo.
1851. DE THÜNEN. Recherches sur l'Influence que le Prix des Grains, la Richesse du Sol, et les Impôts exercent sur les Systèmes de Culture. Traduit par Laverrière. Paris. 8vo.
1854. WOLKOFF (Mathieu). Opuscules sur la Rente Foncière. Paris. 8vo. 231 pp.
1854. GOSSEN (Hermann Heinrich). Entwickelung der Gesetze des menschlichen Verkehrs, und der daraus fliessenden Regeln für menschliches Handeln. Braunschweig. 8vo. 278 pp. See Article on Gossen by Hooper, Journal of the Statistical Society, September 1879. Pp. 727-733.
1855. JENNINGS (Richard, M.A.) Natural Elements of Political Economy. London. 8vo. 275 pp.
1856. BENNER. Théorie Mathématique de l'Economie Politique.
1856. WOLKOFF (M.) Journal des Economistes, 1856. Paris.
1857. DE THÜNEN. Le Salaire Naturel, et son rapport au taux de l'Interêt. Traduit de l'Allemand par M. Wolkoff. Paris.
1857. MACLEOD (Henry Dunning). The Elements of Political Economy. London. 8vo.
1857. BOCCARDO (Gerolamo). Dizionario della Economia Politica e Commercio, etc. Tarino. 4to. (Vol. ii, pp. 653-659, etc.)
[1859. VAN HOUTEN (S.) Verhandeling over de Waarde.]
1860. DU MESNIL-MARIGNY. Les Libre Echangistes et les Protectionnistes Conciliés. 8vo. Paris.
1861. WOLKOFF (M.) Lectures d'Economie Politique Rationelle. Paris. 12mo.
1862. DE MORGAN (Augustus). Athenæum, 15th November, No. 1829, p. 632.
1862. JEVONS (William Stanley). Notice of a General Mathematical Theory of Political Economy. Report of the 32d meeting of the British Association for the Advancement of Science, held at Cambridge in October, 1862. Reports of Sections, p. 158. London, 1863. 8vo.
1862. MACLEOD (H. D.) On the Definition and Nature of the Science of Political Economy. Report of the 32d meeting of the British Association, etc. Reports of Sections, pp. 159-161. Also separately printed, Cambridge and London. 16 pp.
1863. COURNOT (Augustin). Principes de la Théorie des Richesses. Paris. 8vo. iv, 527 pp.
1863. MACLEOD (H. D.) A Dictionary of Political Economy: Biographical, Bibliographical Historical, and Practical. Vol. i. London. 8vo. (Article Credit, p. 567.)
1863. DU MESNIL-MARIGNY. Catéchisme de l'Economie politique basée sur des principes rationnels. Paris. 18mo. 355 pp.
1863. MANGOLDT (H. von). Grundriss der Volkswirthschaftslehre. Stuttgart. xvi, 224.
1863. THÜNEN (J. H. von). Der isolirte Staat. Zweiter Theil. Zweite Abtheilung. Der naturgemässe Arbeitslohn, etc. Rostock. 8vo. ix, 444 pp.
1864. FAUVEAU (G.) Considérations mathématiques sur la Théorie de l'Impôt. Paris. 8vo. 64 pp.
1865. KNAPP (George Friedrich). Zur Prüfung der Untersuchungen Thünen's über Lohn und Zinsfuss im isolirten Staate. Braunschweig. 8vo. 35 pp.
1866. JEVONS (W.S.) Brief Account of a General Mathematical Theory of Political Economy. Journal of the Statistical Society of London, June 1866. Vol. xxix, pp. 282-287. London. 8vo.
1867. COURCELLE-SENEUIL (J. G.) Traité Théorique et Pratique d'Economie Politique. 2me Ed. Paris. 8vo. Tome I, livre i, chap. 2.
1867. FAUVEAU (G.) Considérations mathématiques sur la théorie de la valeur. Journal des Economistes. 3e série, 2e année, t. v, pp. 31-40.
1867. BRENTANO (L. J.) Ueber J. H. von Thünen's Naturgemässen Lohn und Zinsfuss. Göttingen. 61 pp.
1868. RAU (Karl Heinrich). Grundsätze der Volkswirthschaftslehre. Achte Ausgabe. Erste Abtheilung, p. 368. Leipzig und Heidelberg. 8vo.
1868. JENKIN (Fleeming). Trades Unions. How far Legitimate. North British Review, March 1858. 8vo. (Footnote.)
1868. WOLKOFF (Mathieu). Précis d'économie politique rationnelle. Paris. In-18, 329 pp.
1869. FAUVEAU (G.) Etude sur la théorie de l'impôt. Journal des Economistes, 3e série, 4e année, t. xiii, pp. 391-403.
1869. FAUVEAU (G.) L'impôt sur le revenu du capital et sur le revenu du travail. Journal des Économistes, 3e série, 4e année, t. xvi, pp. 466-468.
1869. SCHUMACHER (H.) Ueber J. H. von Thünen's Gesetz vom naturgemässen Arbeitslohne. Rostock. 84 pp.
1870. JENKIN (Fleeming). The Graphic Representation of the Laws of Supply and Demand, and their application to Labour. Recess Studies, edited by Sir Alexander Grant. Edinburgh. 8vo. (Pp. 151-185.)
1871. JEVONS (W. S.) The Theory of Political Economy. 8vo. London. xvi, 267 pp.
1871. JENKIN (Fleeming). On the Principles which regulate the incidence of Taxes, Proceedings of the Royal Society of Edinburgh. Session 1871-72. (Pp. 618-631.)
1871. FAUVEAU (G.) Rendement maximum de l'impôt indirect. Journal des Economistes. 3e série, 6e année, t. xxiv, pp. 445-448.
[1871. MENGER (Carl). Grundsätze der Volkswirthschaftslehre. Wien.]
[1872. LAUNHARDT (Wilhelm). Kommerzielle Trassirung der Verkehrswege. Hannover.]
