The Economics of Welfare

Pigou, Arthur C.
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Part IV, Chapter III


§ 1. IN undertaking that study we are forced to avail ourselves of a somewhat rough method of approximation. Our inquiry is concerned with the comparative effects of certain causes upon the size of the national dividend and upon its distribution among rich and poor persons. No machinery exists by which effects upon distribution in this sense can be directly investigated. But economists have carried through, and have made common property, a very full analysis of the influences that affect distribution in another sense, namely, distribution among the various "factors of production." These two sorts of distribution are not the same. They would be the same if each factor were provided exclusively by a set of persons who provided nothing of any other factor. But, of course, in real life the same man often provides portions of several factors, obtaining part of his income from one and part from another. A landlord is not merely the owner of "the original and indestructible properties of the soil." On the contrary, he frequently invests a great deal of capital in his land, and sometimes also considerable mental labour in choosing his tenants, exercising a certain control over their methods, and deciding, it may be, upon the necessity of evictions. A shopkeeper provides capital, or waiting, to some extent, but he also provides, especially if his sales are on credit, much mental labour in judging the "standing of his customers" and not a little uncertainty-bearing in respect of bad debts. A large capitalist employer is still more obviously capitalist, brain-worker, and uncertainty-bearer combined. Finally, an ordinary manual worker is frequently, in some measure, also a capitalist. In view of these considerations, it is plain that doctrines about distribution among factors of production cannot be applied directly and unreservedly to problems concerning distribution among people. The difficulty is not, however, as it so happens, of decisive practical importance. By far the largest part of the poorer classes in this country consists of wage-earning workpeople. It is true, of course, that "there is no definite line between wage-earners and persons working directly for customers and small employers and small farmers..., nor is there any clear and uniform division between wages and salaries."*15 But the dominant position of wage-earners among the poor is illustrated by the fact that, whereas, before the war, they numbered some fifteen and a half millions, persons other than wage-earners with incomes below £160 a year numbered, say, three and a half millions.*16 Moreover, it is reasonable to suppose that a large number of persons earning small salaries or small incomes from working on their own account are affected by the main body of relevant economic causes in much the same way as wage-earners proper. For the purpose of the present discussion, therefore, though not, of course, for all purposes, we shall not commit any serious error if we treat manual workers and the poor as roughly equivalent classes. Furthermore, statistics show that by far the most important income-yielding instrument actually possessed by the poor of the United Kingdom, as thus defined, is manual labour. Persons in receipt of wages number, as I have said, some fifteen and a half millions, and it is probable that persons dependent upon wages amount to 30,000,000, or nearly two-thirds of the population. The accumulated property of these persons before the war—it is, of course, a good deal larger now—was estimated at £450,000,000, and the interest on it might, therefore, be put at some £20,000,000 a year. This was probably little more than 1/35th part of the total income of the wage-earners, all the rest being received as wages of labour.*17 Hence, just as we have agreed roughly to identify the poor with the wage-earners, we may agree also to identify the earnings of wage-earners with the earnings of the factor labour. No appreciable error is introduced by this simplification. When we have made it, the familiar analysis of economists can be directly applied.


§ 2. We may divide the factors of production, from whose joint operation the national dividend results, into two broad groups, labour and the factors other than labour. Of course, neither labour nor the factors other than labour constitute a homogeneous group made up of similar units. Labour embraces the work both of wholly unskilled workpeople and of numerous sorts of skilled artisans. The factors other than labour embrace, along with the work of Nature, the work of many kinds of mental ability and of various sorts of capital instruments. This circumstance is not, however, relevant to our present problem. That problem is to determine whether and how far economic causes, which affect the national dividend as a whole in one sense, can affect the receipts of the factor labour in the opposite sense. In the present chapter attention will be concentrated upon two sets of causes of the broadest kind, namely, those that act respectively on the supply of capital in general and on the supply of labour in general. It will be convenient to begin with capital.


