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• Preface to the Third Edition (1928)
• Note to the Fourth Edition (1932)
• Part I: Welfare and the National Dividend
• Chapter I: Welfare and Economic Welfare
• Chapter II: Desires and Satisfactions
• Chapter III: The National Dividend
• Chapter IV: What Is Meant By Maintaining Capital Intact
• Chapter V: Changes In the Size of the National Dividend
• Chapter VI: The Measurement of Changes In the Size of the National Dividend
• Chapter VII: Economic Welfare and Changes In the Size of the National Dividend
• Chapter VIII: Economic Welfare and Changes In the Distribution of the National Dividend
• Chapter IX: Reactions Through the Numbers of the Population
• Chapter X: The National Dividend and the Quality of the People
• Chapter XI: The Method of Discussion to Be Followed
• Part II: The Size of the National Dividend and the Distribution of Resources Among Different Uses
• Chapter I: Introductory
• Chapter II: The Definition of Marginal Social and Private Net Products
• Chapter III: The Values of Marginal Social Net Products and the Size of the National Dividend
• Chapter IV: Rates of Return and the Values of Marginal Private Net Products
• Chapter V: The Effects of Eliminating Obstacles to Movement
• Chapter VI: Hindrances to Equality of Returns Due to Imperfect Knowledge
• Chapter VII: Hindrances to Equality of Returns Due to Imperfect Divisibility of the Units In Terms of Which Transactions Are Conducted
• Chapter VIII: Hindrances to Equality of Returns Due to Relative Variations of Demand In Different Occupations and Places
• Chapter IX: Divergences Between Marginal Social Net Product and Marginal Private Net Product
• Chapter X: Marginal Private and Social Net Products In Relation to Industrial Forms
• Chapter XI: Increasing and Decreasing Supply Price
• Chapter XII: State Regulation of Competitive Prices
• Chapter XIII: State Regulation of Supplies
• Chapter XIV: The Conditions of Monopolisation
• Chapter XV: Monopolistic Competition
• Chapter XVI: Simple Monopoly
• Chapter XVII: Discriminating Monopoly
• Chapter XVIII: The Special Problem of Railway Rates
• Chapter XIX: Purchasers' Associations
• Chapter XX: Intervention By Public Authorities
• Chapter XXI: Public Control of Monopoly
• Chapter XXII: Public Operation of Industries
• Part III: The National Dividend and Labour
• Chapter I: Industrial Peace
• Chapter II: The Classification of Industrial Differences
• Chapter III: Voluntary Arrangements For Conciliation and Arbitration
• Chapter IV: Mediation
• Chapter V: Coercive Intervention
• Chapter VI: An Analytical View of Industrial Peace
• Chapter VII: Hours of Labour
• Chapter VIII: The Methods of Industrial Remuneration
• Chapter IX: The Distribution of Labour Among Occupations and Places
• Chapter X: Employment Exchanges
• Chapter XI: Unemployment Versus Short Time
• Chapter XII: The Practicability of Interference to Raise Wages
• Chapter XIII: Methods of Engaging Labour
• Chapter XIV: Interference to Raise Wages In Places and Occupations Where They Are Unfair
• Chapter XV: Fair Wages Inside Particular Industries
• Chapter XVI: Fairness As a Variable Relation
• Chapter XVII: Interference to Raise Wages In Places and Occupations Where They Are Already Fair
• Chapter XVIII: Wage Rates and Capacity
• Chapter XIX: A National Minimum Time-wage
• Chapter XX: Fixed and Fluctuating Wage Rates In Particular Industries
• Part IV: The Distribution of the National Dividend
• Chapter I: The General Problem of Disharmony
• Chapter II: Pareto's Law
• Chapter III: The Supply of Capital and Labour
• Chapter IV: Inventions and Improvements
• Chapter V: The Manipulation of Wages
• Chapter VI: Rationing
• Chapter VII: Subsidies to Wages
• Chapter VIII: Direct Transferences From the Relatively Rich to the Relatively Poor
• Chapter IX: The Effect On the National Dividend of the Expectation of Transferences From the Relatively Rich
• Chapter X: The Effect On the National Dividend of the Expectation of Transferences to the Poor
• Chapter XI: Bounties On Things Purchased By the Poor
• Chapter XII: The Effect On the National Dividend of the Fact of Transference From the Relatively Rich to the Poor
• Chapter XIII: A National Minimum Standard of Real Income
• Appendix I Uncertainty-bearing As a Factor of Production
• Appendix Ii the Measurement of Elasticities of Demand
• Appendix Iii a Diagrammatic and Mathematical Treatment of Certain Problems of Competition and Monopoly

Chapter XIII

A NATIONAL MINIMUM STANDARD OF REAL INCOME

§ 1. WHEN we desire to determine whether the fact and the expectation of the fact, taken together, of any given annual transference of resources from the relatively rich to the relatively poor are likely to increase the national dividend, all the various considerations set out in the preceding chapters must be taken into account. There is little doubt but that plans could be devised, which would enable transferences, involving a very large amount of resources, to be made with results advantageous to production. Since the generality of these transferences will also increase the real incomes of the relatively poor, they must redound to the advantage of economic welfare in a wholly unambiguous way. Transferences which diminish the national dividend, on the other hand, are liable, through various reactions which have been indicated in the course of this discussion, to diminish the real earnings of the relatively poor; and, if their amount is kept constant, they may do this to so great an extent that the earnings per year of the relatively poor plus the transference made to them will ultimately be less than their earnings alone would have been, had no transference been made. When this happens, these transferences also affect economic welfare in an unambiguous way: this time by injuring it. There remains, however, one further sort of transference, the results of which cannot be unambiguous. I refer to a system of transferences varied from year to year in such a way as to compensate for any reduction that may come about in that part of the income of the poor which accrues to them through earnings. An arrangement of this sort is implicitly introduced whenever a government establishes a minimum standard of real income, below which it refuses to allow any citizen in any circumstances to fall. For the establishment of such a minimum standard, implying, as it does, transferences to the poor of a kind that differentiate in favour of poverty, is likely to diminish the national dividend, while it will, at the same time, for an indefinitely long period, increase the aggregate real income of the poor. To determine the effect, which the establishment of this kind of minimum standard is likely to exercise upon economic welfare, involves, therefore, a balancing of conflicting considerations.

§ 2. Before this balancing is attempted, it is desirable to obtain a clear notion of what precisely the minimum standard should be taken to signify. It must be conceived, not as a subjective minimum of satisfaction, but as an objective minimum of conditions. The conditions, too, must be conditions, not in respect of one aspect of life only, but in general. Thus the minimum includes some defined quantity and quality of house accommodation, of medical care, of education, of food, of leisure, of the apparatus of sanitary convenience and safety where work is carried on, and so on. Furthermore, the minimum is absolute. If a citizen can afford to attain to it in all departments, the State cares nothing that he would prefer to fail in one. It will not allow him, for example, to save money for a carouse at the cost of living in a room unfit for human habitation. There is, indeed, some danger in this policy. It is a very delicate matter for the State to determine authoritatively in what way poor people shall distribute scanty resources among various competing needs. The temperaments and circumstances of different individuals differ so greatly that rigid rules are bound to be unsatisfactory. Thus Dr. Bowley writes: "The opinion is quite tenable that the poor are forced (by the effect of the law to enforce a minimum quality and quantity of housing accommodation) to pay for a standard of housing higher than they obtain in food, and that they would make more of their income if they were worse housed and better fed."30 This danger must be recognised; but the public spirit of the time demands also that it shall be faced. A man must not be permitted to fall below the minimum in one department in order that he may rise above it in others. Again, if a citizen cannot afford to attain the minimum in all departments, but, by failing in one, can remain independent, that does not justify the State in standing aside. The State must not permit anywhere hours of child labour or of women's labour or conditions of housing accommodation incompatible with the minimum standard, on the ground that, by resort to them, some given family could, and, without resort to them, it could not, support itself; for, if that is the fact, the family ought not to be required to support itself. There is no defence for the policy of "giving poor widows and incapable fathers permission to keep their children out of school and take their earnings."31 Rather, the Committee on the Employment of Children Act are wholly right when they declare: "We feel, moreover, that the cases of widows and others, who are now too often economically dependent on child labour, should be met, no longer by the sacrifice of the future to the present, but, rather, by more scientific, and possibly by more generous, methods of public assistance."32 The same type of reasoning applies, with even greater force, to the common plea that women should be allowed to work in factories shortly before and shortly after confinement, because, if they are not allowed to do this, they and their children alike will suffer shocking poverty. In these circumstances it is the duty of the State, not to remit the law, but to defend those affected by it from this evil consequence.

§ 3. There is general agreement among practical philanthropists that some minimum standard of conditions ought to be set up at a level high enough to make impossible the occurrence to anybody of extreme want; and that whatever transference of resources from relatively rich to relatively poor persons is necessary to secure this must be made, without reference to possible injurious consequences upon the magnitude of the dividend.33 This policy of practical philanthropists is justified by analysis, in the sense that it can be shown to be conducive to economic welfare on the whole, if we believe the misery that results to individuals from extreme want to be indefinitely large; for, then, the good of abolishing extreme want is not commensurable with any evils that may follow should a diminution of the dividend take place. Up to this point, therefore, there is no difficulty. But our discussion cannot stop at this point. It is necessary to ask, not merely whether economic welfare will be promoted by the establishment of any minimum standard, but also by what minimum standard it will be promoted most effectively. Now, above the level of extreme want, it is generally admitted that increments of income involve finite increments of satisfaction. Hence the direct good of transference and the indirect evil resulting from a diminished dividend are both finite quantities; and the correct formal answer to our question is that economic welfare is best promoted by a minimum standard raised to such a level that the direct good resulting from the transference of the marginal pound transferred to the poor just balances the indirect evil brought about by the consequent reduction of the dividend.

§ 4. To derive from this formal answer a quantitative estimate of what the minimum standard of real income established in any particular country at any particular time ought to be, it would be necessary to obtain and to analyse a mass of detailed information, much of which is not, in present circumstances, accessible to students. One practical conclusion can, however, be safely drawn. This is that, other things being equal, the minimum can be advantageously set higher, the larger is the real income per head of the community. The reason, of course, is that every increase in average income implies a diminution in the number of people unable by their own efforts to attain to any given minimum standard; and, therefore, a diminution, both absolute and proportionate, in the damage to the dividend which an external guarantee of that standard threatens to bring about. It follows that, when we have to do with a group of pioneer workers in rough and adverse natural circumstances, the minimum standard may rightly be set at a low level. But, as inventions and discoveries progress, as capital is accumulated and Nature subdued, it should be correspondingly raised. Thus it is reasonable that, while a relatively poor country makes only a low provision for its "destitute" citizens, a relatively rich country should make a somewhat better provision for all who are "necessitous."34

§ 5. In this connection it is important that there should be no confusion as to what is meant by a rich country. For the present purpose country means, not Government, but people. There is a widespread impression that a nation's duty to make provision for its poorer citizens depends upon the amount of money that the Government has to provide for other purposes; and from this it is inferred that the great increase in the British Budget required to meet the annual charges on the war debt justifies, and, indeed, commands, large retrenchments in social expenditure. This idea is, in great measure, illusory. It is true, of course, that the indirect effect in checking production of the expectation of continuous taxation sufficient to yield 800 million post-war £s annually is a good deal greater than that of the expectation of taxes yielding 200 million pre-war £s. But this, though important, is a secondary matter. The essential fact is that, when interest is paid to domestic holders—the case is, of course, different with foreign holders—of Government securities, no part of the real income of the country is directly used up. Resources are merely transferred from one group of citizens to another. No doubt, when a nation has to provide funds for a large internal debt in consequence of a war, this is a sign that resources have been expended on war that might have been expended on building up capital equipment and so making the real income larger. It must not be forgotten, however, that a large part of the resources that were lent, for example, to the British Government by its citizens in the Great War, was not withdrawn from what would have been real capital, but was the result of economies in consumption and special activities in production, which, but for the war, would not have taken place. Even, therefore, as a sign of a country's capacity to give help to its poor, the magnitude of an internal war debt is of little use. The true test of this capacity is the direct one—aggregate real income compared with population. It is, indeed, proper to subtract from this the resources which are necessarily used up in unproductive ways. Thus, when a country is so situated that it has to devote an exceptionally large proportion of its real income to the upkeep of powerful armaments, or to the payment of interest to foreigners, who, in the past, have lent money to its Government, or to machinery for preserving internal order, account must be taken of these things. As a rule, however, they are relatively unimportant. The amount of the aggregate real income in relation to the number of the population is the dominant relevant fact.