1872. MARCHAND (J.) Recherche sur la méthode à adopter pour la discussion des éléments de la statistique. Journal des Actuaires français. T. i, pp. 267-273 and 393-409.
1873. BING OG PETERSEN. Bestemmelse af den rationelle Arbeidslön samt nogle Bemærkninger om Oekonomiens Methode. Nationaloekonomisk Tidsskrift. Förste Bind, p. 296. Copenhagen.
1873. MARCHAND (J.) Recherche sur la méthode à adopter pour la discussion des éléments de la statistique. Journal des Actuaires français. T. ii, pp. 58-78 et 251-263.
1873. PETERSEN, FREDERIKSEN, etc. Nationaloekonomisk Forening. Diskussion om Oekonomiens Methode. National-oekonomisk Tidsskrift, Maanedsskrift for Oekonomie, etc. Andet Bind, p. 248. Copenhagen.
1873. POCHET (Léon). Géométrie des jeux de Bourse. Journal des Actuaires français. T. ii, pp. 153-160.
1873. LEFÈVRE (H.) Physiologie et mécanique sociales. Journal des Actuaires français. T. ii, pp. 211-250 et 351-388.
1874. WALRAS (Léon). Principe d'une théorie mathématique de l'échange. Mémoire lu à l'Académie des sciences morales et politiques (Séances des 16 et 23 août 1873). Orléans. 8vo. 24 pp.
1874. JEVONS et WALRAS. Correspondance. Extrait du Journal des Economistes (numéro du 15 juin 1874). Paris. 8vo. 8 pp.
1874. BOCCARDO (Gerolamo). Dizionario Universale della Economia Politica e del Commercio. Milano. 8vo.
1874. LEFÈVRE (H.) Principe de la Science de la Bourse. Méthode approuvée par la Chambre syndicale des Agents de Change de Paris. Paris. 8vo. 113 pp.
1874. WALRAS (Léon). Éléments d'économie politique pure, ou théorie de la richesse sociale. Premier fascicule. Lausanne, Paris et Bâle. 8vo. viii, 208 pp.
1874. ZANON (Giovanni Antonio). Sulla teoria matematica dello scambio del professore M. L. Walras, lettera al professore Alberto Errera. Estratto dalla Rassegna di Agricoltura, Industria e Commercio. Padova. 8vo. 7 pp.
1874. LETORT (Charles). De l'application des mathématiques à l'étude de l'économie politique. L'Economiste français, 31 octobre 1874, p. 540.
1874. D'AULNIS DE BOUROUILL (Johan). Het Inkomen der Maatschappij. Eene Proeve van theoretische Staathuishoudkunde. Leiden. 8vo. xiii, 215 pp.
1874. LEFÈVRE (H.) Physiologie et mécanique sociales. Journal des Actuaires français. T. iii, pp. 93-118.
1874. DORMOY (Emile). Les matières premières. Etablissement des coefficients d'élaboration. Journal des Actuaires français. T. iii, pp. 142-162.
1874. AVIGDOR (Septime N.) Question d'économie sociale. Journal des Actuaires français. T. iii, pp. 300-306.
1874. MARCHAND (J.) Recherche sur la méthode à adopter pour la discussion des éléments de la statistique. Journal des Actuaires français. T. iii, pp. 307-325.
1875. JEVONS (W. Stanley). The progress of the mathematical theory of Political Economy, with an explanation of the principles of the theory. Transactions of the Manchester Statistical Society. Pp. 1-19. 8vo. (Read Nov. 11, 1874.)
1875. DARWIN (George H.) The Theory of Exchange Value. Fortnightly Review. New series. Vol. xvii, pp. 243-253. London. 8vo.
1875. BOCCARDO (Gerolamo). Del metodo in economia politica. Estratto dal Giornale degli Economisti. Padova. 8vo. 23 pp.
1875. BOCCARDO (Gerolamo). L'économia politica odierna come scienza le come ordinamento sociale. Introduzione generale alla Biblioteca dell' Economista. 3a série, pp. 1-43.
1875. ERRERA (Alberto). Appunto bibliografico. Éléments d'économie politique pure par Léon Walras. Estratto dal giornale La Perseveranza. Milano. 18mo. 16 pp.
1875. BOCCARDO (Gerolamo). Dell' applicazione dei metodi quantitativi alle scienze economiche, statistiche e sociali. Saggio di logica economica. Prefazione al 2° volume della Biblioteca dell' Economista. Pp. i-lxxii.
1875. WHEWELL (W.) Esposizione matematica di alcune dottrine di economia politica. Due Memorie. Biblioteca dell' Economista. 3a serie. Vol. ii, pp. 1-65.
1875. COURNOT (Agostino). Ricerche intorno ai principii matematici della teorica delle ricchezze. Biblioteca dell' Economista. 3a serie. Vol. ii, pp. 67-170.
1875. JEVONS (W. Stanley). La teorica dell' economia politica. Biblioteca dell' Economista. 3a serie. Vol. ii, pp. 173-311.
1875. NEWCOMB (Simon). North American Review, No. CCXLIX. Review of Cairnes's Logical Method of Political Economy.
1875. PIERSON (N. G.) Grondbeginselen der Staathuishoudkunde. Haarlem. 1875-76. 2 vols.
1875. ACHARD (M. A.) Influence des taxes qui frappent les obligations sur leur prix d'après un taux déterminé. Journal des Actuaires français. T. iv, pp. 70-74.
1875. FONTANEAU (E.) Principes de chrématistique. Journal des Actuaires français. T. iv, pp. 75-83 et 151-172.
1875. LAURENT (H.) Démonstration simple du principe de M. Menier. Journal des Actuaires français. T. iv. pp. 84-87 (also printed in Menier's Théorie et Application de l'Impot sur le Capital. 2me Ed. Paris. 1875. 12mo. Appendice, pp. 607-612).
1875. FONTANEAU (E.) De la valeur. Journal des Actuaires français. T. iv, pp. 175-199 et 267-277.
1875. FALCK (G. von). Die Thünensche Lehre vom Bildungsgesetz des Zinsfusses und vom naturgemässen Arbeitslohn. Leipzig. 55 pp.