§ 3. Capital, or to put the same thing in concrete terms, capital instruments, are the embodiment of labour itself, waiting for the fruits of labour and uncertainty-bearing. Consequently, apart from inventions and improvements, which will be considered presently, an increase in the supply of capital instruments can only mean that people have been willing to undertake more waiting for the fruits of labour and more exposure of those fruits to uncertainty. In other words, the supply of waiting, or of uncertainty-bearing, or of both, has been increased. It is obvious that a cause of this kind will make for an increase in the national dividend as a whole. Can it at the same time make for a decrease in the real income of labour? The analysis relevant to this question has been developed by Marshall. Subject to certain important qualifications, which do not affect the present argument, this analysis shows, first, that every factor of production, including entrepreneurs' work,*18 tends to be remunerated at a rate equivalent to its marginal net product of commodities in general. It shows, secondly, that, other things being equal, the marginal net product, in this sense, of every factor diminishes as the supply of the factor increases beyond a fairly low minimum.*19 For, as the supply of any factor increases, the supplies of all the other factors being given, it pushes forward an irregular boundary along a great number of routes;*20 and, the more of it there is, the smaller is the quantity of other factors, with which to co-operate and from which to derive assistance, that each new unit finds available. This proposition expresses what may be called the law of diminishing returns to individual factors of production. This law must not be confused with the law of diminishing returns to resources in general invested in a given occupation, referred to in Part II. Chapter XI.


§ 4. From this analysis an important proposition directly relevant to our present problem can be derived. This proposition has two sides, and is to this effect: If the quantity of any factor of production is increased, the reward per efficiency unit reaped by all factors completely rival to that factor (in the sense of being perfect substitutes) will be diminished, and the reward per efficiency unit reaped by all factors completely co-operant with it, and in no degree substitutes, will be increased. The former half of this proposition is obvious. The advent of Chinese immigrants in the retailing business must injure the British retail shopkeepers of New Zealand, and the steady flow of low-grade European immigrants must keep down the wages of unskilled workmen in the United States.*21 The latter half of the proposition is easily proved as follows. Since each unit of the increased factor must be paid at the same rate, and the rate for the new units is less than the old rate, a part of the product of the old as well as of the new units is handed over to the co-operant factors.*22 As an illustration, we may note that a high level of wages generally prevails in new countries, because, first, there is a large quantity of land available, and, secondly, by mortgaging the land to foreigners, the inhabitants can obtain a large quantity of capital also.*23


§ 5. If, as is, of course, generally true in the concrete, different factors are partly co-operant and partly rival, the effect of an increase in the quantity of one of them upon the reward obtained by the others can be analysed in this wise. Suppose that the quantity of factor A increases from A to (A + a), and that x of the new units are substituted in uses formerly occupied by mx units of the other factor B. Then the effect produced on the reward per unit of B is equal to that which would have been produced had the two factors been entirely co-operant, and had the quantity of A increased from A to (A + a - x) and the quantity of B from B to (B + mx). It is obvious that this effect may represent either an increase or a decrease in the reward per unit of B, and that it is more likely to represent an increase, the larger is (A + a - x)/A relatively to (B + mx)/B. It is not possible, in the absence of knowledge as to the form of the function representing the relations between the factors and their product, to make any statement more precise than this. Interpreted roughly, the condition, under which, on the hypothesis taken, an increase in the quantity of A would lead to an increase in the reward per unit of B, is that the predominant part of the extra units of A can be profitably turned to uses other than those formerly occupied by units of B. Hence, in general, where two factors are partly co-operant and partly rival, an increase in the quantity of the one will augment the reward per unit, and, therefore, the absolute share of the dividend, enjoyed by the other, if the relation of co-operation between the two factors is more important than the relation of rivalry.


