Front Page Titles (by Subject) Chapter XIII: A NATIONAL MINIMUM STANDARD OF REAL INCOME - The Economics of Welfare
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Chapter XIII: A NATIONAL MINIMUM STANDARD OF REAL INCOME - Arthur Cecil Pigou, The Economics of Welfare 
The Economics of Welfare (4th ed.) (London: Macmillan, 1932).
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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."
|Workmen under 20s....||1.16|
|From 20s. to 25s....||1.31|
|From 25s. to 30s....||1.62|
|From 30s. to 35s....||1.25|
|From 35s. to 40s....||2.46|
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
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.
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 xr.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 xr, 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 xr 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.
§ 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 xr for the output of the equilibrium firm, the money costs of the equilibrium firm are measured by Fr(xr). 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 Fr(xr,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; xr the output of the equilibrium firm; Fr(xr,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 xr to (xr + Δxr), 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 xr to (xr + Δxr), 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, xr must be such as to make a minimum. To obviate a possible misunderstanding, it may be added that, since xr 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 Fr(xr,y) degrades to Fr(xr). 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 xr, and consequently Fr'(xr), 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 SSm represents the marginal costs that various amounts of output involve to the equilibrium firm, and the curve SSa 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 SSm in Q and SSa 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 SSm slopes downward
at first, then turns upward and thereafter continues to rise, the curve SSa will continue to slope downward until the point at which the now upward moving SSm intersects it, and will then itself turn upward. This case is represented by Fig. 3. If SSm slopes upward at first, then turns downward and thereafter continues to fall, SSa will, in like manner, slope upward until SSm
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 SSm and SSa 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 SSm and SSa 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 SSm and SSa; but, nevertheless, both the selling price and the output of the equilibrium firm may be different from what they were before the change.
§ 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.
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 xr 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 pq. 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
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.
- (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.
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 xr 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
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.
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
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 HD1, 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.
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.
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.] The Measurement of Social Phenomena, p. 173.
[31.] Cf. Henderson, Industrial Insurance in the United States, p. 301.
[32.] Report, p. 15.
[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.] This is the term employed by the Majority Commissioners of the 1909 Report on the Poor Laws.
[35.] Cf. Bowley, The Division of the Product of Industry, pp. 20 et seq.
[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.] For a summary of a number of laws on this matter, cf. Grunzel, Economic Protectionism, pp. 281 et seq.
[38.] Cf. ante, pp. 161-2, footnote.
[39.] Cf. Marshall, Industry and Trude, p. 255.
[40.] Bowley, Elements of Statistics, p. 305.
[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.] Industry and Trade, p. 256.
[43.] The Nature and Necessity of Interest, p. 126.
[44.] Inglis, Report of the Board of Trade Railway Conference, 1909, p. 33.
[45.] Iles, Inventors at Work, p. 483.
[46.] Principles of Economics, pp. 109 et seq.
[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.] Economic Journal, 1914, pp. 212 et seq.
[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.] 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.] 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.] Cf. my article "A Method of Determining the Numerical Value of Elasticities of Demand," Economic Journal of December 1910.
[53.] Cf. ante, Part II. Ch. XI.
[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.] 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.] 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.] 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.] 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.] 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.] 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.] Cf. Part II. Ch. XI. § 13.
[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.