1876. WALRAS (Leone). Un nuovo ramo della matematica. Dell' applicazione delle matematiche all' economia politica. Estratto dal Giornale degli Economisti. Padova. 8vo. Vol. iii. Fascicolo N. I. Aprile 1876. 40 pp.
1876. WALRAS (Léon). Equations de l'échange. Equations de la production. Mémoires lus à la Société vaudoise des sciences naturelles. (Séances des 1er et 15 décembre 1875, 19 janvier et 16 février 1876.) Lausanne. 8vo. 66 pp.
1876. ZAMBELLI (Andrea). La teoria matematica dello scambio del signor Leone Walras. Lettera diretta al prof. Errera dott. Alberto. Padova. Gr. in-8. 28 pp.
1876. JEVONS (W. Stanley). The Future of Political Economy. Fortnightly Review, November 1, 1876. Vol. xx, pp. 617-631.
1876. WALRAS (Léon). Équations de la capitalisation. Mémoire lu à la Société vaudoise des sciences naturelles (Séance du 5 juillet 1876). 8vo. 40 pp.
1876. FONTANEAU (E.) Chrématistique. Journal des Actuaires français. T. v, pp. 70-96 et 341-365.
1876. MADSEN (C. L.) Den Sandsynlige Lov for den internationale Telegraraftrafik. Copenhagen. 8vo.
[1876. WESTERGAARD (Harald). Den moralske Formue og det moralske Haab. Tidsskrift for Mathematik.]
1877. MADSEN (C. L.) Nye Undersögelser om Loven for den internationale Trafik. Geografisk Tidskrift. 1ste Bind, pp. 192-201.
1877. MADSEN (C. L.) Recherches sur la loi du Mouvement télégraphique international. Copenhague, Paris. 8vo. ix, 68 pp., avec 10 tableaux.
1877. JEVONS (W. Stanley). Le passé et l'avenir de l'économie politique. Les méthodes. Les économistes contemporains. Le political economy club. Journal des Economistes. Mars 1877. 3e série. T. xlv, pp. 325-342.
1877. WALRAS (Léon). Eléments d'économie politique pure, ou théorie de la richesse sociale. Deuxième fascicule. Lausanne, Paris et Bále. Pp. 209-407. 8vo.
1877. MOLL (L. A.) Der Werth. Eine neue Theorie desselben. Leipzig. 48 pp.
1878. WESTERGAARD (Harald). Den Sandsynlige Lov for den internationale Telegraftrafik. Anmeldt af H. W. National-oekonomisk Tidsskrift. Bind xi. Copenhagen. 8vo.
1878. DU MESNIL-MARIGNY. L'économie politique devenue science exacte ou les libre-échangistes et les protectionnistes conciliés. 3e édition. Paris. Gr. in-8. 413 pp.
1878. WALRAS (Leone). Teoria matematica della richezza sociale. Quattro memorie lette all' Accademia delle science morali e politiche, a Parigi, ed alla Societa Valdese delle scienze naturali, a Losanna. Biblioteca dell' Economista. 3e série. Vol. ii, pp. 1289-1388.
1878. WEISZ (Dr. Bela, of Budapesth, Hungary). Die Mathematische Methode in der Nationalökonomie. Hildebrandt's Jahrbücher für Nationalökonomie und Statistik. Article VI, vol. xxxi, pp. 295-316. Jena.
1878. NICOLINI. Un antico Economista Matematica (Ceva). Giornale degli Economisti, vol. viii. fasc. 1. Oct. Padova. 8vo.
[1878. MADSEN (C. L.), and Westergaard (H.) Correspondence. Nationaloekonomisk Tidsskrift.]
[1878. MADSEN (C. L.) Den sandsynbige Lov og den internationale Telegraftrafik. Nationaloekonomisk Tidsskrift. Bind xi, pp. 171-183.]
[1878. MADSEN (C. L.) On the Law of International Telegraph Traffic. Journal of Society of Telegraph Engineers. London.]
1879. MADSEN (C. L.) Danmarks, Sveriges og Norges Samkvem med Udlandet. 1871-77. 26, xxiv pp. 4to. Copenhagen.
1879. VAN DEN BERG (C. P. J.) De theorie van het arbeidsloon. Utrecht. 35 pp. 8vo.
[1879. S. De la Mesure de l'Utilité des Chemins de fer. Journal des Économistes.]
1879. MARSHALL (Alfred). The Pure Theory of Foreign Trade. The Pure Theory of (Domestic) Values. Cambridge. 8vo. Privately printed.
1879. MARSHALL (Alfred—and Mary Paley). The Economics of Industry. London. 18mo. xiv, 231 pp.
1879. WALRAS (Léon). Théorie Mathématique du Billet de Banque. Bull. Soc. Vaud. Sc. Nat. xvi, 83 pp. 8vo.
1880. WALRAS (Léon). Théorie Mathématique du Prix des Terres et de Leur Rachat par l'État. Bull. Soc. Vaud. Sc. Nat. xxii, 85. 8vo.
[1880. SCHFFLER (Hermann). Ueber die Normirung der Einkommensteuer. Vierteljahrsschrift für Volkswirthschaft und Culturgeschichte.]
1880. BERG (C. P. J. van den). The Theory of Wages. Translated from the Dutch. 25 pp. 8vo. London.
1881. EDGEWORTH (F. Y.) Mathematical Physics. An Essay on the Application of Mathematics to the Moral Sciences. 8vo. London. viii, 150 pp.
1881. GIDE (Charles). La Théorie de l'économie politique de M. Stanley Jevons. Journal des Economistes. Nov. Pp. 179-191.
[1881. SACHER (Eduard). Grundzüge einer Mechanik des Gesellschaft. I. Theoretischer Theil. Jena. 246 pp. 8vo.]