§ 6. For the United Kingdom the best available estimate gives an aggregate national income, for 1913-14, represented at then prices by some 2250 million pounds. Deducting some 250 millions for rates and taxes and some 230 millions for new investments, we have left a sum sufficient, if it could have been divided up equally without being diminished in the process, to yield an income of £162 to each representative family of 4½ persons.35 Of course, as a matter of fact, it would have been quite impossible to pool the national income in this way without a large part of the flow of goods and services, which this money figure represents, disappearing altogether. Apart from great improvements in productive organisation, which may, perhaps, be hoped for, but certainly cannot be predicted with confidence, there is no reason to expect that the real income per head of the country—we need not trouble about its swollen reflex in the glass of money—will be substantially greater in the near future than it was in 1913-14. In view of these facts it is plain that, wealthy as this country is, as compared both with itself in the past and with most of its neighbours in the present, it is not wealthy in an absolute sense. As things are it is literally impossible for it, by any manipulation of distribution, to provide for all its citizens a really high standard of living. In so far, therefore, as social reformers rely upon improvements in the distribution of wealth, as distinguished from improvements in production, they are bound to chasten their hopes. The national minimum may rightly be set now much higher than it could have been set a hundred or fifty years ago. But, with the national average no larger than it is, it is inevitable that the national minimum must still be set at a deplorably low level.

§ 7. So far nothing has been said of the common view that, in determining the minimum standard which it will establish for itself, one country must have regard to the policy of other countries. It is widely held that the prohibition in England of socially undesirable practices, such as the employment of women at night, the use of unfenced machinery, the building of factories without proper sanitary arrangements, or the working of unduly long hours, involve a larger real cost to us if undertaken here alone than if undertaken by all industrial countries together. The reason commonly given for this view, that isolated action here would cause a flood of imports from abroad destructive of our industries, fails to take account of the fact that, subject to certain well-known qualifications, imports cannot expand in the long period without exports expanding correspondingly; so that our industries as a whole could not suffer injury in the manner contemplated. It is true, however, that, if a handicap is imposed on productive methods in one country only, there will be a tendency for employing power, capital and labour to leave that country. If all leave in equal proportions, the general scale of the country's industry will be correspondingly reduced, the rate of pay per unit of every factor remaining much as before. The national dividend need not fall as much as production falls, because capitalists may still live and receive income here while employing their capital elsewhere. Since, in fact, capital—at all events if we suppose the obstacle of double income-tax to be done away with by international and intra-imperial agreement—is more mobile than labour, the presumption is that capital will leave in a somewhat larger proportion, and that, therefore, the earnings per head of work-people will fall. In whatever way the detail of the movement is worked out, it is plain that economic welfare in the country affected is likely to be lessened. The injury thus inflicted on it cannot, it should be observed, be prevented by setting up a tariff against imports from countries where labour legislation is less advanced. On the contrary, such a tariff, by interfering with the normal distribution of the country's resources among different occupations, would, in general, make the national dividend smaller, and the injury, therefore, worse. If, however, the handicap of these high minima is extended to all important countries by international labour legislation, the danger that our capital will be driven abroad is removed—at the cost of some slight damage to us in the terms on which our goods exchange against foreign goods.

§ 8. From these considerations it appears that the extension by international labour legislation of regulations, which are both desirable in themselves and also a real handicap to industry, is likely, though in a way different from that commonly supposed, to lessen the burden which these regulations would inflict on any country adopting them in isolation. To this extent it will, therefore, really be easier for a country to rule out injurious methods and processes, if it can persuade other nations to move forward in company with it. Moreover, when the injurious methods specially affect particular industries, an international agreement will really make it easier for the persons engaged in those industries to accept a veto upon injurious methods; and it will almost always be thought to make this easier both for those persons and for the community regarded as a whole. Hence the development of machinery for international labour legislation may be expected to accomplish something solid in speeding up improvements in industrial conditions. The advantage to be looked for is the greater in that many improvements in method, which are not really handicaps at all, but, through their effect on efficiency, net benefits, are, nevertheless, popularly believed to be handicaps, and are, therefore, unlikely to be adopted by cautious statesmen without some outside stimulus. International negotiation may often furnish such a stimulus and give strength to reformers in a country where the social movement is slack or the power of vested interests strong. There can be little doubt, for example, that the Franco-Italian treaty of 1906 led indirectly to a general improvement in Italian practice in the supervision and enforcement of labour laws. At the same time it would be a mistake to expect from the lever of internationalism more than it has power to give. Inevitably international minima, if they are to secure general or wide assent, must lag behind the practice of the most advanced nations. It would be disastrous if a custom should grow up of regarding these international minima as national maxima; for that would check the forward movement of pioneer nations, and so indirectly of the whole world. Just as a "good" employer, while welcoming the Factory Acts, will keep his own practice well in advance of the legal standards, so also a "good" nation will always maintain national laws more ambitious than those which at the time have international sanction.36

§ 9. One word should be added in conclusion. In spite of what was said in Part I. Chapter IX. about the probable reaction of improved fortunes upon the standard of living, it must be conceded that the establishment by the State of an effective national minimum, since it must in effect, if not in name, differentiate to some extent in favour of large families, may somewhat increase the birth-rate among the poor. It is reasonable to hope that this tendency would not be very pronounced, since the people affected would be mainly those the size of whose families is not determined to any large extent by economic considerations. As much cannot be said, however, of an associated tendency. The establishment of an effective minimum standard, if adopted in one country alone, might well lead to a considerable increase in the numbers of the population through the immigration of relatively inefficient poor persons attracted by the prospect of State aid. If it did lead to this, the new immigrants would consume more than they contributed to the dividend; and, as their numbers grew, the native-born citizens of the country concerned would be more and more heavily mulcted to maintain them. It is, therefore, to the advantage of a State, which has established a minimum standard above that enjoyed by its neighbours, to forbid the immigration of persons who seem unlikely to attain this minimum without help from the public funds. To this end idiots, feeble-minded persons, cripples, beggars and vagrants, and persons over or under a certain age may be excluded, unless they are either accompanied by relatives able to support them, or themselves possess an adequate income derived from investments.37 Unfortunately, however, it is exceedingly difficult to devise machinery which shall be effective in excluding all "undesirable" immigrants without at the same time excluding some that are "desirable."

APPENDIX I
UNCERTAINTY-BEARING AS A FACTOR OF PRODUCTION

§ 1. IT is customary in economic discussion to class together as factors of production, along with the services of Nature, waiting and various sorts of mental and manual labour. In a world in which all future events were perfectly foreseen this catalogue would be substantially adequate. But in the actual world some future events are not perfectly foreseen. On the contrary, in the vast majority of enterprises, in the conduct of which resources are waited for, they are also exposed to uncertainty; they are turned, that is to say, into a use, the result of which cannot be certainly predicted. In these circumstances it is proper that there should be added to the list of factors of production enumerated above a further group comprising various sorts of uncertainty-bearing.

§ 2. The principal reason why this arrangement is not usually adopted seems to be that, in practice, uncertainty-bearing is bound up in such intimate association with waiting that the possibility of separating the two in analysis is not immediately apparent. Reflection, however, makes it plain that the connection between them is not a necessary or inherent connection,—that they are, in fact, two things generally found together, and not a single thing. Thus let us imagine a man in possession of a vase, which, as a vase, is worth £100, but, if broken, would be worth nothing; and let us suppose the owner to know that this vase contains something, whose value is equally likely to be anything between nothing and £250. If the owner breaks the vase, he is, then, equally likely to lose any sum up to £100 or to gain any sum up to £150. The actuarial value of his chance is, therefore, £25, and, if there were a million people in his position, and they all elected to break their vases, the aggregate wealth of them all would probably be increased by about £25,000,000. In other words, the services of these million people, in bearing the uncertainty of placing £100 each in a position where it is equally likely to become anything between nothing and £250, are responsible for an addition of £25,000,000 to national wealth. This example shows that uncertainty-bearing, though generally associated with waiting, is analytically quite distinct from it. Nor was it really necessary to seek an illustration so far removed from actual life. If a man contracts to deliver 100 bushels of wheat six months hence, with the intention of buying them for that purpose on the day of delivery at a price which he hopes will be lower than his contract price, that man, no less than the breaker of the vase, provides uncertainty-bearing without providing any waiting. Uncertainty-bearing is thus seen to be an independent and elementary factor of production standing on the same level as any of the better-known factors.

§ 3. In the way of this general conception there are two serious difficulties. The first of them can be set out as follows. It is well known that the ordinary factors of production are two-dimensional, in the sense that a unit of any of them can only be expressed as a quantity of stuff multiplied by a quantity of time. Waiting consists in the provision of a given quantity of resources, and labour in the provision of a given quantity of labour, during a given period. Thus the unit of waiting is said to be a year-pound, and the unit of labour a year-labourer.38 It would seem, therefore, that, if uncertainty-bearing, as a factor of production, is to stand on a level with waiting and labour, it must somehow bear a relation to time analogous to that which they bear. But uncertainty-bearing, unlike waiting and labour, is in its essence independent of time, and, so far as pure theory goes, capable of instantaneous consummation. Consequently, the provision of a given quantity of uncertainty-bearing of any sort for a given period seems at first sight a mere phrase without substantial meaning. The difficulty thus suggested is, however, obviated by the fact that, as a matter of practice, the consummation of any act of uncertainty-bearing is not instantaneous, but involves a process in time. The uncertainty-bearing, for example, which a company promoter undertakes, is not completed until the public has come in and allowed him to unload, and this, of course, will not happen till a considerable interval has elapsed. This circumstance enables us to fashion a unit of uncertainty-bearing on the same plan as the units of waiting and of labour. This unit is the exposure of a £ to a given scheme of uncertainty, in an act the consummation of which occupies a year. The exposure of a £ to a succession of like schemes of uncertainty during a year, in acts the consummation of which occupies on the average, say, ten days, will thus embrace 365/10 of these units. We have in this way obtained a two-dimensional unit of uncertainty-bearing analogous to the units of waiting and of labour, and the difficulty, which this section was designed to discuss, has been overcome.

§ 4. The second difficulty is in this wise. Labour and waiting are objective services, the aversion to providing which may vary with different people, but which, in themselves, are the same for everybody. Uncertainty-bearing, however, it may be said, is in its essence a subjective state, invoked, indeed, by external conditions but bearing a quite different relation to these conditions for people of different temperaments and with different information. It would seem, therefore, at first sight that the amount of uncertainty-bearing involved in carrying through any operation must depend, not only on the nature of the operation, but also on the temperament and knowledge of the people who bear the uncertainty. Such a conception, however, is fatal to the symmetry of our analysis. If there is to be any real parallel with labour and waiting, we must define uncertainty-bearing objectively. Thus the uncertainty-bearing involved in the investment of any given amount of resources means for us the uncertainty-bearing which that investment would involve if it were made by a man of representative temperament and with representative knowledge. If the investment is actually made by a man who never feels subjective uncertainty, whatever the evidence, or by a man who possesses information adequate to destroy subjective uncertainty, we shall say, not that less uncertainty-bearing has been taken up, but that a given amount has been taken up by a person, who, from temperament or information, is an exceptionally ready bearer of uncertainty. There is, it must be admitted, an arbitrary and artificial appearance about this method of defining our key term; but there appears to be no way in which this can be avoided.