§ 6. The question whether the relation between waiting and uncertainty-bearing in general and labour in general is, in the concrete, mainly co-operant or mainly rival is not one to which an a priori answer can be given. If the only sort of capital instruments which mankind had learned how to make were a kind of Frankenstein monster capable of exactly duplicating the labour of manual workers, and not capable of doing anything else, this relation would be wholly one of rivalry. What it is in actual fact, therefore, chiefly depends on the nature of the things which people are able, by combining labour with waiting and uncertainty-bearing, to create. If we consider realistically what these things in the main are—and, of course, when what is contemplated is a general increase in the supply of waiting and uncertainty-bearing, we must imagine the new supplies to be used in an all-round addition to existing capital instruments—it is apparent that their work is mainly co-operant. Railways, ships, factory buildings, machines, motor cars and houses, whether in the hands of private people or of business men who let them out on hire, taken broadly, are tools for, and not rivals to, men. By giving help, they enable any nth worker to produce more stuff or service than he could have produced without them; they do not, by supplanting him, compel him to produce less. This is the general teaching of experience. In particular instances, indeed, the relation is predominantly one of rivalry. But, comparatively, these are unimportant. As Marshall well writes: "There is a real and effective competition between labour in general and [waiting to which should be added uncertainty-bearing] in general. But it covers a small part of the whole field, and is of small importance relatively to the benefit which labour derives from obtaining cheaply the aid of capital, and, therefore, of efficient methods in the production of things that it needs."*24 In other words, the relation between capital as a whole and labour as a whole is predominantly one of co-operation. It follows that the question set out for discussion in § 2 must be answered in the negative. It is not, in present conditions, practically possible that a cause (other than inventions and improvements, which will be considered in the next chapter) operating to expand the national dividend by increasing the supply of capital generally should at the same time lessen the real income of labour. Similarly, of course, it can be shown that a cause operating to contract the dividend by diminishing the supply of capital generally cannot at the same time increase the real income of labour. In this field, in short, disharmony cannot occur.


§ 7. This conclusion leads up to the difficult problem of capital investments abroad. Apart from the special qualifications indicated on page 188, it may be presumed that, since nobody will invest abroad rather than at home unless he expects a better return, freedom to invest abroad will augment the national dividend. As against this, it seems at first sight that it will diminish the real income of labour. The funds for investment must be obtained either by exporting goods or by refraining from the import of goods to which we have a claim. It makes very little difference whether or not the granting of a loan is made conditional upon the proceeds of it being expended in purchasing the railway material, or other things, which it is destined to pay for, in the lending country. If this is done, the kind of goods that we export may be altered, but the volume of them will not be substantially affected. In any event the volume of things immediately available in this country will be diminished. This is practically certain to involve a direct injury to labour, either by making the things workpeople buy more expensive, or by reducing the supply of tools and machines that help them in production. It is true that, since some capital will have been withdrawn from home uses, the rate of interest here will go up, and this will encourage saving to create more capital. But this tendency can only mitigate, and not wipe out, the initial injury to labour. It follows that labour must be less well-off in terms of things in general than it would have been if the opening for investing capital abroad had been closed.


This result, however, is not decisive. In certain circumstances, even though this happens, labour may, nevertheless, be better off in terms of the particular things which workpeople are interested to buy. For, as an indirect effect of our foreign investments, these things may have been substantially cheapened. In actual fact this has happened. Sir George Paish, writing in 1914, stated: "In the aggregate, Great Britain has supplied the world outside these islands with nearly £600,000,000 for the construction of railways in the last seven years (out of a total so supplied by her of upwards of eleven hundred millions), and all of the money has been placed in countries upon which we depend for our supplies of food and raw material."*25 When our foreign investments are of this character, the real income of labour, in the only sense that signifies, is fairly certain to be increased, so that no disharmony arises. No doubt, if there were special reason to believe that, had the export of capital been forbidden, the funds set free would have been devoted to domestic uses specially beneficial to workpeople, such as the erection of a large number of healthy workmen's cottages, this conclusion would not hold good. But there is not, in general, special reason to believe this.


Moreover, it is necessary to take account of certain more remote consequences of foreign investment. When the export of capital is free, the opportunity to obtain higher interest abroad both causes more British capital to be created—in lieu of consumption—than would have been created otherwise, and also enables a part of it to be invested in enterprises yielding a larger return than would otherwise have been open to it. Thus freedom to export capital at one time exercises a twofold influence in enlarging the aggregate real income of the country at a later time. It follows that, other things being equal, the amount of new capital that can be created there at a later time will be enlarged. This effect will repeat itself cumulatively year after year. In the end, therefore, if we suppose the amount of capital annually exported to remain constant—though not, of course, if we suppose the interest earned on capital invested abroad always to be itself invested there—the extra capital created at home as an indirect result of past exportation must exceed the amount withdrawn by contemporary exportation. On this supposition, in the end, labour as a whole will be benefited and not injured. Though, therefore, disharmony may prevail from the point of view of a short period, in the higher unity of the long view it may well be resolved. The practical inference is that all proposals to restrict the export of capital in the interests of labour—apart from the special reasons discussed on page 188 cited above—should be subjected to a very cautious and critical scrutiny.