1881. WALRAS (Léon). Théorie Mathématique du Bimétallisme. Paris. 8vo.
1881. WALRAS (Léon). Mathematische Theorie der Preisbestimmung der Wirthschaftlichen Güter, Vier Denkschriften, etc. Translated by Ludwig von Winterfeld. Stuttgart.
1882. LAUNHARDT (Wilhelm). Der zweckmässigste Standort einer gewerblichen Anlage. Zeitschrift des Vereins deutscher Ingenieure.
1882. WALRAS (Léon). De la Fixité de Valeur de l'Etalon Monétaire. Journal des Economistés. October. 8vo.
1883. EDGEWORTH (F. Y.) The Method of ascertaining a Change in the Value of Gold. Jour. Statistical Society, London, vol. xlvi, pp. 714-718.
1883. LAUNHARDT (Wilhelm). Wirthschaftliche Fragen des Eisenbahnwesens. Centralblatt der Bauverwaltung.
1883. WALRAS (Léon). Théorie mathematique de la Richesse sociale. 253 pp. 4to. Lausanne.
1884. EDGEWORTH (F. Y.) The Rationale of Exchange. Jour. Statistical Society, London, vol. xlvii, pp. 164-166.
1884. POYNTING (J. H.) A Comparison of the Fluctuations in the Price of Wheat, and in Cotton and Silk Imports into Great Britain. Jour. Statistical Society, London, vol. xlvii, pp. 34-64.
1884. WALRAS (Léon). Monnaie d'Or avec Billon d'Argent Regulateur. Bruxelles. 8vo.
1884. PIERSON (N. G.) Leerboek der Staathuishoudkunde. Erste deel. Haarlem.
1884. WIESER (F. von). Ueber den Ursprung und die Hauptgesetze des wirthschaftlichen Werthes. Wien.
1884. HOUDARD (Adolphe). Théorie générale de la valeur. Journal des Économistes.
1884. WICKSTEED (Philip H.) Das Kapitab. A criticism. Today, Oct. London.
1884. GIDE (Charles). Principes d'economie politique. Paris.
1885. WALRAS (Léon). D'une Methode de Régularisation de la Variation de Valeur de la Monnaie. Bull. Soc. Vaud. Sc. Nat. 22 pp. 8vo.
1885. SIMON (Alfred) and WALRAS (Léon). Contribution à l'étude des variations des prix. Bull. Soc. Vaud. Sc. Nat. 11 pp. 8vo.
1885. LAUNHARDT (Wilhelm). Mathematische Begründung der Volkswirthschaftslehre. Leipsig. viii, 216 pp. 8vo.
1885. LAUNHARDT (Wilhelm). Das Wesen des Geldes. Leipsig. vi, 75 pp. 8vo.
1886. GROSSMAN. Die Mathematik im Dienste der National-ökonomie. 1ste Lieferung. 80 pp. 4to. Vienna.
1886. NEWCOMB (Simon). Principles of Political Economy. 8vo. New York. xvi, 543 pp.
1886. BOEHM-BAWERK. Grundzüge der Theorie des Wirtschaftlichen Güterwerts. Jahrbücher für Nationalökonomie und Statistik N. F. Band xiii. Jena.
1886. PIERSON (N. G.) Grondbeginselen der Staathuishoudkunde Tweede Druk. Haarlem.
1886. FEAUVEAU (G.) Études sur les Premiers Principes de la Science Économique. Journal des Economistes.
1886. ANTONELLI (G. B.) Sulla Teoria Mathematica della economica politica. Pisa.
1886. WALRAS (Léon). Théorie de la Monnaie in 8vo. xii, 120 pp. Lausanne.
1886. GROSSMANN (Ludwig). Die Mathematik im Dienste der Nationalökonomie. II Lieferung. Vienna.
1887. EDGEWORTH (F. Y.) On the Method of ascertaining and measuring Variations in the Value of the Monetary Standard. Report of the British Association for the Advancement of Science.
1887. EDGEWORTH (F. Y.) Metritike, or the Method of measuring Probability and Utility. London: Temple Co.
1887. AIKIN-KAROLY. Solutions nouvelles de deux Questions Fondamentales d'Économie Sociale. Revue d'Economie Politique.
1887. LAUNHARDT (Wilhelm). Theorie des Trassirens. Heft. I. Die kommerzielle Trassirung. Second Edition. iv, 112 pp. Hannover.
1887. HELM (G.) Die Bisherigen Versuche, Mathematik auf Volkswirthschaftliche Fragen anzuwenden. Ges. Isis. in Dresden. Abh. I. 13 pp.
1887. VAN DORSTEN (Dr. R. K.) Mathematische onderzoe-kingen op het gebied der Staathuishoudkunde. Ar chief voor politieke en sociale rekenkunde, 1ste deel, 3de en 4de aflevering.
1887. WESTERGAARD (H.) Mathematiken i Nationalökonomiens Tjeneste. In the volume Smaaskrifter Tilegnede A. F. Krieger. Copenhagen.
1887. PANTALEONI (Maffeo). Teoria della pressione tributaria e metodi per misurarla. Parte prima Teoria della pressione tributaria. 78 pp. Roma.
1888. EDGEWORTH (F. Y.) The Mathematical Theory of Banking. Jour. Statistical Society, London, March 1888.
1888. WICKSTEED (Philip H.) The Alphabet of Economic Science. I. Elements of the Theory of Value or Worth. London.
[Back to Table of Contents]APPENDIX II
List of works and papers upon Economical Subjects, by the author of the present book:—
1857. Comparison of the Land and Railway Policy of New South Wales. The Public Lands of New South Wales. Articles in the Empire newspaper, April 7 and June 23. Sydney, New South Wales.
1862. Diagram, showing all the Weekly Accounts of the Bank of England, since the passing of the Bank Act of 1844, with the Amount of Bank of England, Private, and Joint Stock Bank Promissory Notes in Circulation during each week, and the Bank Minimum Rate of Discount. London. Sheet, 20 x 30 inches, coloured.
This Diagram represents to the eye all the useful results of tables, containing about 113,000 figures.
