The Economics of Welfare

Pigou, Arthur C.
(1877-1959)
CEE
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Editor/Trans.
First Pub. Date
1920
Publisher/Edition
London: Macmillan and Co.
Pub. Date
1932
Comments
4th edition.
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Part II, Chapter III
THE VALUES OF MARGINAL SOCIAL NET PRODUCTS AND THE SIZE OF THE NATIONAL DIVIDEND

II.III.1

§ 1. LET us suppose that a given quantity of productive resources is being employed, that there are no costs of movement between different occupations and places, and that conditions are such that only one arrangement of resources will make the values of marginal social net products everywhere equal.*11 On these suppositions it is easy to show that this arrangement of resources will make the national dividend larger than it would be under any other arrangement. This follows from the definition of changes in the size of the national dividend given in Part I. Chapter V. The value of the marginal social net product of resources in any use is the money measure of the satisfaction which the marginal increment of resources in that use is yielding. Whenever, therefore, the value of the marginal social net product of resources is less in any one use than it is in any other, the money measure of satisfaction in the aggregate can be increased by transferring resources from the use where the value of the marginal social net product is smaller to the use where it is larger. It follows that, since, ex hypothesi, there is only one arrangement of resources that will make the values of the marginal social net products equal in all uses, this arrangement is necessarily the one that makes the national dividend, as here defined, a maximum.*12

II.III.2

§ 2. This conclusion may be extended to show that, when complete equality among the values of marginal social net products is wanting, a diminution in the degree of inequality that exists among them is likely to benefit the national dividend. This result cannot, however, be set down without explanation. If the uses in which resources are employed were only two in number, its meaning would be perfectly clear and its validity undoubted. In fact, however, these uses are very numerous. This circumstance gives rise to a difficulty, which has already been referred to in another connection.*13 The meaning of the concept of greater or less equality among a large number of values is ambiguous. Are we to measure the degree of equality by the mean deviation from the average value, or by the standard deviation, or by the "probable error," or by some other statistical measure? If we use the standard deviation as our criterion, reasoning akin to that of the footnote on p. 97 shows that a decrease in the degree of inequality subsisting among the values of marginal social net products in different uses will probably lead to an increase in the national dividend. But it is not certain to do this unless the decrease of inequality is brought about by a group of (one or more) changes of individual values, each one of which taken by itself tends to decrease inequality. Thus, if the distribution of resources is so altered that a number of values of marginal social net products which are below the average are all increased, or if a number which are above the average are all diminished, it is certain that the dividend will be increased. But, if a cause comes into play, which, while decreasing the degree of inequality among the values of marginal social net products on the whole, yet increases some values that are above the average and diminishes some that are below it, this is not certain. This type of difficulty is not, however, of great practical importance, because the obstacles to equality with which we have to deal are, for the most part, general obstacles, and operate in the same sense at nearly all points where they operate at all.

II.III.3

§ 3. Let us next take account of the fact that in real life costs are often involved in moving resources from one place or occupation to another, and let us inquire in what, if any, respects this fact makes it necessary to modify the conclusions set out above. The kernel of the matter can be displayed as follows. Suppose that between two points A and B the movement of a unit of resources can be effected at a capital cost equivalent to an annual charge of n shillings for every year during which a unit that is moved continues in productive work in its new home. In these circumstances the national dividend will be increased by the movement of resources from A to B, so long as the annual value of the marginal social net product at B exceeds that at A by more than n shillings; and it will be injured by any movement of resources which occurs after the excess of the value of the marginal social net product at B has been reduced below n shillings. If the initial distribution of resources between A and B is such that the value of the marginal social net product at B exceeds (or falls short of) the value of the marginal social net product at A by any number of shillings less than n, say by (n - h) shillings, the existing arrangement—that under which the values of the marginal social net products at the two points differ by (n - h) shillings—is the best arrangement, not indeed absolutely, since, if there were no costs, a better arrangement would be possible,*14 but relatively to the fact of the initial distribution and the existing costs of movement. It is not, be it noted, the best arrangement relatively to the existing costs of movement alone. We cannot say that, when the costs of movement are equivalent to n shillings, the national dividend is best served by a distribution under which the values of the marginal social net products at A and B differ by such and such a defined number of shillings. The only accurate statement is: when the costs of movement between A and B are equivalent to n shillings, the national dividend is best served by the maintenance of the existing distribution, whatever that may be, provided that this distribution does not involve a divergence in the values of marginal social net products greater than n shillings; and, if the existing distribution does involve a divergence greater than n shillings, by a new distribution brought about by the transference of sufficient resources to bring the divergence down to n shillings.