§ 8. We turn to the second main group of causes distinguished in § 2, those, namely, which operate through the supply of labour. It is evident that, if this supply is increased, whether the increase comes about through an addition to the number of workpeople or through an addition to their average capacity, the national dividend must be increased. Our problem, therefore, is to ascertain the effect that will be produced upon the aggregate real income of labour. The analysis set out in the preceding section shows that the marginal net product of labour, in terms of things in general, and, therefore, its real earnings per unit, must be diminished. Whether its aggregate earnings will be increased depends, therefore, on whether the elasticity of the demand for labour in general is greater or less than unity. If this elasticity is greater than unity, labour in the aggregate will receive a larger absolute quantity of dividend than before; whereas, if the elasticity is less than unity, it will receive a smaller absolute quantity.*26 It is, therefore, necessary to determine whether in fact the elasticity of demand is greater or less than unity.*27


Let us begin by ignoring the fact that an addition to the supply of labour available in industry is likely to react upon the supply of other factors co-operating with it. It may then be observed that there is a certain field of personal service where labour works practically unaided by other factors, where, therefore, its productivity per unit would not appreciably fall with an increase in its quantity, and where a good deal could be absorbed without greatly reducing the value of its product in terms of other things. This circumstance points, pro tanto, to a fairly low rate of diminution in the (real) demand for labour in general as the quantity of it increases; though exactly how rapid the rate of diminution would be, or, in other words, how elastic is the demand for labour, it is quite impossible to say. In real life, however, it is illegitimate to ignore reactions, indirectly brought about by an increase in the supply of labour, on the supply of other factors. In particular, the supply of capital is known to be very far from rigidly fixed. When the quantity of labour increases, and, hence, indirectly, the return per unit of capital is enhanced—though, no doubt, those people who have decided to leave some definite sum to their descendants will not be willing to save so much as before—people in general will be willing to save more than before, and so to create a greater quantity of capital.*28 Moreover, owing to the greater size of the national dividend, their ability to save will be increased. The resultant increase in the supply of capital will react to increase the marginal productivity of any given quantity of labour. On the whole, therefore, it is probable that the demand for labour, even viewed from the general standpoint of the whole world, is fairly elastic.*29 The probability is far stronger as regards the demand for labour in any single country. For capital is so mobile that a small increase in the return per unit obtainable by it in any one country must inevitably—apart from complications due to double income-tax, about which it may be hoped that international arrangements will soon be made—bring about a large influx from foreign countries, or, what comes to the same thing, a large contraction of the outflow that formerly went to foreign countries. Hence the elasticity of the aggregate demand for British labour is greater than the elasticity of that part of the demand which depends on British capital alone. It is, indeed, so much greater that, with any reasonable assumption as to this latter elasticity, the elasticity of the aggregate demand is practically certain, from the standpoint of a long period, which is alone in question here, to be immensely larger than unity.


Hence it follows that an increase in the supply of labour, whether through an increase in the number of units of labour of given efficiency that the average workman provides, or through an increase in the number of workmen providing, on the average, a given number of units of labour, must increase the absolute quantum of dividend that labour in the aggregate receives. It is, no doubt, true that, within the broad group labour, an increase in capacity, which only affected some of the sub-groups, might involve injury to other subgroups, whose capacity has not been improved. Even this danger, however, is likely to be avoided where the different sub-groups are not strictly homogeneous, but are partly co-operant, and where, as occurs when some unskilled labourers are trained to trades, the group, which is not made more capable, is diminished in numbers by the indirect operation of the change that has occurred. Furthermore, these incidents within the broad group labour are, in any event, of subordinate interest. So soon as it is shown that the absolute share of labour as a whole possesses, along with the aggregate dividend, the property of increasing with increases in the supply of labour, the only proposition that is of direct relevance to the present argument is established.