§ 5. Up to this point we have taken no account of the fact that uncertainty-bearing, like labour, is a term embracing a large group of factors of production, rather than a single factor. It must now be observed, however, that, just as there are many different sorts of labour, so there are many different sorts of uncertainty, embodied in many different schemes of prospective returns, to which, in the course of industry, resources may be exposed. A scheme of prospective returns can be represented diagrammatically in the following manner. Along a base-line OX mark off all possible yields that may result from the exposure of a £ to the scheme in question; and, through each point on OX, draw an ordinate proportionate to the probability, on the evidence, of the corresponding return. Join the tops of all these ordinates, as in the figure on the next page. Evidently any scheme of prospective returns can be represented by a curve formed upon this plan. Furthermore, the principal species of schemes that are liable to occur can be distinguished into certain broad groups. Find on OX a point B, such that OB represents the actuarial value of the chances of the returns indicated on the curve, or, in other words, such that OB is equal to the sum of the products of each several ordinate multiplied by the corresponding abscissa, divided by the sum of the ordinates; and let the ordinate through B cut the curve in H. In like manner, find on OX a point M, such that OM represents the most probable, or most "frequent," return relevant to the scheme of prospective returns under review; and let the ordinate through M cut the curve in K. On this basis we may distinguish, in the first place, between curves which are symmetrical, in such wise that BH and MK coincide, and curves which are asymmetrical. The symmetrical group includes schemes of such a sort that, if r is the actuarial value of a pound exposed to any scheme, the chance of obtaining a return (r - h) is equal to the chance of obtaining a return (r + h), for all values of h. The asymmetrical group includes all other schemes. The symmetrical type is only possible when the conditions are such that the exposure of a pound to uncertainty cannot yield a gain greater than a pound, since, from the nature of things, it cannot yield a loss greater than this. Secondly, within the symmetrical group we may distinguish curves which are spread out, like open umbrellas, and curves which are narrow, like closed umbrellas. The former sort represent schemes in which a wide divergence, the latter schemes in which only a small divergence, of the actual from the most probable return is probable. Thirdly, within the asymmetrical group we may distinguish curves in which MK lies respectively to the right and to the left of BH. The former sort represent schemes in which the most probable outcome is a moderate return on the money invested, but a small return is more probable than a large one. A scheme of this kind would be embodied in a lottery offering a great number of small prizes and one or two blanks. Again, a £ might be lent to somebody: and there might be 96 chances of its return in full, 1 chance that 10s. would be returned, 1 chance that 5s. would be returned, and 2 chances that none would be returned. The actuarial value of this scheme of prospect is £ 968/100: the most probable return is £1. The latter sort of curves represent schemes in which the most probable outcome is a small return, but large returns are possible. A lottery of the ordinary kind, containing a few large prizes and many blanks, affords an example of this sort of scheme. Within each of the groups thus distinguished an indefinite number of further subdivisions could be made. Of course a great many schemes of prospective returns are not represented by continuous curves, but by a few isolated points with gaps between them, these gaps corresponding to returns which are not possible.

§ 6. The existence of the great variety of schemes of prospective returns, each representing different sorts of uncertainty, might seem at first sight to vitiate the attempt, which was made in an earlier section, to treat "the factor uncertainty-bearing" and "the factor waiting" on the same footing. For waiting is a single thing, while uncertainty-bearing is a group of different things. The meaning of a change in the supply of waiting is, therefore, clear; but how are we to conceive of a change in the supply of uncertainty-bearing? This difficulty, though it is a natural one to raise, is easily overcome. For, after all, uncertainty-bearing in this regard stands in exactly the same position as labour. Labour in general includes an immense variety of different sorts and qualities of labour. This circumstance does not prevent us from making use of the general concept labour alongside of the concept waiting. In order to render this procedure legitimate, all that we need do is to select in an arbitrary manner some particular sort of labour as our fundamental unit, and to express quantities of other sorts of labour in terms of this unit on the basis of their comparative values in the market. In this way all the various sorts of labour supplied or demanded at any time can be expressed in a single figure, as the equivalent of so much labour of a particular arbitrarily chosen grade. Exactly the same device is available for uncertainty-bearing. The uncertainty involved in exposing a pound to a particular arbitrarily chosen scheme of prospective returns can be selected as a fundamental unit, and the uncertainty involved in other exposures can be reduced, on the basis of comparative market values, to its equivalent in terms of this unit. So soon as this is understood, an apparently formidable obstacle in the way of assimilating uncertainty-bearing to the other factors of production can be successfully overcome.

§ 7. When the assimilation is accomplished, and all the various sorts of uncertainty, to which, in different industries, people submit resources, are translated into terms of the uncertainty-bearing involved in some representative scheme of prospective returns, there will be a supply schedule and a demand schedule for pounds to be exposed to this scheme, just as there are a supply and a demand schedule for pounds to be exposed to "waiting." The demand price or the supply price for the exposure of any given quantity of pounds is the excess of money offered or asked above the actuarial value of a £ so exposed. For different quantities of uncertainty-bearing the demand price and the supply price will, of course, both be different. For some quantities the supply price will be negative. Up to a point, people will gamble because they like the excitement, even though they know that, on the whole, they are likely to lose money. But, though some amount of uncertainty-bearing, like some amount of labour, would be forthcoming for industry, even if there were no expectation of reward, in present conditions more is wanted than can be obtained on those terms. The main reason is that an uncertain prospect actuarially worth £100 of money is much less satisfactory than a certain prospect also worth £100 of money. This follows from the law of diminishing utility. One income of £90 plus one of £110 carry less satisfaction, other things being equal, than two incomes each of £100. Thus, in respect of such quantities of uncertainty-bearing as are actually made use of in modern industry, the supply price, like the supply price of the other factors of production, is positive; and the general conditions determining the value, or price, of uncertainty-bearing are similar to those determining the price of those factors.

§ 8. It must be clearly understood that the payment thus asked and offered for uncertainty-bearing is by no means the same thing as the exceptional profits obtained by persons who have succeeded in risky businesses. An uncertain undertaking is a risky undertaking. But the term risk is generally used to mean the chance of obtaining a smaller return than the actuarially probable return. This must be compensated by a corresponding chance of obtaining a larger return than this. Even though no payment whatever is made for uncertainty-bearing, the successful undertakings in a risky business would still need to make exceptional profits as an offset to the exceptional losses of those which fail. Otherwise the whole body of investors in the business, taken collectively, would be obtaining less than normal returns from investment in it. The payment for uncertainty-bearing, therefore, consists, not in the whole of the excess above normal profits earned by these successful undertakers, but only in that (generally small) part of this excess which is not cancelled by the corresponding losses of other undertakers who have fallen out of the race.

§ 9. It has next to be observed—and here we follow the line of though indicated in § 4—that the supply of uncertainty-bearing, as defined in the objective manner there set out, will be increased by anything that enables people with more knowledge to undertake risky enterprises in lieu of people with less knowledge. Every form of organisation that enables risks to be shifted on to the shoulders of specialists—the resort of farmers to speculators in grain prices through hedging on the produce exchange, the resort of bankers to specialist bill-brokers in negotiating the discount of bills, the resort of manufacturers for the foreign market to specialist export houses, and so on, has this effect. It may be added that a similar effect is produced when risky undertakings are taken over by rich persons instead of by poor persons. For, if a man possesses (x + 100)£, to expose £100 to a 5 per cent range of uncertainty is to accept an even chance of having (x + 105)£ or £(x + 95). But there is reason to believe that, not merely the desire for an extra unit of resources in general, but also the rate of diminution of this desire, diminishes as the number of units in our possession grows. It follows that the probable loss of satisfaction involved in accepting the above even chance instead of a certain (x + 100)£ is smaller the larger is the value of x.

§ 10. Like any other factor of production, uncertainty-bearing may improve in technical efficiency. The central fact, upon which the improvements in it that have actually taken place depend, is that forecasts based upon existing knowledge are, in general, more certain when they are made about collections than when they are made about individual members of collections. If all the individual members were so linked together that they necessarily always acted in the same way, this, of course, would not be so. But in many collections there are some individual members that are complementary to one another. Thus, on a holiday, it is uncertain whether indoor entertainers will make a great deal of money or very little money, because it is uncertain whether the weather will be wet or fine. In like manner and for the same reason it is uncertain whether outdoor entertainers will make very little money or a great deal of money. But the amount that the two sorts of entertainers together will make may be susceptible of nearly accurate forecast.39 The case is similar with exporters and importers between countries the mutual exchange rate of whose moneys is varying; the exporters and importers will be affected in opposite senses if the exchange moves up or down between the making and the completion of foreign trade contracts. In circumstances such as these, so soon as an organisation is set up that combines the two complementary uncertainties under a single head, they neutralise or destroy one another. Nor is it only when uncertainties are complementary that combination reduces them. The same result follows, though in a less marked degree, when they are simply independent. The measure of reduction to be expected from combination in these circumstances is indicated in the familiar corollary to the normal law of error, which asserts that the "precision of an average is proportional to the square root of the number of terms it contains."40 This implies that, if there is an even chance that the investment of £100 in one assigned venture will yield a return greater than £95 and less than £115, there is an even chance that £100 scattered among a hundred similar investments will, if all the causes affecting the different investments are independent, yield a return lying between £104 and £106. If only some of the causes are independent and some common, the range within which it is more probable than not that the return will lie will be greater than that enclosed between £104 and £106, but it will still be smaller than that enclosed between £95 and £115. It follows, that, if out of a hundred people, each of whom has £100 to invest, every one divides his investment among a hundred enterprises, the aggregate amount of uncertainty-bearing undertaken by the group is smaller than it would have been had every investor concentrated on a single enterprise. The physical results of the investments taken together must, however, be the same. Therefore, whenever more or less independent uncertainties are combined together, a given result can be attained by a smaller amount of uncertainty-bearing, or, to put the matter otherwise, the factor uncertainty-bearing has been made technically more efficient.41 The principle thus explained is fully recognised by business men, and has long lain at the root both of insurance and of much speculative dealing on 'Change. Thus the segregation of the speculative element in certain forms of business and its concentration upon a relatively small number of speculators have not only changed the distribution, but have reduced the aggregate amount, of uncertainty-bearing required in industry. In modern times the range over which this principle can be applied has been greatly extended by three important developments. Of these the first is a legal change, namely, the concession to joint-stock companies of the privilege of limited liability; the second an economic change, namely, the development of organised speculative markets; the third also an economic change, namely, the development of the means of transport and communication. The ways in which these three changes have facilitated the application of the above principle will now be examined.