1862. Diagram, showing the Price of the English Funds, the Price of Wheat, the Number of Bankruptcies, and the Rate of Discount, monthly, since 1731; so far as the same have been ascertained. London. Sheet, 20 x 30 inches, coloured.
This Diagram is drawn from tables carefully compiled for the purpose, and containing more than 12,000 figures.
Explanatory Notes and References are appended to each Diagram.
1862. (1) On the Study of Periodic Commercial Fluctuations. With five diagrams. (2) Notice of a general Mathematical Theory of Political Economy. Papers read in the F section of the British Association at the Cambridge Meeting. Report. Proceedings of Sections, pp. 157, 158.
1863. A serious Fall in the Value of Gold Ascertained, and its social effects set forth. With two diagrams. London: Edward Stanford, Charing Cross. 8vo. 73 pp.
1865. The Coal Question; an Inquiry concerning the Progress of the Nation, and the Probable Exhaustion of our Coal Mines. London and Cambridge: Macmillan & Co. 8vo. xix, 349 pp.
1865. On the Variation of Prices, and the Value of the Currency since 1782. Paper read before the London Statistical Society, May 1865. Journal of the Statistical Society, vol. xxviii, pp. 294-320. With four diagrams.
1866. On the frequent Autumnal Pressure in the Money Market, and the Action of the Bank of England. Paper read before the Statistical Society, April 1866. Journal of the Statistical Society of London, vol. xxix, pp. 235-253.
1866. Brief Account of a General Mathematical Theory of Political Economy. (Read at the British Association, 1862.) Journal of the Statistical Society of London, vol. xxix, pp. 282-287.
1866. The Coal Question, etc. Second edition. London. 8vo. xxvi, 383 pp.
1866. An Introductory Lecture on the Importance of diffusing a Knowledge of Political Economy. Delivered in Owens College, Manchester, at the opening of the Session of Evening Classes, on October 12. Manchester. 12mo. 35 pp.
1867. Science Lectures for the People. Lecture IX. On Coal: its importance in manufactures and trade. Delivered in the Carpenters' Hall, Manchester, January 16, 1867. (Science Lectures, vol. i, pp. 128-140.)
1867. On the Analogy between the Post-Office, Telegraphs, and other systems of Conveyance of the United Kingdom, as regards Government Control. Paper read before the Manchester Statistical Society, April 1867. Transactions, 1866-67, pp. 89-104.
1868. A Lecture on Trades' Societies: their Objects and Policy. Delivered by request of the Trades Unionists' Political Association, March 31. Manchester. 8vo. 16 pp.
1868. Lecture on the Probable Exhaustion of our Coal Mines. Royal Institution of Great Britain. Friday Evening, March 13. 8vo. 7 pp.
1868. On the International Monetary Convention, and the Introduction of an International Currency into this kingdom. Paper read before the Manchester Statistical Society, May 13. Transactions, 1867-68, pp. 79-92.
1868. On the Condition of the Metallic Currency of the United Kingdom, with reference to the Question of International Coinage. Paper read before the Statistical Society of London, November. Journal of the Statistical Society of London, vol. xxxi, pp. 426-464.
1869. Letter on the Value of Gold. Economist Newspaper, May 8. Reprinted in the Journal of the Statistical Society of London, December, vol. xxxii, p. 445.
1869. On the Work of the Society in connection with the Questions of the Day. Inaugural Address read before the Manchester Statistical Society, November 10, 1869. Transactions, 1869-70, pp. 1-14.
1870. Opening Address of the President of Section F (Economic Science and Statistics) of the British Association for the Advancement of Science at the Fortieth Meeting, at Liverpool, September 1870. Report. Transactions of the Sections, pp. 178-187. Journal of the Statistical Society of London, vol. xxxiii, pp. 309-326.
1870. On Industrial Partnerships. A Lecture delivered under the auspices of the National Association for the Promotion of Social Science, April 5, 1870. London, 1 Adam Street, Adelphi. 12mo. 39 pp.
1871. The Match Tax: a Problem in Finance. London. 8vo. 66 pp.
1871. The Theory of Political Economy. London and New York: Macmillan & Co. 8vo. xvi, 267 pp.
1874. The Progress of the Mathematical Theory of Political Economy, with an explanation of the Principles of the Theory. Paper read before the Manchester Statistical Society, November 11. Transactions, 1874-75, pp. 1-19, with a diagram. Reprinted in the Journal of the Statistical Society of London, vol. xxxvii, p. 478.
1875. On the Progress of the Coal Question. British Association, Bristol, 1875. Transactions of Sections, p. 216.
1875. The Post-Office Telegraphs and their Financial Results. Fortnightly Review, December 1, vol. xviii, N. S., pp. 826-835.
1875. La Teorica dell' Economia Politica, esposta da W. Stanley Jevons. Biblioteca dell' Economista. 3n serie, tome ii, pp. 175-311. (Translated under the superintendence of Professor Gerolamo Boccardo.)
1875. Money and the Mechanism of Exchange (International Scientific Series, vol. xvii). London: H. S. King & Co.; New York: D. Appleton & Co. Post 8vo. xviii, 349 pp.
1876. La Monnaie et le Mécanisme de l'Echange. Paris: Librairie Germer Baillière et Cie. (Bibliothèque Scientifique Internationale, vol. xx.) 8vo. viii, 288 pp.
1876. Geld und Geldverkehr. Leipzig: F. A. Brockhaus (Internationale Wissenschaftliche Bibliothek, xxi Band). 8vo. xvi, 359 pp.
1876. La Moneta et il Mecanismo dello Scambio. Milano: Fratelli Dumolard. (Biblioteca Scientifica Internazionale, vol. vi.) 8vo. xxix, 319 pp.
1876. On the United Kingdom Alliance and its Prospects of Success. Paper read before the Manchester Statistical Society, March 8. Transactions, pp. 127-142.