§ 9. When the increase in the supply of labour comes about through an increase in the capacity of labouring people, it is obvious that the consequent increase in the absolute share of dividend accruing to them carries with it, in accordance with the argument of previous chapters, an increase in their economic welfare. When, however, the increase of supply comes about through an increase in numbers, the absolute share per man is lessened, despite the fact that the absolute share of the group as a whole is increased. If there were reason to believe that the loss per man were large, we should hesitate to conclude that an increase of this sort in the supply of labour involves an increase in the economic welfare of labour. In fact, however, it can be shown that, under the conditions now existing in this country, the loss per man would be very small. That it would be very small in terms of commodities in general follows from the fact already established, that the elasticity of the demand for labour in England is large. If the conditions were such that an increase in numbers would lead to a material increase in the price of food or other articles predominantly consumed by the working-classes, it might, indeed, be large in terms of the things that are of significance to them. At present, however, the fact that we are able to import food freely from abroad, makes it impossible that an increase in the population of a small country such as ours should, to any important extent, evoke the law of increasing supply price in respect of it. Hence, in all senses, the diminution of real wages per head of the working-classes would be very small.*30 Consequently, it seems reasonable to conclude that an increase in the absolute share of labour, even when it results from an increase in the numbers of the population, will carry with it an increase in the economic welfare of working people. It is not necessary, therefore, to qualify our conclusion, that causes impinging upon the supply of labour affect the aggregate amount of the dividend and the aggregate real earnings of labour in the same sense, by emphasising the caution that the welfare of labour is sometimes diminished by causes that increase its wealth.


§ 10. The results that have been reached in this chapter serve to rebut two popular opinions. The first of these has to do with hours of labour, and is to the effect that a general shortening of the working day, because it will cut down the supply of labour, will enable workpeople as a whole to secure terms so much better than before that their aggregate real income must be increased. The truth is that, in so far as a diminution in the hours of work leads to a more than corresponding increase in capacity, both the national dividend and the absolute share of labour will benefit. But, if the reduction of hours is pushed beyond this point, so that it injures the national dividend, the real income of labour must, in view of the elasticity of the demand for labour, necessarily be injured also. The second popular opinion is that the compulsory withdrawal from work of persons in receipt of State assistance would increase the aggregate real earnings of the poor, and, therefore, from the point of view of labour, ought to be encouraged. Two schemes were submitted to the Royal Commission on the Aged Poor, one of which contained, as a condition for the receipt of a pension, "the abstention from all work of pensioners, male and female," while the other would have awarded pensions to "every one over sixty, and prohibited work beyond that age."*31 The defence proffered for those schemes was that, if pensioners did not abstain from work, independent workpeople would find their earnings diminished. From a long-period point of view, however, the interests of the poor should be identified, not with those of independent workpeople only, but with those of all workpeople; for all workpeople are liable to become dependent at some period of their lives. But it follows directly from what was said in the preceding section that, if the supply of labour is contracted, the aggregate earnings of independent and dependent workpeople together will be diminished. Hence, so far as the present argument goes, it is inadvisable to adopt the policy embodied in these two pension schemes. It should be noted, however, that the cessation of work by pensioners can be defended from a more special point of view. It may be held desirable that the qualification for a pension should be, not age, but declining strength. This cannot be tested directly, but, if abstention from work were made a condition for receiving, say, a 10s. pension, conformity to the condition would ensure that recipients were really incapable of earning much more than 10s. regularly. Hence such an arrangement, though it would abolish work on the part of many persons below the 10s. line, might, nevertheless, be desirable as a means of preventing many other persons from obtaining pensions, and, in consequence of obtaining or expecting them, from relaxing their efforts in industry. The pension policy pursued by certain friendly societies seems to be based on considerations of this order.*32 Clearly, however, this argument is not relevant where the condition for the receipt of a pension is, not declining strength, but the attainment of some definite age.