§ 11. So long as liability was unlimited, it was often against a man's interest to spread his investments; for, if he did so, he multiplied the points from which an unlimited call on his resources might be made. The English Limited Liability Act of 1862 and its foreign counterparts enabled investments to be spread without evoking this danger. Furthermore, intermediary organisations, themselves fortified by limited liability, have been developed, capable of spreading investments on behalf of persons whose resources are too small to allow of their spreading them for themselves. Since the minimum share in industrial enterprises is seldom less than £1, the small investor's capacity for direct spreading is narrowly restricted. Savings banks, friendly societies, trade unions, building societies, co-operative societies, trust companies and so forth—all of them limited liability associations—are able, however, to put him in a position as favourable in this respect as is occupied by the large capitalist. Nor is it only the spreading of investments that the system of limited liability has facilitated. It has also made possible the spreading, or combination, of risks in a wider sense. For, in general, each business deals directly or indirectly with many businesses. If one of them fails for a million pounds, under unlimited liability the whole of the loss falls on the shareholders or partners—provided, of course, that their total resources are adequate to meet it—but under limited liability a part of it is scattered among the shareholders or partners of a great number of businesses. Hence any shareholder in one business combines with the uncertainty proper to his own business some of that proper to other businesses also. It follows that the range of uncertainty, to which a normal £100 invested in industry is subjected by reason of failures, is still further diminished in amount. This advantage is additional to, and quite distinct from, any direct national gain which limited liability may give to a country by throwing a part of the real cost of its unsuccessful enterprises upon foreigners.

§ 12. The development of organised speculative markets enables the producing classes to shift uncertainty-bearing on to speculators, in whose hands they in great part cancel out. Thus the miller, who is contracting to deliver flour at a fixed price some months hence, can protect himself by buying "a future" in wheat at the same time that he makes his contract, and afterwards selling the "future" pari passu with purchases of "spot" wheat of various grades as he needs them for his milling. In like manner, the farmer can protect himself by selling a future at an early stage, and afterwards buying to cover it in the speculative market at the same time that he sells his actual wheat in the spot market. Plainly these processes involve a large reduction in the amount of uncertainty-bearing that has to be undergone to accomplish a given result. The chief conditions needed to render any class of products suitable to be handled in the type of organised market that permits of their use have been succinctly stated by Marshall as follows: "(1) That the product is not quickly perishable; (2) that the quantity of each thing can be expressed by number, weight, or measure; (3) that the quality can be determined by tests that yield almost identical results when applied by different officials, assumed to be expert and honest; and (4) that the class is important enough to occupy large bodies of buyers and sellers."42

§ 13. There remains the development of the means of communication. This facilitates the combination of uncertainties in one very simple way. It puts investors into contact with a greater number of different openings than were formerly available. This effect, though of great importance, is so obvious and direct that no comment upon it is required. There is, however, a more subtle way in which the development in the means of communication works. Dr. Cassel has observed that industrial firms have, in recent times, been lessening the quantity of stock that they carry in store waiting to be worked up, relatively to their total business. The improvement in this respect applies all round. As regards production, "there is, in the best-organised industries, very little in the way of material lying idle between two different acts of production, even if these acts have to be carried out in different factories, perhaps at great distances from each other. A modern iron-works has no large stock either of raw materials or of their product, yet there is a continuous stream of ore and coal entering, and of iron being turned out of it."43 In like manner, factories are coming to keep a smaller amount of capital locked up in the form of reserve machines not ordinarily in use. The same tendency is apparent in retail trading. The ratio of the average amount of stock kept to the aggregate annual turn-over is smaller than it used to be. "Under modern conditions the trade of the country is conducted on a retail system which is growing year by year. The practice of keeping large stocks has almost ceased, and goods are ordered in quantities only sufficient to meet the current demands."44 One reason for this is the improvement in the means of communication. "The trunk lines of America, with their wide-spreading branches, enable merchants in the cities and the larger towns to replenish their counters and shelves every day. Stocks, therefore, need not be so large as of old, when, let us say, a whole winter's goods were laid in by October.... The inter-urban roads are extending these advantages to the village storekeeper, who, in the morning, telephones his wants to Toledo, Cleveland, or Detroit, and, in the afternoon, disposes the ordered wares on his shelves."45 Now, prima facie, this change of custom would seem to be of little significance. After all, a reduction in the amount of finished goods held by retailers, of reserve machinery held by manufacturers, and so on, does not necessarily imply a reduction in the aggregate amount of these things held by the whole body of industrialists. On the contrary, we are naturally inclined to suggest that the wholesaler and the machine-maker must increase their stocks pari passu with the decrease in the stocks of their clients. As a matter of fact, however, this suggestion is incorrect. The reason is that the wholesaler and the machine-maker represent points at which uncertainties can be combined. The development of the means of communication, therefore, in so far as it directly transfers to them the task of bearing uncertainty, indirectly lessens the amount of uncertainty that needs to be borne. Uncertainty-bearing, in short, is rendered more efficient. The same result as before can be achieved with a smaller quantity of it, or, what comes to be the same thing, with a smaller quantity of waiting designed to obviate the need for employing it.

APPENDIX II
THE MEASUREMENT OF ELASTICITIES OF DEMAND

§ 1. WITH the information at present available it is not possible to lay down any propositions about the elasticity of demand for different commodities beyond those general propositions that are set out in Part II. Chapter XIV. As has been pointed out by Marshall,46 attempts to determine the elasticity of demand for any commodity in any market by a direct comparison of the prices and the quantities consumed at different times are exposed to very great difficulties. If it could be presumed that the reactions exercised by price-changes upon quantity demanded came about immediately, if the association of actual price-changes with people's expectation of connected future price-changes in the same or the opposite direction could be eliminated, and if allowance could be made for those upward and downward shiftings of demand schedules, for which movements of confidence and alterations in the supply of monetary purchasing power are responsible, a comparison of the percentage changes of price between successive years with the percentage changes in consumption between the same years might, for commodities about which adequate statistics exist, yield a rough numerical measure of elasticity for amounts of consumption in the neighbourhood of the average actual consumption.47 It seems that for certain commodities the above presumption can reasonably be made. On the basis of it Professor Lehfeldt calculated, immediately before the war, that the elasticity of the aggregate demand for wheat in the United Kingdom was about -0.6.48 But there is little hope that many elasticities will lend themselves to calculation in this direct way. It is, therefore, important to inquire whether any indirect method of calculation is available for overcoming difficulties due to the slowness with which reactions work themselves out.49

§ 2. Some years ago I devised a method, the basis of which is a comparison of the amounts of a commodity consumed by persons of different incomes at a given price, instead of a comparison of the amounts consumed by persons of given incomes at different prices. Statistical data needed for this method are found in family budgets. Considerable attention has been paid both by State Departments and by private persons to the study of these budgets; and a number of tables have been printed to show the proportion of their income which families in different income groups expend upon the various principal sorts of commodities. It is possible so to manipulate these data as to derive from them information about certain elasticities of demand.

§ 3. Let us suppose that the data are better than they are, and that our tables give the expenditure of the group of workpeople whose wages lie between 30s. and 31s., of the group whose wages lie between 31s. and 32s., and so on continually for all wage levels. With this close grouping we may fairly assume that the tastes and temperament of the people in any two adjacent groups are approximately the same. That is to say, the desire for the xth unit of any commodity (or group of commodities), the demand for which is not markedly correlated with the demand for other commodities, is equal for typical men in the 30s. to 31s. group and in the 31s. to 32s. group. Let the quantity of desire for the xth unit of the commodity be φ(x): or, in other words, y being the desire for the xth unit, let the desire curve for the commodity be represented by y = φ(x). We are entitled to assume further, in the absence of special knowledge as to the existence of correlation, that the desire curve of both groups for the commodity is independent of the quantity of other commodities consumed and, therefore, of the marginal desiredness of money. Let this marginal desiredness to the lower and higher income groups respectively be µ₁ and µ₂, and the quantities of the commodity consumed by these groups x₁ and x₂. Then, since the price paid for the commodity must be the same for both groups, we know that this price p is equal both to and to . These two expressions are, therefore, equal to one another. But, if, as it is reasonable to suppose when the incomes of the two groups are close together, x₂ differs only slightly from x₁, φ(x₂) may in general be written φ(x₁) + (x₂—x₁)φ'(x₁); But the elasticity of the desire curve in respect of any consumption x₁ is known to be equal to . Let this elasticity be written η_x1. It follows that But, since a small change in the consumption of any ordinary commodity, on which a small proportion of a man's total income is spent, cannot involve any appreciable change in the marginal desiredness of money to him,50 the elasticity of the desire curve in respect of any consumption x₁ is equal to the elasticity of the demand curve in respect of that consumption. Therefore the elasticity of demand, as well as the elasticity of desire, of the lower income group, in respect of its consumption of x₁ units, may be represented by η_x1, when: .

§ 4. If we knew the relative values of µ₁ and µ₂, this equation would enable us to determine the elasticity of demand of the lowest income group for any commodity, the demand for which is not markedly correlated with the demand for other commodities, in respect of such quantity of the commodity as that group is consuming. Similar equations would enable us to determine the corresponding elasticities of each of the other income groups. If it is objected that our result would in practice be impaired by the fact that the higher income groups are apt to consume a better quality of commodity, and not merely a greater quantity, than the lower income groups, the difficulty is easily overcome by substituting in our formula for the quantities of the commodity that are consumed by the different groups figures representing their aggregate expenditures upon it. This device escapes the suggested objection by treating improved quality as another form of increased quantity. In order to obtain the elasticity of demand for the commodity as a whole, it would be necessary to calculate the separate elasticities for all income groups and to combine them on the basis of the quantity of purchases to which they respectively refer.

§ 5. Unfortunately we do not know, and cannot ascertain, the relative values of µ₁ and µ₂. Consequently we are estopped from using the above analysis to determine the elasticity of the demand for any commodity in absolute terms.51 But this does not block our investigation. For, by the process indicated above, the elasticities of demand in any income group can be determined, for all the things consumed in that income group, in expressions into which µ₁ and µ₂ enter in exactly the same way, namely, as the term . If, then, the several elasticities be η_x, η_y, η_z, and so on, any one of them can be expressed in terms of any other without reference to µ₁ and µ₂. These unknowns are eliminated, and we obtain the formula This result, it should be observed, only follows directly from the preceding argument, provided that the commodities concerned are both such that only a small part of a typical man's income is normally spent upon them. In general, however, though the absolute formula for elasticities, from which the result is derived, is only valid on this assumption, the above comparative formula is approximately valid also for two commodities on which a large part of a typical man's income is spent, so long as the part spent on the one does not differ greatly from that spent on the other. The reason for this is that the errors in the two formulae for absolute elasticities, which have to be combined, will tend to balance one another. Our comparative formula is seriously suspect only when it is used to obtain the relative elasticities of the demands of a group for two things, on one of which that group spends a large proportion, and on the other a small proportion, of its income. Apart from this, the formula, when applied to the statistics of quantities of, or expenditures upon, different commodities by neighbouring income groups, enables us to determine numerically the ratio of the elasticity of demand of any income group for any one commodity (in respect of the quantity of the commodity actually consumed by it) to the elasticity of demand of the group for any other commodity. This information will often be valuable in itself. It is important to know whether the demand of workers with 35s. a week for clothes is about twice, or about ten times, as elastic as their demand for food. But the information is also valuable indirectly. For, if we can in some other way—through the examination of shopkeepers' books or otherwise—determine the elasticity of demand of any income group, or collection of income groups, for one thing, we have here a bridge along which we may proceed to determine the elasticity of their demand for all other things.