1876. On the Frequent Autumnal Pressure in the Money Market, and the action of the Bank of England. Paper reprinted from the Journal of the Statistical Society of London, 1866, in the Transactions of the Manchester Statistical Society. Appendix, pp. 17-41.
1876. The Future of Political Economy. Introductory Lecture at the Opening of the Session, 1876-77, at University College, London. Faculty of Arts and Laws. Fortnightly Review, December, vol. xx, pp. 617-631. (See also Appendix I, 1877, Jevons.)
1877. The Silver Question: A Paper read by Hamilton A. Hill, of Boston, before the American Social Science Association at Saratoga, September 5. Boston: Published for the Association by A. Williams & Co., pp. 26-32. Reprinted in the London Bankers' Magazine, December. 7 pp.
1878. Science Primers—Primer of Political Economy. London: Macmillan & Co. 18mo. 134 pp.
1878. L'Economie Politique, par W. Stanley Jevons, traduite par Henri Gravez, Ingénieur. Paris: Librairie Germer Baillière et Cie. (Bibliothèque Utile, vol. xliv.) 18mo. 184 pp.
1878. Money and the Mechanism of Exchange. London: C. Kegan Paul & Co. Fourth edition.
1878. The Periodicity of Commercial Crises and its Physical Explanation. Paper read before the F section of the British Association at the Dublin Meeting, August 19. Report. Transactions of Section F, p. 666. Published in the Journal of the Statistical and Social Inquiry Society of Ireland, August, 1878. Vol. vii, pp. 334-342.
1878. Commercial Crises and Sun-spots. Article printed in Nature of November 14, vol. xix, pp. 33-37.
1878. Remarks on the Statistical use of the Arithmometer. Journal of the Statistical Society of London, vol. xli, pp. 597-601.
1879. Methods of Social Reform, No. II. A State Parcel Post. Article in the Contemporary Review of January, vol. xxxiv, pp. 209-229.
1879. Sun-spots and Commercial Crises. Nature, April 24, vol. xix, pp. 588-590.
1881. Bimetallism. Article in Contemporary Review of May, vol. xxxix, pp. 750-757.
1884. Investigations in Currency and Finance. Edited, with Introduction, by H. S. Foxwell, M.A. London: Macmillan & Co. 8vo. xliv, 414 pp.
Printed by R. & R. Clark, Edinburgh.
[1[1]]Principles of Political Economy, book iii. chap. vi. sec. i. l. This definition occurs at the beginning of a carefully prepared summary of the principles of the theory of value.
[1]Hermathena, No. iv., 1876, pp. 1-32. Republished in Mr. Leslie's collected Essays in Political and Moral Philosophy, Dublin, 1879, pp. 216-242.
[[3]]Journal of the London Statistical Society, December 1878, vol. xli. pp. 602-629. Journal of the Statistical and Social Inquiry Society of Ireland, August 1878, vol. vii. Appendix. Also as a separate publication, Longmans, London, 1878.
[1]"The Future of Political Economy," Fortnightly Review, November 1876, vol. viii., N. S., pp. 617-631. Translated in the Journal des Economistes, March 1877, 3me Série, vol. xlv. p. 325.
[1]See p. ix of this edition.
[[6]]Traité d'Economie Politique... 5me ed., Paris, 1863, pp. 700-702.
[1]Some Leading Principles of Political Economy Newly Expounded, pt. 1, chap. iii. p. 97.
[1]Book iii. chap. xviii. sec. 7.
[1]1720. Hutcheson. An Inquiry, 1729, etc., pp. 186-198.
[1]1728. Hutcheson. An Essay, etc., pp. 34-43, and elsewhere.
[1]Elemens d'Ideologie, iv., et ve Parties. Traité de la Volonté et de Ses Effets, Paris, 1815, 8vo, p. 499. Edition of 1826, p. 335. American Edition, A treatise on Political Economy, translated from the unpublished French original. Georgetown, D.C. 1817, p. xiii.
[2]Observations on the Effects of the Corn Laws, and of a rise or fall in the price of Corn on the Agriculture and General Wealth of the Country. London, 1814, p. 30: 3d ed., 1815, p. 32.
[1]Traité d'Economie Politique, Cinquième Edition, p. 701.
[2]Theorie und Geschichte der National-Oekonomik, 1858, vol. i. p. 9.
[1]A copy of Gossen's book will be found in the Library of the British Museum (Press mark 8408, cc). It was not acquired by that institution until May 24, 1865, as shown by the date stamped upon the copy.
[1]Transactions of the Connecticut Academy, 1877, vol. iv. pp. 151-232.
[1]"Land Systems and Industrial Economy of Ireland, England, and Continental Countries." London, 1870. Appendix, pp. 357-379.
[2]London, 1877, Trübner.
[1]Chap. v. vol. i. p. 304.
[2]Principles of Political Economy, book iii., chap. v., sec. 2, paragraph 3.
[1]Principles of Political Economy, book iii., chap. vi., sec. 1, article 9.
[[2]]Reports of Sections, p. 158.
[[23]]Journal of the Statistical Society, vol. xxix. p. 282.
[[24]]The large type or non-symbolic portion of the Treatise has been reprinted in a separate volume, under the title Elements of Natural Philosophy, by Professors Sir W. Thomson and P. G. Tait. Part I. Oxford, Clarendon Press, 1873. But the authors appear to me to be inaccurate in describing this work, in the preface, as non-mathematical. It is comparatively non-symbolic, but equally mathematical with the complete Treatise.
[1]This subject of the approximate character of quantitative science is pursued, at some length, in my Principles of Science, chap. xxi., on "The Theory of Approximation," and elsewhere in the same work.
[[2]]Thomson and Tait's Treatise on Natural Philosophy, vol. i. p. 337.
[[1]]See Principles of Science, chap. xiii., on "The Exact Measurement of Phenomena," 3d ed., p. 270.
[[1]]Formal Logic, p. 175.
[[1]]Chapter iv., on the "Value of a Lot of Pleasure or Pain, How to be measured," sec. v. 5.