Notes for this chapter

Bowley, The Division of the Product of Industry, p. 12.
Ibid. p. 11.
Cf. Chiozza-Money, Riches and Poverty, p. 49.
The special case of the entrepreneur's earnings is discussed in detail by Professor Edgeworth in the Quarterly Journal of Economics for February 1904; it is also touched upon in his paper on "Mathematical Theories" in the Economic Journal of December 1907.
This idea is well expressed by Turgot in an elaborate figure (cf. Cassel, Nature and Necessity of Interest, p. 22). In illustration, it may be noticed that, as the rate of interest falls, instrumental goods come to be built more solidly and to be repaired and renewed more readily when need arises.
The significance of this qualification is that, in a given state of the other factors, an increase in the supply of one factor up to the amount required to provide a single group-unit on the optimum scale—e.g. a sufficient number of men to lift a heavy tree or a sufficient number to run one factory of optimum size in each occupation—need not yield diminishing returns. It is not relevant to the present argument that an increase in the scale of population, by generating closer contacts and mutual stimulation of thought, may indirectly lead to an increase in the supply of capital and to improved organisation, and that, therefore, output may increase in a larger proportion than population. The law of diminishing returns is concerned with the effects of an increase in the supply of one factor of production when the supply of other factors is not increased.
Professor Taussig wrote in 1906 that, whereas most money incomes in the United States have increased, "the wages of ordinary day labour and of such factory labour as is virtually unskilled seem to have remained stationary and sometimes seem even to have fallen" (Quarterly Journal of Economics, 1906, p. 521). Whether the unskilled immigrants are mainly rival or mainly co-operant with the skilled workers of America is another and more difficult question. Dr. Hourwich writes on this point: "It is only because the new immigrants have furnished the class of unskilled labour that the native workmen and older immigrants have been raised to the plane of an aristocracy of labour" (Immigration and Labour, p. 12). In the same sense Prof. Prato (Le Protectionisme ouvrier, p. 72) maintains that, in general, the low-grade immigrant takes on occupations which native-born workpeople wish to leave, and that this is true, not only of the Chinese and European immigrant into the United States, but also of the Italian and Belgian immigrant to France, Switzerland, and Germany.
It is not relevant to the present argument to note, though the point may be added for completeness, that, in response to the improved demand, the co-operant factors tend to increase in quantity, but, since their supply curve is inclined positively, not to a sufficient extent to reduce their receipts to the old level.
Cf. Marshall, Royal Commission on Labour, Q. 4237-8.
Principles of Economics, p. 540.
"The Export of Capital and the Cost of Living," Manchester Statistical Society, Feb. 1914, p. 78.
The general proposition, of which the statement in the text is a special instance, is that, other things being equal, an increase in the quantity of any one factor of production will be accompanied by an increase in the absolute share of product accruing to that factor, provided that the demand for the said factor has an elasticity greater than unity. The condition on which it will be accompanied by an increase in the proportionate share of product accruing to the factor is different from this, and can be determined as follows. The supply functions of the other factors being given, the aggregate output P depends on the quantity of the variable factor, in such wise that, if x represents this quantity, P=f(x). The absolute share accruing to the variable factor is, therefore, represented by xf', and the proportionate share by xf'/f. The condition that this latter magnitude shall increase when x increases is that

is positive.

Let e represent the elasticity of demand for the factor in question. Then

and the above condition can be expressed, by easy substitution, in the form

Thus e exceeds unity by a larger amount, the larger is the proportionate share of the product accruing, before the variation, to our variable factor. The condition set out above in symbols can be expressed in words, as Dr. Dalton has pointed out, by the statement that "the elasticity of demand is greater than the reciprocal of the relative share of all other factors taken together" (The Inequality of Incomes, p. 187).

The term elasticity of demand, as employed by Marshall and in the text above, signifies proportionate change in quantity divided by proportionate change in price when the changes are very small (strictly infinitesimal). It is what Dr. Dalton calls "point elasticity" (cf. The Inequality of Incomes, pp. 192-7). Hence, in order that the argument of the text may hold good of substantial increases of supply, we must suppose that the elasticity of demand is greater or less than unity, as the case may be, not merely in respect either of the old or of the new quantity of supply, but also in respect of all the quantities intermediate between these two.
Cf. Marshall, Principles of Economics, p. 235.
Cf. Edgeworth, "On the Use of the Differential Calculus in Economics," Rivista di Scientia, vol. vii. pp. 90-91.
Cf. Marshall, Principles of Economics, p. 672.
Report of the Royal Commission on the Aged Poor, p. 72.
Royal Commission on the Aged Poor, Minutes of Evidence (Q. 10,880).

Part IV, Chapter IV

End of Notes

60 of 73

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