§ 6. In explaining the above method I have, as indicated at the outset, assumed that our data are better than they are. This, I think, is legitimate, because there is no reason in the nature of things why these data should not be improved; and, indeed, there is little doubt that they will be improved. Even then, of course, any one attempting a detailed application of the method is certain to encounter serious difficulties, among which, perhaps, not the least will be that of deciding how far to treat different commodities separately and how far to group them together according to the purpose which they jointly serve. When put to the test, these difficulties may, no doubt, in some applications, prove insurmountable. From the results of an experiment made upon figures given in the second Fiscal Blue-book (pp. 215 and 217), I am, however, tempted to hope for better things. The figures refer to the expenditure upon "food" and "clothing" of groups of workpeople whose wages were respectively under 20s., between 20s. and 25s., between 25s. and 30s., between 30s. and 35s., and between 35s. and 40s. My method gave the ratio of the elasticity of demand for clothes to that for food for the several groups as follows:

Apart from the drop in the ratio for workpeople earning from 30s. to 35s.—and it may be remarked in passing that the instances from which the average in this group is made up are only half as numerous as those in the two adjacent groups—these figures are continuous and in no wise incompatible with what we should expect from general observation. It is natural that among the very poor the demand for clothes should be nearly as inelastic as the demand for food, and that, as we proceed to groups of greater wealth, its relative elasticity should grow. This small experiment, therefore, is not discouraging, and it is much to be desired that some economist should undertake a more extended study along similar lines.52

APPENDIX III
A DIAGRAMMATIC AND MATHEMATICAL TREATMENT OF CERTAIN PROBLEMS OF COMPETITION AND MONOPOLY

THE purpose of this Appendix is to investigate certain matters of pure theory which cannot be handled easily without the help of some sort of technical apparatus.

I
NORMAL SUPPLY PRICE

§ 1. I define the normal supply price of any quantity of output as the price which will just suffice to call out a regular flow of that quantity when the industry under review is fully adapted to producing that quantity and no monopolistic action is undertaken. Prima facie the supply price of an industry may fall, remain stationary or rise, as the output of the industry increases. According as it does one or other of these things, the industry will be said respectively to obey the law of decreasing, constant or increasing supply price.53 The same industry may, of course, obey one of these laws in respect of some quantities of output and another in respect of other quantities. It is proposed to study generally the way in which the relation between variations in normal supply price and the variations in quantity of output is determined.

§ 2. Most industries are made up of a number of firms, of which at any moment some are expanding, while others are declining. Marshall, it will be remembered, likens them to trees in a forest. Thus, even when the conditions of demand are constant and the output of an industry as a whole is correspondingly constant, the output of many individual firms will not be constant. The industry as a whole will be in a state of equilibrium; the tendencies to expand and contract on the part of the individual firms will cancel out; but it is certain that many individual firms will not themselves be in equilibrium and possible that none will be. When conditions of demand have changed and the necessary adjustments have been made, the industry as a whole will, we may suppose, once more be in equilibrium, with a different output and, perhaps, a different normal supply price; but, again, many, perhaps all, the firms contained in it, though their tendencies to expand and contract must cancel one another, will, as individuals, be out of equilibrium. This is evidently a state of things the direct study of which would be highly complicated. Fortunately, however, there is a way round. Since, when the output of an industry as a whole is adjusted to any given state of demand, the tendencies to expansion and contraction on the part of individual firms cancel out, they may properly be regarded as irrelevant so far as the supply schedule of the industry as a whole is concerned. When the conditions of demand change, the output and the supply price of the industry as a whole must change in exactly the same way as they would do if, both in the original and in the new state of demand, all the firms contained in it were individually in equilibrium. This fact gives warrant for the conception of what I shall call the equilibrium firm. It implies that there can exist some one firm, which, whenever the industry as a whole is in equilibrium, in the sense that it is producing a regular output y in response to a normal supply price p, will itself also individually be in equilibrium with a regular output x_r.54 The conditions of the industry are compatible with the existence of such a firm; and the implications about these conditions, which, whether it in fact exists or not, would hold good if it did exist, must be valid. For the purpose of studying these conditions, therefore, it is legitimate to speak of it as actually existing. For any given output, then, of the industry as a whole, the supply price of the industry as a whole, must be equal to the price which, with the then output of the industry as a whole, leaves the equilibrium firm in equilibrium. The industry, therefore, conforms to the law of increasing, constant or decreasing supply price according as the price which leaves the equilibrium firm in equilibrium increases, remains constant or decreases with increases in the regular rate of output—we are not here concerned with short-period fluctuations—of the industry as a whole. In industries which consist, not of many firms but of one firm only, the industry as a whole and the equilibrium firm are, of course, identical, and there are no firms other than the equilibrium firm. In what follows we are concerned (1) with industries in which the outputs of the individual firms are small relatively to the output of the whole industry, which implies that x_r, the output of our equilibrium firm, is small relatively to y; (2) with industries consisting of one firm only. The difficult intermediate case of an industry in which x_r is neither small relatively to y nor yet equal to y—a case involving some measure of indeterminateness—will be left out of account. It is assumed throughout that outsiders are not excluded from the industry under review by legal rules or clubbing devices.

II
MANY-FIRM INDUSTRIES

§ 3. Marshall's discussion of internal and external economies has made familiar in a general way the idea that the long-period production costs of an individual firm in a many-firm industry sometimes depend, not on the size of its own output only, but also on that of the industry as a whole. This idea needs, however, to be set out in precise form. Three stages may be distinguished. In the simplest stage the individual firm's costs depend solely upon its own output. There are no external economies or diseconomies, and such internal economies or diseconomies as there are are wholly unaffected by variations in the scale of the industry as a whole. If we write y for the output of the industry as a whole and x_r for the output of the equilibrium firm, the money costs of the equilibrium firm are measured by F_r(x_r). In the next stage the individual firm's money costs consist of two parts, one depending on the size of its own output, the other on that of the output of the whole industry. We may call the former, if we will, internal costs, the latter external costs. The latter will consist of the firm's expenditure on the materials, machinery and so on which it buys, and the price of which will vary with variations in the demand for them on the part of the industry as a whole. Here the money costs of the equilibrium firm are measured by . In the third stage the relation between costs and the individual and collective outputs are more complex. It is no longer proper to regard the individual firm's money costs as consisting of two separate and independent parts. These costs will undergo different variations in consequence of a given change in its output according to the level at which the output of the industry as a whole stands; and they will undergo different variations in consequence of a given change in the output of the industry as a whole according to the level at which the individual firm's own output stands. The costs of the equilibrium firm are measured by F_r(x_r,y). This last formula, which is a general one, of course includes the two simpler formulae as special cases. It will, therefore, be convenient in the first instance to conduct our analysis by means of it.

§ 4. Let y be the output of an industry as a whole; x_r the output of the equilibrium firm; F_r(x_r,y) the total costs of the equilibrium firm; and p the supply price of the industry's product. The following quantities have then to be distinguished.

First, the marginal additive cost to the equilibrium firm, i.e. the difference made to the total cost of that firm by increasing its output from x_r to (x_r + Δx_r), the output of the other firms remaining unchanged, = .

Secondly, the marginal substitute cost to the equilibrium firm, i.e. the difference made to the total cost of that firm by increasing its output from x_r to (x_r + Δx_r), the output of the industry as a whole remaining unchanged (i.e. that firm's increase being balanced by an equal decrease elsewhere),

=

Thirdly, the average cost to the equilibrium firm

=

§ 5. When a firm is considering what difference will be made to its total costs by adding to or substracting from its output a small increment, it will measure the difference by marginal additive cost if it reckons that the output of other firms will not be altered in consequence of its action, and by marginal substitute cost if it reckons that other firms will be driven by its expansion to contract their output correspondingly, so that the output of the whole industry, including itself, will be unaltered. It may reckon that something intermediate between these two things will happen, in which case it will look to something intermediate between marginal additive cost and marginal substitute cost. If the total cost to any one firm producing a given output is the same, whatever quantity other firms are producing, these two sorts of marginal cost coincide. In any event, so long as the output of the industry as a whole is large relatively to the output of any one firm, they are not likely to differ very much. The technique of the discussion will be slightly different according as we suppose that the equilibrium firm reckons that a small increase in its output would involve an equal, nil or intermediate addition to the output of the industry as a whole, but no difference will be made to the broad result. Since, therefore, the analysis is simplest if the equilibrium firm thinks of small changes in its output as involving equal and opposite changes in the output of its competitors, I shall proceed on the assumption that it in fact does this. Hence, so long as we are considering many-firm industries, no further reference will be made to marginal additive cost; and the term marginal cost will be used without adjective to signify marginal substitute cost, namely,

§ 6. It is then easy to see that, if the supply price of the industry were less than the marginal cost of the equilibrium firm, sales at the supply price would involve a loss to it and it would tend to contract. If the supply price were greater than the marginal cost to the equilibrium firm, that firm would gain by expanding at the expense of other firms, because, while the cost of its old output would still be covered by the selling price—which would be unchanged, since aggregate output is unchanged—the cost of its new output would be more than covered.55 Hence in neither case would the equilibrium firm be in equilibrium. Since then, ex hypothesi, it must be in equilibrium, the supply price of the industry must be equal to the marginal cost of the equilibrium firm. That is,

§ 7. If the supply price were less than the average cost of the equilibrium firm, it is obvious that that firm would be making a loss and, therefore, would tend to contract, thus belying its nature as an equilibrium firm. Therefore, the supply price cannot be less than the average cost of the equilibrium firm. Again, if the supply price is greater than the average cost of the equilibrium firm, outsiders will be tempted to come into the industry, forming themselves into similar firms and thus increasing the producing capacity of the industry, until the supply price of an output y is no longer in excess of the average costs of the equilibrium firm. Therefore the supply price cannot be greater than the average costs of the equilibrium firm. Hence the supply price is equal to the average costs of the equilibrium firm,56i.e.

§ 8. Expressed in words, this condition and the preceding condition together state that the normal supply price of the product of a many-firm industry is, in respect of all quantities of output, equal both to the marginal cost and to the average cost of the equilibrium firm; cost being understood, of course, in the sense of money cost. These two conditions are fundamental and of general application. The resultant equality can also be derived directly from the proposition that, when y is given, x_r must be such as to make a minimum. To obviate a possible misunderstanding, it may be added that, since x_r is an implicit function of y, the supply function of the industry as a whole can, if desired, be expressed as a function of one variable, and is, therefore, capable of being represented by a plane diagram.

§ 9. There are three sorts of equilibrium—unstable equilibrium, neutral equilibrium, and stable equilibrium. A system is in stable equilibrium if, when any small disturbance takes place, forces come into play to re-establish the initial position; it is in neutral equilibrium if, when such a disturbance takes place, no re-establishing forces, but also no further disturbing forces, are evoked, so that the system remains at rest in the position to which it has been moved; it is in unstable equilibrium if the small disturbance calls out further disturbing forces which act in a cumulative manner to drive the system away from its initial position. A ship with a heavy keel is in stable equilibrium; an egg lying on its side in neutral equilibrium; an egg poised on one of its ends in unstable equilibrium. Obviously for practical purposes unstable equilibrium is no equilibrium at all: its presence would involve the system running down to one in which the industry consists of a single firm. In order that the equilibrium may be neutral, we require the further condition that is constant over a certain range: in order that it may be stable, the further condition that

§ 10. Let us now consider in turn the three cases distinguished in § 3. In the simplest of these, where the costs of the equilibrium firm are dependent only on its own output and not at all on the output of the industry as a whole, the expression F_r(x_r,y) degrades to F_r(x_r). The two conditions of equilibrium become and the condition that the equilibrium shall be neutral or stable becomes In a many-firm industry condition (3) in conjunction with condition (1) rules out the law of decreasing supply price in respect of outputs equal to or greater than what is being actually sold. For, if that law holds for the industry as a whole, it must hold for some individual firm belonging to it, and such a firm, once getting an accidental start, would cumulatively undersell and oust all the others. Condition (3) is not, however, really necessary to exclude the law of decreasing supply price. For conditions (1) and (2) in conjunction exclude both this law and also the law of increasing supply price. This is easily proved. The two conditions together yield This implies that x_r, and consequently F_r'(x_r), are determined independently of the output of the industry as a whole; and this implies in turn that the supply price of the industry is the same whatever the magnitude of its output. In other words, the industry is necessarily conducted in accordance with the law of constant supply price.