II.III.4

§ 4. The results set out in the two preceding sections rest upon the assumption that there is only one arrangement of resources which makes the values of marginal social net products everywhere equal—or as nearly equal as, in view of costs of movement, it is to the interest of the national dividend that they should be made. This assumption would be justified if the value of the marginal social net product of resources employed in each several use was always smaller, the greater the volume of resources employed there. There are, however, two sets of conditions in which this is not so. First, the employment of additional resources in the production of a commodity may, after a time, enable improved methods of organisation to be developed. This means that decreasing supply price*15 prevails, in such wise that the marginal (physical) net product of a greater quantity of resources exceeds the marginal (physical) net product of a smaller quantity: and, whenever this happens, it is possible, though, of course, it is not necessary, that the value of the marginal social net product of several different quantities of resources that might be engaged in producing the commodity will be the same. Secondly, the employment of additional resources in the production of a commodity may, after a time, lead to an increase in the price per unit offered by consumers of any given quantity of it. For their taste for it may be lastingly enhanced—obvious examples are afforded by the taste for music and tobacco—through experience of it. When this happens the value per unit of a larger product will (after an appropriate interval of time) be greater than the value per unit of a smaller product. It follows that, even for commodities whose production is not subject to conditions of decreasing supply price in the sense defined above, there may be, though, of course, there need not be, several different quantities of invested resources, the values of whose marginal social net products are the same.*16 Hence, the conclusions set out above require to be restated in a modified form. Allowance being made for costs of movement, it is true that the dividend cannot reach the maximum attainable amount unless the values of the marginal social net products of resources in all uses are equal. For, if they are not equal, the dividend can always be increased by a transference of resources from the margin of some uses to the margin of others. But, when the values of the marginal social net products in all uses are equal, the dividend need not attain an unequivocal maximum. For, if several arrangements are possible, all of which make the values of the marginal social net products equal, each of these arrangements does, indeed, imply what may be called a relative maximum for the dividend; but only one of these maxima is the unequivocal, or absolute, maximum. All of the relative maxima are, as it were, the tops of hills higher than the surrounding country, but only one of them is the highest hill-top of all. Furthermore, it is not necessary that all positions of relative maximum should represent larger dividends than all positions which are not maxima. On the contrary, a scheme of distribution approximating to that which yields the absolute maximum, but not itself fulfilling the condition of equal marginal yields, would probably imply a larger dividend than most of the schemes which do fulfil this condition and so constitute relative maxima of a minor character. A point near the summit of the highest hill may be higher than any summit except the highest itself.

II.III.5

§ 5. These considerations show that, even though the values of marginal social net products were every where equal or differed only in ways "justified" by the costs of movement, there might still be scope for State action designed to increase the magnitude of the national dividend and augment economic welfare. Benefit might be secured by a temporary bounty (or temporary protection) so arranged as to jerk the industrial system out of its present poise at a position of relative maximum, and induce it to settle down again at the position of absolute maximum—the highest hill-top of all. This is the analytical basis of the argument for the temporary protection, or other encouragement, of infant industries; and, if the right infants are selected, the right amount of protection accorded, and this protection removed again at the right time, the argument is perfectly valid. Benefit might also be secured by a permanent bounty at a different rate from that contemplated above, so arranged as to force the industrial system from the summit of the hill-top on which it is found to any position, that overtops its present site, on the slope of a higher hill. The conditions in which bounties are likely to have this effect, rather than that of shifting the economic system to a different position on the hill that it is on already, are somewhat special. But it can be proved that, in certain states of demand and supply, some rates of bounty must have this effect.*17


Notes for this chapter


11.
The considerations developed in Part III. Chapter IX. § 2 are here provisionally ignored.
12.
A minor point should be noticed in passing. In occupations in which no resources are employed, the value of the marginal net product of resources will, in general, be smaller than it is in occupations where some resources are employed, This circumstance clearly does not imply the existence of inequality among the values of marginal net products in any sense incompatible with the maximisation of the national dividend. But, if it should anywhere happen that the value of the marginal net product of resources in an occupation where no resources are employed is larger than it is in occupations where some resources are employed,—e.g. a profitable venture which for some reason people have failed to exploit,—that inequality would be an effective inequality and would be incompatible with the maximisation of the dividend.
13.
Çf. ante, Part I. Chapter VIII. § 7.
14.
Cf. post, Ch. V. § 6.
15.
For a study of this concept cf. post, Chapter XI.
16.
If equality of the values of marginal net products is attained when 1000 units of resources are devoted to the production of a particular thing, and also, because of decreasing supply price, when 5000 units are so devoted, the national dividend is necessarily larger under the latter arrangement. If equality is attained with 1000 units and also, because of reactions upon tastes, with 5000 units, both economic welfare and the national dividend, from the point of view of the period in which the 5000 units are operating, are necessarily larger under the latter arrangement. But the national dividend, from the point of view of the other period, may be smaller under the 5000 units arrangement. In these circumstances, the definition of p. 54 compels us to conclude that, from an absolute point of view, the dividends under the two arrangements are incommensurable.
17.
The shapes of the demand and supply curves and the size of the bounty must be such that, when the demand curve is raised by the bounty, it does not cut the supply curve at any point corresponding to its former point of intersection, but does cut it at a point corresponding to a point of stable equilibrium further to the right than this. This condition can readily be depicted in a diagram.

Part II, Chapter IV

End of Notes


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