[[1]]The Emotions and the Will, 1st ed., p. 447.
[[1]]Concerning the meaning and employment of Averages, see Principles of Science, chap. xvi., on "The Method of Means."
[[2]]System of Logic, book vi., chap. ix. sec. 3.
[[1]]2d ed. (Macmillan), 1875.
[[2]]Principles of Science, chaps. vii., ix., xii., etc.
[[1]]Principles of Science, chap. xix., on "Experiment."
[[1]]Hermathena, No. iv., Dublin, 1876, p. 1.
[[2]]Statistical Journal, January 1879, vol. xli. p. 602. Also reprint by Longmans, 1878.
[[2]]Fortnightly Review, December 1876; "The Future of Political Economy."
[[1]]An Introduction to the Principles of Morals and Legislation, by Jeremy Bentham. Edition of 1823, vol. i. p. 1.
[[2]]Principles of Moral and Political Philosophy, book i., chap. vi.
[[1]]The Emotions and the Will, 1st ed., p. 460.
[[1]]An Introduction to the Principles of Morals and Legislation, 2d ed., 1823, vol. i. p. 49. The earliest writer who, so far as I know, has treated Pleasure and Pain in a definitely quantitative manner, is Francis Hutcheson, in his Essay on the Nature and Conduct of the Passions and Affections, 1728, pp. 34-43, 126, etc.
[[1]]Introduction, p. 50.
[[1]]1st ed., p. 30.
[[2]]See above, p. 28.
[[1]]The Emotions and the Will, 1st ed., p. 74.
[[1]]Essays on some Unsettled Questions of Political Economy, p. 132.
[[1]]Inquiry into the Nature and Origin of Public Wealth, 2d ed., 1819, p. 306 (1st ed. 1804).
[[2]]Encyclopœdia Metropolitana, art. "Political Economy," p. 133. 5th ed. of Reprint, p. 11.
[[1]]Harmonies of Political Economy, translated by P. J. Stirling, 1860, p. 65.
[[2]]Traité Théorique et Pratique d'Economic Politique, par J. G. Courcelle-Seneuil, 2me ed., Paris, 1867, tom. i. p. 25.
[[3]]Ib., p. 33.
[[4]]2d ed., p. 11.
[[1]]The theory of dimensions of utility is fully stated in a subsequent section.
[[1]]Encyclopœdia Metropolitana, p. 133. Reprint, p. 12.
[[1]]London: Longmans.
[[2]]Cairnes is, however, an exception. See his work on The Character and Logical Method of Political Economy. London, 1857, p. 81. 2d ed. (Macmillan), 1875, pp. 56, 110, 224 App. B.
[[1]]Pp. 96-99.
[[1]]It is used precisely in its present economical sense in the remarkable "Processe of the Libelle of English Policie," probably written in the fifteenth century, and printed in Hakluyt's Voyages.
[[1]]J.D. Everett's Illustrations of the Centimetre-gramme-second System of Units, 1875; Fleeming Jenkin's Text-Book of Electricity and Magnetism, 1873; Clerk Maxwell's Theory of Heat, or the commencement of his great Treatise on Electricity, vol. i. p. 2.
[[1]]Condillac, Le Commerce et le Gouvernement, Seconde Partie, Introduction. Œuvres Complètes. Paris, 1803. Tom. vii. p. 2.
[[2]]Garnier, Traité d' Economie Politique, 5me ed., p. 11.
[[1]]See chap. iv.
[[2]]See chap. vii.
[[1]]Principles of Political Economy, book iii., chap. i. sec. 1.
[[1]]Principles of Political Economy, book iii., chap. vi.
[[1]]Wealth of Nations, book i., chap. iv., near the end.
[[1]]De l'Intérêt Social, 1777, chap. i. sec. 4.
[[1]]Le Commerce et le Gouvernement, 1776; Œuvres Complètes de Condillac, 1803, tom. 6me, p. 20.
[[1]]I find that Cournot has long since defined the economical use of the word market, with admirable brevity and precision, but exactly to the same effect as the text above. He incidentally says in a footnote (Récherches sur les Principes Mathématiques de la Théorie des Richesses, Paris, 1838, p. 55), "On sait que les économistes entendent par marché, non pas un lieu déterminé ou se consomment les achats et les ventes, mais tout un territoire dont les parties sont unies par des rapports de libre commerce, en sorte que les prix s'y nivellent avec facilité et promptitude."
[71.[71]]Waterston's Cyclopœdia of Commerce, ed. 1846, p. 466.
[[1]]Principles of Science, 1st ed., vol. i. p. 422; 3d ed., p. 363.
[[1]]It is, I believe, verified in the New York Stock Markets, where it is the practice to sell Stocks by auction in successive lots, without disclosing the total amount to be put up. When the amount offered begins to exceed what was expected, then each successive lot brings a less price, and those who bought the earlier lots suffer. But if the amount offered is small, the early buyers have the advantage. Such an auction sale only exhibits in miniature what is constantly going on in the markets generally on a large scale.
[[1]]Principles of Political Economy, book iii., chap. ii. sec. 4.
[[1]]See Magnus's Lessons, sec. 91.
[[1]]Seconde Édition, Paris, 1833, sec. 12, vol. i. p. 14.
[[1]]Since the above was written the value of Cleopatra's Needle has actually formed the subject of decision in the Admiralty Court, in connection with the award of salvage. The fact, however, is that in the absence of any act of exchange concerning such an object, the notion of value is not applicable at all. At the best the value assigned, namely £25,000, is a mere fiction arbitrarily invented to represent what might conceivably be given for such an object if there were a purchaser. It is, moreover, curious that since the first edition was printed Russia has actually made an exchange of islands with Japan.
[[1]]Thornton On Labour; its Wrongful Claims and Rightful Dues (1869), p. 58.
[[1]]See the author's "History of the Floods and Droughts of New South Wales," in the Australian Almanack, Sydney, 1859, p. 61. Also Mr. H. C. Russell's Climate of New South Wales.