§ 11. In this simple case, since the cost function of the equilibrium firm can be—as of course it cannot in the more complex cases—represented by a plane diagram which is valid and

the same whatever the output of the industry as a whole, it may be of service to persons who prefer diagrams to algebra to set out the implications of the foregoing analysis by these means.

In the annexed figures the curve SS_m represents the marginal costs that various amounts of output involve to the equilibrium firm, and the curve SS_a the average costs. These two curves are, of course, bound together by a rigid relation; such that, if M be any point on Ox and a perpendicular be drawn through M cutting SS_m in Q and SS_a in P, the area SQMO is equal to the rectangle RPMO, whatever be the shapes of the two curves. It is easy to

see that, if either curve slopes downward throughout (as in Fig. 1), the other must also do this; and, if either slopes upward throughout (as in Fig. 2), so also must the other. If SS_m slopes downward

at first, then turns upward and thereafter continues to rise, the curve SS_a will continue to slope downward until the point at which the now upward moving SS_m intersects it, and will then itself turn upward. This case is represented by Fig. 3. If SS_m slopes upward at first, then turns downward and thereafter continues to fall, SS_a will, in like manner, slope upward until SS_m

intersects it, and will then itself turn downward. This case is represented in Fig 4.

Finally, if, either initially or after a point of intersection between the two curves, either of them henceforward

moves horizontally, the other must coincide with it and do the same. This case is represented in Figs. 5, 6 and 7.57 The conditions of equilibrium for the equilibrium firm, set out in the preceding section, imply that it is producing such a quantity of output OM that an ordinate drawn perpendicular to OM cuts the curves SS_m and SS_a at the same point. Hence in the conditions represented in Figs. 1 and 2 no equilibrium of any sort is possible. In those represented by Fig. 4 there is a single point of unstable equilibrium: in those represented by Figs. 5 to 7 there are ranges of neutral equilibria: and in those represented by Fig. 3 there is a single point of stable equilibrium; the point, namely, at which internal economies have reached their limit, in such wise that the average cost of production is at a minimum. Unstable equilibrium is, as we have seen, for practical purposes impossible. If neutral

equilibrium prevails, changes in the output of the equilibrium firm may take place, but cannot be caused by associated changes in the output of the industry as a whole. If stable equilibrium prevails, the output of the equilibrium firm cannot change. It is fixed rigidly, and changes in the output of the industry as a whole can only come about through an alteration either in the number of firms employed or in the magnitude of the non-equilibrium firms. In any event, whether neutral or stable equilibrium prevails, the average (and marginal) cost of the equilibrium firm, and so the supply price of the industry, is the same for all outputs of the industry: i.e. the industry conforms to conditions of constant supply price.

§ 12. In the second class of case distinguished in § 3 the formula for the costs incurred by the equilibrium firm degrades to The two conditions of equilibrium become and the condition that the equilibrium shall be neutral or stable becomes, as before, As in the previous case, conditions (1) and (2) yield So far, therefore, as the internal position and what we may term the internal costs of the equilibrium firm are concerned, everything is exactly the same as it was in that case. Internal costs per unit of product are determined at a fixed level independent of the output of the industry as a whole, and the size of the equilibrium firm is also independent of that output. In this case, however, these results do not imply that the industry as a whole must conform to the law of constant supply price. For, though is fixed independently of y, the element , and, therefore, are, so far as the present argument goes, free to vary up or down as y varies. Thus, if a growth in the output of the cotton industry led to a rise in the price of its material, raw cotton, the cotton industry as a whole would conform to the law of increasing supply price; if its expansion led to a fall in the price of raw cotton, to the law of decreasing supply price. To determine whether in fact the price of materials, machinery and so on supplied to an industry by others will rise, fall or remain constant when the output of that industry increases, we should need to step outside the industry primarily under review and investigate the conditions of production in the others.

§ 13. In the third and most general case distinguished in § 3 it is obvious that the three governing conditions impose no restrictions on the relations that may subsist between variations in the supply price and in output. It is still true that, for any given output of the industry as a whole, the output of the equilibrium firm must be such as to make its marginal costs and its average costs equal. But, as the output of the industry as a whole varies, both the output of the equilibrium firm which will make these two things equal and also their magnitude when they are equal may vary indefinitely in either direction. Even, therefore, if the prices of the materials and machinery bought from outside do not vary with variations in the scale of our industry, its own supply price may vary. Many-firm industries of the generalised type are thus perfectly free to conform to the law of increasing supply price, constant supply price, or decreasing supply price, or to any combination of these laws in respect of different quantities of output. Fig. 3 on p. 797 still correctly represents the conditions of supply in the equilibrium firm when the aggregate demand is such that OM units are being purchased from that firm at a price PM per unit. But now, when the aggregate demand alters, the curves SS_m and SS_a alter also. They move upwards or downwards, or they change their shape, or they do both these things. After the change, as before, equilibrium is only attained when the selling price is equal to both the average cost and the marginal cost of the equilibrium firm. The output of that firm is still measured by OM, where M is the base of a perpendicular drawn from the point of intersection of SS_m and SS_a; but, nevertheless, both the selling price and the output of the equilibrium firm may be different from what they were before the change.

III
ONE-FIRM INDUSTRIES

§ 14. Let us now revert to the laws of supply price in relation to an industry of one firm only. Here the equilibrium firm and the industry as a whole become identical, so that there is no need to employ a function of two variables. Moreover, marginal cost is no longer ambiguous: it must signify marginal additive cost, since there is no such thing as marginal substitute cost. If we were to follow blindly the lead of the preceding discussion, we should conclude that equilibrium requires that This would mean that there can only be a supply price in respect of one, or, if the curves of marginal cost and of average cost cross one another several times, in respect of a few isolated quantities of output, unless the industry conforms to conditions of constant supply price. Only then, it would seem, is the existence of a continuous supply schedule of the ordinary type possible. It is not difficult to see, however, that the foundation of this argument is unsound. For the equilibrium firm of a many-firm industry it is true that equilibrium is only attainable if both its average cost and its marginal cost are equal to the supply price of the industry. But for the equilibrium firm of a one-firm industry that is not true. There can, indeed, be no equilibrium if the average cost is greater than the supply price and the industry is selling at the supply price; for, in such conditions, there will be a tendency to contraction. Likewise there can be no equilibrium if the marginal cost is greater than the supply price and the industry is selling at the supply price; for here, again, there will be a tendency to contraction. But, since we have to do with one firm only, equilibrium does not necessarily forbid average cost to be less than the supply price.58 Again, if, where average cost is equal to the supply price, marginal cost is less than this, and the industry is selling at the supply price, there is no tendency for output to expand, since any expansion would necessarily involve a loss, and, therefore, equilibrium is not incompatible with this arrangement.59 Hence we conclude that in a one-firm industry the supply price of any given quantity of output is equal to average cost or to marginal cost, according as the one or the other of these is the greater. So far as formal considerations go, the industry is free to conform to decreasing, constant or increasing (money) supply price. If it conforms to decreasing supply price throughout, the supply curve is coincident with the curve of average cost: if it conforms to increasing supply price throughout, with the curve of marginal cost: if it conforms to constant supply price throughout, with both these curves. If it conforms to conditions of increasing supply price in respect of some outputs, and of decreasing supply price in respect of other outputs, the supply curve lies along the curve of average cost where this is higher than the curve of marginal cost, and along the curve of marginal cost where that is the higher of the two.

IV
THE IDEAL OUTPUT IN A MANY-FIRM INDUSTRY

§ 15. I call the output in any industry which maximises the national dividend, and, apart from the differences in the marginal utility of money to different people, also maximises satisfaction, the ideal output. As was shown in Chapter XI. of Part II. this output is attained—the possibility of multiple maximum positions being ignored—when the value of the marginal social net product of each sort of resource invested in the industry under review is equal to the value of the marginal social net product of resources in industries in general, or, more strictly, in the central archetypal industry of Part II. Chapter XI. § 1. In this central archetypal industry each sort of productive resource will have a value in money per unit equal to the value of the net product of a marginal unit of it. Hence the ideal output in our particular industry will be that output which makes the demand price of the output equal to the money value of the resources engaged in producing a marginal unit of output; in other words, it will be the output that makes demand price and marginal supply price to the community equal.

§ 16. Let the quantities of the several domestically owned ingredients (including, of course, factors of production), which are required, directly or through things made by them, to produce an output x_r in the equilibrium firm of an industry, whose total output is y, be respectively a, b, c, and the prices p₁, p₂, p₃. Let the quantity of foreign owned ingredient (e.g. imported machinery or raw material) be q and its price p_q. We may then, in a many-firm industry, distinguish the following quantities:

First, the supply price equals (1) Secondly, the marginal supply price to the industry, i.e. the difference made to the total money expenses of the industry by adding a small increment of output, (2) Thirdly, the marginal supply price to the community, i.e. the difference made to the total money expenses of the community by adding a small increment of output, (3) Fourthly, the rate of change from the standpoint of the industry in the supply price as output increases (4) Fifthly, the rate of change from the standpoint of the community in the supply price as output increases

(5)

This last expression is derived from the preceding one by eliminating the elements that represent increments of transfer between the equilibrium firm in our industry and domestic owners of the ingredients it employs.

§ 17. The foregoing expression (4) multiplied by y measures the excess of expression (2) over expression (1); and the expression (5) multiplied by y measures the excess of expression (3) over expression (1). Hence:

(1) In all industries where the rate of change from the standpoint of the industry in the supply price, as output increases, is positive (i.e. where conditions of increasing supply price simpliciter prevail), the supply price is less than the marginal supply price to the industry: in the converse case it is greater.

(2) In all industries where the rate of change from the standpoint of the community of the supply price is positive (i.e. where conditions of increasing supply price from the standpoint of the community prevail) the supply price is less than the marginal supply price to the community: in the converse case it is greater.

§ 18. It was shown in § 10 of Part II. Chapter XI. that the expression is unlikely to be negative: and in § 7 of the same chapter that the expression is extremely unlikely to be positive. We may take it that, though exceptions are possible, both these inequalities hold good in general. On the other hand, the expression may be positive if is positive: and, of course, the expression for the rate of change from the standpoint of the industry in the supply price may be either positive or negative.

Hence:

• (1) In general the rate of change from the standpoint of the industry in the supply price, as output increases, is greater than or equal to the rate of change from the standpoint of the community in the supply price. Hence decreasing supply price (simpliciter) implies decreasing supply price from the standpoint of the community: but increasing supply price (simpliciter) does not imply increasing supply price from the standpoint of the community.
• (2) In general, except in industries that make use of imported materials of increasing supply price, the rate of change in supply price from the standpoint of the community, as output increases, is nil or negative, and the supply price is equal to or greater than the marginal supply price to the community.
• (3) In the generality of industries the marginal supply price to the industry is equal to or greater than the marginal supply price to the community.

§ 19. The ideal output is attained, as was stated above, when the marginal supply price to the community is equal to the demand price.

The output proper to simple competition is attained when the supply price is equal to the demand price.

The output proper to discriminating monopoly of the first degree is attained when the marginal supply price to the industry is equal to the demand price.

The following inferences hold good in general (i.e. when the inequalities set out in § 18 are valid):

• (1) Except in industries that make use of imported materials of increasing supply price, the output proper to simple competition is equal to or less than the ideal output.
• (2) In any industry the output proper to discriminating monopoly of the first degree is less than the ideal output if the marginal supply price to the community and the marginal supply price to the industry differ, i.e. if the rate of change from the standpoint of the industry in the supply price and the rate of change from the standpoint of the community in the supply price differ: it is equal to the ideal output if they coincide.
• (3) The output proper to simple competition is less or greater than the output proper to discriminating monopoly of the first degree according as the industry conforms to conditions of decreasing or increasing supply price simpliciter.
• (4) When decreasing supply price simpliciter prevails, the output proper to simple competition falls short of the ideal output by more than the output proper to discriminating monopoly of the first degree falls short of it. But, when increasing supply price (simpliciter) prevails, the output proper to simple competition, while greater than the output proper to discriminating monopoly of the first degree, may be either greater or less than the ideal output. In the former case the national dividend fares better than it would do under discriminating monopoly: in the latter it may fare better or may fare worse.

§ 20. The analysis of head (4) in the preceding paragraph may be illustrated thus. Suppose that wheat-growing conforms to the law of constant supply price from the standpoint of the community, but to that of increasing supply price from that of the industry (i.e. simpliciter), because, and only because, the price of land is raised when more of it is wanted for wheat-growing. In this case the supply price is equal to the marginal supply price to the community, and the output proper to simple competition is identical with the ideal output. But, if wheat farmers, who are supposed to hire their land from landlords, combine and exercise discriminating monopoly of the first degree, they will cut down their wheat-growing, because, by so doing, they will cause the rent per acre that they have to pay to fall. Their output will then be less than the ideal output, instead of being, as it was before, equal to it. If wheat farmers own their land, and do not hire it, the distinction between the interests of the industry and of the community disappears; and the output of wheat will be the same under discriminating monopoly of the first degree as under simple competition, i.e. equal to the ideal output.

V
THE IDEAL OUTPUT IN A ONE-FIRM INDUSTRY

§ 21. In a one-firm industry when and the supply price of an output y is, therefore, the analysis of the preceding discussion is applicable, the formal expression of it needing to be modified only so far as to provide for the identity of x_r and y. In a one-firm industry, in which marginal cost exceeds average cost, something different is needed. The marginal supply price to the industry and the supply price are both equal to F'(y). Therefore, if no transfer elements are involved, so that the marginal supply price to the industry is equal to the marginal supply price to the community, and output equating supply price and demand price—which, in this case, is the output proper alike to simple competition and to discriminating monopoly of the first degree—will be equal to the ideal output, in spite of the fact that the industry conforms to the law of increasing supply price. This case in general can only occur when imported ingredients of increasing supply price are being used. If transfer elements are involved, an output which equates supply price and demand price will be less than the ideal output.60

VI
DEMAND PRICE AND MARGINAL DEMAND PRICE

§ 22. In the preceding discussion it has been tacitly assumed that the demand curve is also what may be called, by analogy with supply, a curve of marginal demand prices. This is not necessarily so. The marginal demand price of a quantity y of any commodity is the difference between the desiredness (as measured in money) to consumers in the aggregate of annual (or weekly) purchases of a quantity y and of a quantity (y + Δy) respectively. The demand price of y units is the price that maintains an annual (or weekly) purchase of a quantity y. Hence it is equal to the desiredness (as measured in money) of the least desired increment (Δy) in a quantity y to the purchaser of that increment. If then the purchase of the marginal unit indirectly increases or diminishes the desiredness of their holdings to the purchasers of other units, the marginal demand price and the demand price will be different. For commodities the desire for which is partly a desire for the uncommon the curve of marginal demand prices, which, for a nil purchase, coincides with the demand curve, will fall further and further below it as purchases increase: for commodities the desire for which is partly a desire for the common the opposite of this is true; while for commodities which are desired solely on account of the direct satisfaction they confer, the two curves are identical.61 When the curves diverge, maximum satisfaction—the parties concerned being assumed to be similar in wealth and temperament—is attained with an output that equates marginal supply price, not with demand price, but with marginal demand price.

VII
SIMPLE MONOPOLY AND MAXIMUM PRICES

§ 23. If the State, seeking to protect consumers against a monopoly, fixes a maximum price at the level proper to free competition, it is obvious that, under decreasing or constant supply price, the monopolist will gain by increasing his output up to the amount that would have been produced under free competition. If, however, conditions of increasing supply price prevail, the amount which it will pay the monopolist to produce, namely, the amount which will maximise output multiplied by the excess of the regulated price of sale over the supply price, is necessarily less than the competitive output. It may be either greater or less than the output that would result under unregulated monopoly. If the curves of demand and supply are both straight lines, it will be exactly equal to this amount. This is readily seen by inspection of a suitably drawn diagram.

§ 24. If, under conditions of increasing supply price, the State fixes a maximum price, less than the monopoly price but greater than the competitive price, it is probable in general that the output will be intermediate between the competitive output and the output proper to unregulated monopoly. If the curves of demand and supply are both straight lines, this result is certain. Construct a diagram (Fig. 9), such that PM represents the competitive price, and OM the competitive output; while QN represents the monopoly price, and ON the monopoly output. Let the State controlled price, measured by OV, be greater than the competitive price, but less than the monopoly price. Through V draw a horizontal line VBT cutting DD₁ in B and SS₁ in T. It is easily shown that the monopoly output ON is one-half of the competitive output OM, and that the output, which it will pay the monopolist to produce when the price is fixed at OV, will be measured by one-half of the line VT, drawn horizontally through V to cut SS₁ in T, or by the line VB, according as the one or the other of these lengths is smaller. But, since OV is greater than PM, it is obvious that VT is greater than OM. Consequently one-half of VT is greater than one-half of OM. This proves that the output at the controlled price is greater than the monopoly output; and, since VB must be less than RP, it is necessarily less than the competitive output. That is, it lies somewhere between the two.

§ 25. An extension of the foregoing argument shows that, in the conditions contemplated, when the demand and supply curves are straight lines, the level of controlled price, which will make the output larger than any other level would do, will be that which causes the intersection point of VT and DD₁, namely, the point B, to be identical with the middle point of VT, namely, the point H. If the angle SDP be θ and the angle DSP be φ, this output can be shown to be equal to the output proper to simple competition multiplied by the fraction

VIII
SOME PROBLEMS OF DISCRIMINATING MONOPOLY

§ 26. Consider an industry in which conditions of decreasing supply price prevail, but in which the supply curve lies wholly above the demand curve, so that neither under simple competition nor under simple monopoly can any output take place. Draw the demand curve DD₁ and the supply curve SS₁ as in Fig. 10. Through S draw a curve SS₂ such that, if a perpendicular be drawn from any point P on SS₁, to cut SS₂ in Q, and the figure be completed as drawn, the area SQMO is equal, for all positions of P and Q, to the rectangle KPMO. If DD₁ lies throughout below both SS₁ and SS₂, it is obvious that no output can occur under monopoly plus discrimination of the first degree, just as none can occur under simple competition. It may happen, however, in some industries of decreasing supply price, that DD₁, while lying below SS₁ cuts SS₂. If it cuts it once it must obviously cut it a second time. Let it cut it in R and Q. Then, under conditions of simple competition, no output can occur. But under conditions of monopoly plus discrimination of the first degree, provided that the area RQ is greater than the area DRS, an output OM will yield aggregate receipts in excess of aggregate costs, and will, therefore, be forthcoming. This result is more likely to be achieved, the more steeply the curve SS₁ slopes downward (that is to say, the more strongly the law of decreasing supply price works); because, the steeper is SS₁, the larger, when the distance OM is given, is the area PQS, and, therefore, the greater is the range of demand curves that will make the area

RQ greater than the area DRS. Given the inclination of SS₁, it is also more likely to be achieved, if the demand curve does not slope downward steeply in its earlier stages (that is to say, if the demand is elastic till fairly low price levels have been reached).

§ 27. Monopoly plus discrimination of the second degree, as defined on p. 279, approximates in its effects towards monopoly plus discrimination of the first degree, as the number of different prices which it is possible for the monopolist to charge increases. This result, which is obvious in general, can be worked out exactly in a particular case. Let the output proper to discrimination of the first degree be a, and let n be the number of different price-groups. On the hypothesis that the demand and supply curves are straight lines, it can be shown that, when the commodity obeys the law of constant supply price, the output will be equal to for all values of n. That is to say, if one price only can be selected, the output will be ½ a: if two prices can be selected, 2/3 a, and so on. When the commodity obeys the law of decreasing supply price, the output, if n is equal to 1, will still be equal to , but, if n is greater than 1, it will be somewhat less than this.

§ 28. Our next problem has to do with the relative outputs under discriminating monopoly of the third degree—as defined on p. 279—and of simple monopoly respectively. Let conditions of constant supply price prevail, and let there be two markets only. Then if the curves of demand in both markets are straight lines, precise results can be obtained. Let D₁D₂ and D'₁D'₂ represent the demand curves of the two markets, and let SS' be drawn at a vertical distance OR above the base line, where OR measures the constant cost of production. Through D'₁ draw D'₁H parallel to SS', and, through H, draw a straight line HT, such that PT is equal to RP'. Then under discriminating monopoly the output for the two markets will be respectively ½RP' and ½RP. Under simple monopoly, if PH is greater than HD₁, the output will be ½RT. But, since

PT is equal to RP', ½RT = ½RP' + ½RP. Therefore, subject to the condition italicised above, the outputs under simple monopoly and under discriminating monopoly will be the same. If PH is less than HD_1, the output under simple monopoly will, in some conditions, be ½RP, and there will be no consumption in the less favourable market. When these conditions prevail, so that under simple monopoly nothing would be consumed in one of the two markets, the substitution of discriminating for simple monopoly increases the output; but except in these conditions the output is not changed. When the assumption of constant supply price is removed and it is allowed that increasing or decreasing supply price prevails, the results reached above are not modified, since it is only through a change in the quantity of output that increasing or decreasing supply price can be called into play.62 Decreasing supply price, however, opens up a possibility referred to in Part II. Chapter XVII. § 13, and analogous to that examined in § 26 above, to which the preceding discussion has no relevance. This is that, in some conditions under which neither simple monopoly nor simple competition would have led to any output, discriminating monopoly may lead to some output.

IX
METHODS OF INDUSTRIAL REMUNERATION

§ 29. The central argument of Part III. Chapter VIII. can be brought into clear light by means of a diagram. Let us suppose the number of workpeople employed in any industry and the length of the working day to be given. It is then possible to construct a demand curve representing the employers' demand prices (in terms of product) for different amounts of exertion per unit time from a typical workman, and a supply curve representing the workman's supply prices (in terms of product) for different amounts of exertion. Units of exertion are marked off along Ox, and the demand and supply prices (in terms of product) of different amounts of it along Oy.

Since every increase of exertion on the part of workpeople enables employers to finish any given job more quickly, and so to start their machinery upon some other job, the demand curve DD' will slope upwards towards the right. Since, if a man is at work at all, neither public opinion nor his own comfort will allow him to do absolutely nothing, the supply curve SS' will start at a point some distance along Ox, and, thereafter, will slope upward somewhat steeply. Let it cut DD' in P. Through P draw PM perpendicular to Ox, and PR perpendicular to Oy. Then, apart from possible injurious reactions on capacity that are not here considered, the amount of exertion by a typical workman, which is most advantageous to the national dividend and economic welfare, is measured by OM, and the corresponding amount of his output by the rectangle OMPR. If the wage paid to him is wholly independent of his exertions and consequent output, the amount of his exertions will approximate to OS, and his output to OSQK. An amount of exertion OM, and consequent output OMPR, can be obtained either by the offer of a rate (in product) PM for each unit of exertion (which means each PM units of output); or by the offer of an aggregate wage (in product)—per day or whatever the time-unit may be—equal to OMPR, conditional upon the man producing OMPR units of output, any failure to reach this standard involving the payment of a considerably lower wage.