[[1]]Serious Fall in the Value of Gold, 1863, p. 33 (reprinted in Investigations in Currency and Finance, 1885). Money and the Mechanism of Exchange (International Scientific Series), chap. xii. This chapter has been translated by M. H. Gravez, and reprinted in the Bibliothèque Utile, vol. xliv. (Germer Baillière), Paris, 1878. See also Papers on the Silver Question read before the American Social Science Association at Saratoga, September 5, 1877, Boston, 1877, and Bankers' Magazine, December 1877 (reprinted in Investigations in Currency and Finance, 1884).
[[1]]Principles of Political Economy, book iii., chap. xviii., end of the 8th section.
[[1]]Principles of Political Economy, book v., chap. iv. sec. 6.
[[1]]See Jevons' Principles of Science, chap. xxii., new ed., pp. 487-489, and the references there given.
[[1]]Chalmers' Christian and Economic Polity of a Nation, vol. ii. p. 240.
[[1]]Chalmers' Christian and Economic Polity of a Nation, vol. ii. p. 242.
[[1]]Ibid., p. 251.
[[1]]Chalmers' Christian and Economic Polity of a Nation, vol. ii. p. 252.
[[1]]Vol. v. p. 324, etc.
[[1]]Quoted in Lauderdale's Inquiry into the Nature and Origin of Public Wealth, 2d ed., 1819, pp. 51, 52.
[[1]]Ibid.
[[1]]No. 200, quoted by Lauderdale, p. 50.
[[1]]The Political and Commercial Works of Charles Davenant, vol. ii. p. 163.
[[1]]Ibid., p. 224.
[[1]]An Inquiry into the Nature and Effects of the Paper Credit of Great Britain, pp. 270, 271.
[[2]]History of Prices, vol. i. pp. 13-15.
[[1]]Six Lectures on Political Economy. Cambridge, 1862.
[[1]]History of Prices.
[[1]]Todhunter's History of the Theory of Probability, chap. xi., etc.
[[1]]Principles of Political Economy and Taxation, 3d ed., p. 2.
[[1]]On the Principles of Political Economy and Taxation, 3d ed., 1821, p. 2.
[[1]]Mr. W. L. Sargant, in his Recent Political Economy, 8vo, London, 1867, p. 99, states that contracts have been made to manufacture the Enfield Rifle, of identically the same pattern, at prices ranging from 70s. each down to 20s., or even lower. The wages of the workmen varied from 40s. or 50s. down to 15s. a week. Such an instance renders it obvious that it is scarcity which governs value, and that it is the value of the produce which determines the wages of the producers.
[[1]]Wealth of Nations, book i., chap. v.
[[2]]Traité Théorique et Pratique d'Economie Politique, 2d ed., vol i. p. 33.
[[1]]I have altered this definition as it stood in the first edition by inserting the words partly or wholly, and I only give it now as provisionally the best I can suggest. The subject presents itself to me as one of great difficulty, and it is possible that the true solution will consist in treating labour as a case of negative utility, or negative mingled with positive utility. We should thus arrive at a higher generalisation which appears to be foreshadowed in the remarkable work of Hermann Heinrich Gossen described in the preface to this edition. Every act, whether of production or of consumption, may be regarded as producing what Bentham calls a lot both of pleasures and pains, and the distinction between the two processes will consist in the fact that the algebraic value of the lot in the case of consumption yields a balance of positive utility, while that of production yields a negative or painful balance, at least in that part of the labour involving most effort. In a happy life the negative balance involved in production is more than cleared off by the positive balance of pleasure arising from consumption.
[[1]]Plutology, p. 24.
[[1]]Natural Elements of Political Economy, p. 119.
[[1]]Edition of 1847, pp. 454, 455.
[[1]]Query No. 20.
[[1]]While revising this edition it seems to me probable that this, as well as some other parts of the theory, might be more simply and generally stated, but what is given is substantially true and correct, and it must stand for the present. [See also the Errata for this page, which reads "for 'in this respect be taken negatively,' read 'in this respect be taken positively.' ".—Econlib Editor.]
[[1]]Babbage, On the Economy of Machinery and Manufactures, sec. 32, p. 30.
[[1]]Vol. ii. p. 324; vol. iii. p. 289. See also Haughton's Principles of Animal Mechanics, 1873, pp. 444-450. The subject has since been followed up with much care and ability by Professor Francis E. Nipher, of the Washington University, St. Louis, Missouri, U.S. Details of his experiments will be found in the American Journal of Science, vol. ix. pp. 130-137; vol. x., etc.; Nature, vol. xi. pp. 256, 276, etc.
[[1]]Inquiry, etc., p. 45, note.
[[1]]New edition, 1839, p. 444.
[[1]]Elements, p. 17.
[[1]]Book i., chap. v. sec. I.
[[2]]Wealth of Nations, p. 445.
[[1]]Principles of Political Economy, p. 100.
[[2]]Manual of Political Economy, 2d ed., p. 47.
[[1]]Elements of Political Economy, 3d ed., 1826, p. 9.
[[1]]Plutology; or The Theory of the Efforts to Satisfy Human Wants, 1864 (Macmillan), p. 139.
[[1]]Political Economy, by Nassau W. Senior, 5th ed., 1863, p. 59.
[[1]]Minard, Annales des Ponts et Chaussées, 1850, 1er Semestre, p. 57.
[[1]]On the Principles of Political Economy and Taxation, chap. i., sec. 5, 3d ed., p. 36.
[[1]]Wealth of Nations, book i., chap. ix., second paragraph.
[[1]]Wealth of Nations, book ii., chap. i., twelfth paragraph.
[[1]]Wealth of Nations, book ii., chap. i., twelfth paragraph continued.
[[1]]Principles of Political Economy, book i., chap. v., sec. 2.
[[1]]Plutology: or The Theory of the Efforts to satisfy Human Wants. By William Edward Hearn, LL.D., Professor of History and Political Economy in the University of Melbourne. London (Macmillan and Co.), 1864, p. 329.