X
THE MEANING OF EXPLOITATION

§ 30. Let DD' be the employers' demand curve for labour and SS' the workers' supply curve in any district or occupation. Let PM be the wage that would result from free competition, i.e. that is equal to the general rate of wages for workpeople of the grade concerned; QM" the wage most profitable to the workpeople if they were combined; and RM' the wage most profitable to the employers. Then the range of indeterminateness described in Part III. Chapter VI. is constituted by all rates between QM" and RM'. There is necessarily exploitation if the employers succeed in paying any wage less than PM. Let us suppose that they succeed in paying a wage RM'. It follows that, if they obtain an amount of labour represented by OM', then the measure of unfairness in the wage is the excess of PM over RM', but the measure of exploitation is the excess of KM' over RM'. If the workpeople succeeded in establishing a wage larger than PM, the exchange index would necessarily fall on the demand curve to the left of P, say at the point Q, and we might speak of an exploitation of employers by workpeople, measured by the excess of QM" over FM".

[30.][30] The Measurement of Social Phenomena, p. 173.

[31.][31] Cf. Henderson, Industrial Insurance in the United States, p. 301.

[32.][32] Report, p. 15.

[33.][33] It is sometimes suggested that those very improvements in the capacity of labour, which have been discussed in previous parts of this book, are calculated to push some men below the minimum standard. It is true, as a point of analysis, that increased capacity of labour is, in effect, equivalent to an addition to its supply, and, therefore, involves a slight reduction in the real wage of a labour unit of given quality. In view, however, of the elastic character of the demand for labour in general, the number of the unimproved men whom this change would push over the line of self-support would almost certainly be very small.

[34.][34] This is the term employed by the Majority Commissioners of the 1909 Report on the Poor Laws.

[35.][35] Cf. Bowley, The Division of the Product of Industry, pp. 20 et seq.

[36.][36] The International Labour Conference of 1919, in framing its convention on Women's Employment, aimed at a high standard. On each separate provision of the Convention it fell behind the practice of some countries, but the existing law of no country covered the whole requirement of the Convention (G. Hetherington, International Labour Legislation, p. 90).

[37.][37] For a summary of a number of laws on this matter, cf. Grunzel, Economic Protectionism, pp. 281 et seq.

[38.][38] Cf. ante, pp. 161-2, footnote.

[39.][39] Cf. Marshall, Industry and Trude, p. 255.

[40.][40] Bowley, Elements of Statistics, p. 305.

[41.][41] This circumstance, of course, permits the release, partly for immediate consumption and partly for investment, of resources which must otherwise have been stored. For example, the combination of the community's gold reserves in a central bank lowers the amount of aggregate gold reserve necessary, increases the capital available for investment, and pro tanto lowers the rate of interest. (Cf. H. Y. Brown, Quarterly Journal of Economics, 1910, pp. 743 et seq.)

[42.][42] Industry and Trade, p. 256.

[43.][43] The Nature and Necessity of Interest, p. 126.

[44.][44] Inglis, Report of the Board of Trade Railway Conference, 1909, p. 33.

[45.][45] Iles, Inventors at Work, p. 483.

[46.][46] Principles of Economics, pp. 109 et seq.

[47.][47] Professor Moore, in his Economic Cycles (chapters iv. and v.), makes calculations of the "elasticity" of demand for certain commodities without resort to the allowances stipulated for in the text. But, as he himself fully recognises, the elasticity, which his method enables him to measure, is not the same thing as, and is not, in general, equal to, the elasticity of demand as defined by Marshall and employed here. Marshall's elasticity, if known, would make it possible to predict how far the introduction of a new cause modifying supply in a given manner would affect prices; Professor Moore's to predict with what price-changes changes in supply coming about naturally, in company with such various other changes as have hitherto been found to accompany them, are likely to be associated. That this distinction is of great practical importance is shown by the fact that, whereas the elasticity of the demand for pig-iron, in Marshall's sense, is, of course, negative—that is to say, an increase in supply involves a fall in price—the elasticity in Professor Moore's sense, as calculated from his statistics, is positive. The reason for this is that the principal changes in the price of pig-iron that have in fact occurred are mainly caused by expansions of demand (general uplifts in the demand schedule), and not by changes in supply taking place while the demand schedule is unaltered. In certain conditions it might be possible to derive Marshall's elasticity from Professor Moore's elasticity, provided that the reactions exercised by supply changes upon prices could be presumed to take place very rapidly. Apart from this presumption derivation would be impossible, however ample the statistical material.

[48.][48] Economic Journal, 1914, pp. 212 et seq.

[49.][49] The direct method and any possible indirect method are seriously hampered by the fact that the elasticity of demand for a thing may be different in respect of different amounts. Thus suppose we start with a consumption A at a price P: that the price rises by p per cent, and that this rise is the direct and sole cause of a fall in consumption of a per cent. We cannot infer that the elasticity of demand either for consumption A or for consumption is equal to unless p is small—strictly unless it is infinitesimal. If p is not small, some assumption as to the relation of neighbouring elasticities must be made before any inference can be drawn. One possible assumption is that the demand curve is a straight line. On this assumption the elasticity of demand in respect of consumption A will be : and in respect of consumption it will be . Another possible assumption is that the elasticity of demand is constant for all amounts of consumption from A to . On this assumption it can be proved, as Dr. H. Dalton has pointed out to me, that the said elasticity is not but This must lie between and : and is probably not far from

[50.][50] Strictly, of course, such a change must involve some alteration in the marginal desiredness of money, unless the demand for the commodity in question has an elasticity equal to unity. If the elasticity is anything other than this, a change in the consumption of the commodity will be accompanied by a transference of money from expenditure upon it to expenditure upon other things, or vice versa. This must affect the marginal desiredness of money spent on these things, and its marginal desiredness, if affected in one field, is, since it must be the same in all, affected in all.

[51.][51] Professor Vinci, in his very interesting monograph L' elasticità dei consumi, suggests that the method described above can be extended to yield an absolute measure of elasticity by reference to the distinction between nominal and real prices. The money price paid by the higher income group is the same as that paid by the lower income group. But the real price is, he holds, less than this, in the proportion in which the income of the higher income group exceeds that of the lower. Thus, if the higher income group has 10 per cent more income, an equal money price paid by it implies a real price 10/11ths as great; and the elasticity of demand is obtained by dividing a virtual price difference of 1/11th into whatever fraction represents the associated consumption difference (loc. cit. p. 22). This procedure is, however, illegitimate, because, on the assumptions taken, the virtual price of all commodities to the higher income group is 10/11ths of what it is to the lower income group. Consequently, the difference in the consumption of any particular commodity is not due solely to the difference in price of that commodity, and cannot, therefore, in general, be inserted in the formula for elasticity of demand. Professor Vinci has, in fact, tacitly assumed that the marginal desiredness of money is equal for the two groups—an assumption which would only be warranted if the demand of both for the sum of commodities other than the particular one under investigation had an elasticity equal to unity.

[52.][52] Cf. my article "A Method of Determining the Numerical Value of Elasticities of Demand," Economic Journal of December 1910.

[53.][53] Cf. ante, Part II. Ch. XI.

[54.][54] Marshall's statements about his "representative firm" show that this is conceived as an "equilibrium firm." But it is also something more. It is a firm of, in some sense, average size. Marshall pictures it as a "typical" firm, built on a scale to which actual firms tend to approximate; for some purposes he suggests that it might be well to picture to ourselves several different typical firms, one, for example, in the company form, another, probably smaller, in the private business form. That this conception is appropriate to actual conditions is well shown by the studies of the sizes of a number of actual businesses carried out in 1914 by Sir Sydney Chapman and Mr. Ashton. They conclude: "Generally speaking, there would seem to exist in industries, or branches of industries, of adequate size, under given sets of conditions, a typical or representative magnitude to which businesses tend to grow, typical proportions between their parts and typical constitutions.... As there is a normal size and form for a man, so, but less markedly, are there normal sizes and forms of businesses." (The sizes of businesses mainly in the textile industry. Statistical Journal, 1914, p. 512.) This is not surprising. For, if we so far abstract from reality as to suppose that there are large numbers of people of each grade of managing ability, each industry will tend to call to its firms men of that grade whose "comparative efficiency" is greatest there. If y be the output of the industry, x the output of the typical firm, and F(x,y) the total cost to that firm of its output, F will be a definite function determined by technical conditions, and for any assigned value of y, x will be given by the equation For my more limited purpose, however, it is not necessary to postulate that there is any representative or typical size of firms. Firms might be of all varieties of size, not concentrated about any norm. All that is required is that one firm is—or, rather, that the conditions are such as to make it possible for one firm to be—an "equilibrium firm" in the sense defined above.

[55.][55] The argument here would have a slightly different form if marginal additive cost were the relevant form of marginal cost, but the result would be the same. Cf. post, footnote (2) to § 14.

[56.][56] It will be noticed that neither the preceding argument nor the condition set out in § 3, that the tendency of the various non-equilibrium firms to expand and to contract must balance one another, necessarily implies that the supply price is equal to the average cost of the industry as a whole.

[57.][57] We could, of course, if we wished, draw more complicated figures, in which the curves should reverse their direction of movement more than once, but no new principle would be brought to light by this proceeding.

[58.][58] It does not forbid it if the firm's supply schedule is of the type depicted in Fig. 3 and if OM in the figure constitutes a large proportion of the total output which the market is capable of absorbing at a price PM; for in those conditions the one firm may make an abnormal profit without calling new competitors into the field.

[59.][59] This matter is best elucidated by means of a diagram. Let DD' be the demand curve, SSm the curve of marginal costs, and SSa the curve of average costs of a one-firm industry. Let OM units be produced and sold at a price PM, where P is the point of intersection between DD' and SSa. If the industry were to increase its output beyond OM, say to ON, the extra units would cost less than PM per unit to produce. But, nevertheless, on the assumption that all units are sold at the same price, ON units could not be sold at a less price than QN without involving the industry in a loss. Since, however, the portion of DD' that is to the right of P necessarily lies below SSa, it

is impossible for an output ON to be sold at a price as high as QN. Hence, if the industry expands its output beyond OM, it will make a loss; and, therefore, it has no tendency to expand. When the curves SSm and SSa represent the circumstances of one equilibrium firm among many firms, the position is quite different. It is not now proper to draw a demand curve of the form of DD'. The price in the market would be absolutely unaltered by an expansion on the part of the equilibrium firm if its expansion were balanced by the corresponding contraction in other firms, and approximately unaltered—the equilibrium firm being supposed small relatively to the industry as a whole—if the output of other firms remained unchanged. Therefore the equilibrium firm could expand to ON and still sell at approximately the old price PM. Thus it could sell an enlarged output at more than the average cost of that output, and so make a gain. Hence, for one firm among many others, a state of things in which the supply price of the industry is equal to the average cost of the equilibrium firm, but greater than its marginal cost, is not a state of equilibrium

[60.][60] It should be noted that, when, in one-firm industries, actual investment differs from ideal investment, the grounds for this divergence cannot be translated into terms of a difference between marginal social and marginal private net products. Since there is only one firm these two net products necessarily coincide. The ground of divergence, when such exists, is that, owing to the absence of competition, marginal private (which is here equal to marginal social) net product is not equal to average net product. If the one-firm industry is making normal profits, the value of the average net product is equal to the value of the marginal social net product in the imaginary central industry of Part II. Ch. XI. § 1: and, therefore, the value of the marginal social net product in the one-firm industry is not equal to that value.

[61.][61] Cf. Part II. Ch. XI. § 13.

[62.][62] In conditions such that a simple monopoly would sell in market A only, while a discriminating monopoly would sell in B also, it can easily be shown that the introduction of discrimination will affect consumption and price in A as follows. Under constant supply price both will remain unchanged; under increasing supply price consumption will be diminished and price increased; under decreasing supply price consumption will be increased and price diminished. These considerations are of practical importance to a government considering whether native cartels should be allowed to sell abroad at less than the home price.