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 V
THE EFFECTS OF ELIMINATING OBSTACLES TO MOVEMENT

II.V.1

§ 1. THE purpose of this chapter is to study the way in which the size of the national dividend will be affected by a reduction of the obstacles to the movement of productive resources that are set up by ignorance and costs of movement. It is legitimate for this purpose to ignore differences between marginal social net products and margiual private net products; for, though particular obstacles to movement may prevent equality between the values of marginal private net products in such wise as to promote equality between the values of marginal social net products, there is no reason to suppose that obstacles to movement in general act in this way. It is proper to regard divergences between social and private net products as one factor making for inequality in the values of marginal social net products, and obstacles to movement as a second factor superimposed upon this; so that to weaken the force of either factor may be expected, in general, to promote pro tanto the equality that is desired. Assuming this, I shall, for simplicity of diction, in this and the following chapter, speak of marginal net product without any adjective.

II.V.2

§ 2. If the total quantity of productive resources at work be taken as given, it would seem at first sight that a reduction effected without expense in either sort of obstacle must necessarily make the rates of return in different uses and places, that is to say, the values of marginal net products, less unequal, and, consequently, must make the dividend larger. In reality, however, things are not so simple as this. The fact that obstacles to free movement comprise both costs of movement and imperfections of knowledge complicates the situation; for we have to contemplate reductions of costs while knowledge is still imperfect and improvement of knowledge while costs remain.

II.V.3

§ 3. It is plain that, if people think that a larger return can be obtained by sending resources away from A for employment at B, a diminution in costs will cause resources to be sent, which, as a matter of fact, would have been more productive if left where they were. It is thus certainly possible that a reduction of costs in actual life may render the values of marginal net products more unequal, and so lessen the national dividend. In the appended footnote, however, it is shown by a technical argument that this is, on the whole, unlikely.*19

II.V.4

§ 4. There is a different kind of complication when costs of movement remain unchanged but knowledge is improved. This improvement need not lead to an increase in equality among the values of marginal net products. For suppose the conditions to be such that, if perfect knowledge prevailed, the value of the marginal net product of resources at one point A would exceed the corresponding value at another point B by one shilling, and that the cost of moving a unit of resources from B to A would just balance this advantage. But, in fact, let us further suppose, knowledge is imperfect; people believe the value of the marginal net product at A to be higher than it really is; they therefore send more resources from B to A than they would do if better informed; and, therefore, the excess of the value of the marginal net product at A over that at B stands at less than n shillings. In these circumstances the growth of a more correct judgment would evidently increase the degree of inequality prevailing between the values of the marginal net products of resources at A and B. At the same time, however, it would evidently also increase the size of the national dividend. A reduction effected without expense in the obstacles set up by ignorance will thus always increase the national dividend; though it will not always do it by promoting equality among the values of marginal net products.

II.V.5

§ 5. At this point, however, we are brought up against a serious difficulty. Hitherto the total quantity of resources at work has been taken as given. In fact, however, the elimination or reduction of obstacles to the movement of productive resources may modify the quantity of these resources that come into action. We have, therefore, to ask whether the quantity of resources at work will ever be reduced, as a consequence of obstacles being removed, in such a way that the national dividend is made smaller and not larger than before. That this result may be possible is suggested by an argument of Cournot's, in which he shows that, when "communication is opened between two markets, previously separated by a barrier, the total quantity produced of any commodity, which now begins to be exported from one market and imported to the other, will not necessarily be increased."*20 The increase in the output of the (hitherto) cheaper market will not, in some conditions, be as large as the decrease in that of the (hitherto) dearer market. By analogy it would seem that the opening up of communication between occupations and places hitherto separate might cause the aggregate quantity of labour at work, or of capital created, to be reduced; and the reduction might, in some circumstances, suffice to cause a reduction in the size of the national dividend in spite of the fact that part of the labour or capital still left would be operating under more favourable conditions than before. We must, I think, admit that, as a result of the opening up of communication, the amount of labour at work or of capital created may be reduced. I have difficulty, however, in imagining conditions in which the national dividend, as I have conceived it, could be diminished. For why should anybody choose more leisure than before unless the new conditions had given him a bigger aggregate income from work than before; and why should any one choose to save less than before unless the new conditions had given him a bigger aggregate income from savings than before? It may be that a full analysis would reveal possibilities in this matter that I have failed to see; but the possibilities are certainly remote. There can be no doubt that, in a broad general way, the conclusions reached in the preceding sections on the assumption that the quantity of resources at work is given are also valid when that assumption is removed.

II.V.6

§ 6. It remains to clear up an important issue. This has to do with the effect of State bounties designed to lessen ignorance or to reduce the costs of movement.*21 A cheapening of knowledge and movement to individuals, brought about by the transference of a part of the cost of these things to the State, is quite a different thing and works quite differently from a cheapening brought about by a real fall in cost. The two sorts of cheapening have the same tendency to promote—apart from the exceptional cases noticed above—increased equality among the values of marginal net products at different points. But, when the cheapening is due to transference, the resultant increase of equality is an increase beyond what, relatively to existing conditions, is most advantageous. Prima facie this sort of cheapening, though it will generally make the values of marginal net products more equal, is likely to injure the national dividend.*22


Notes for this chapter


19.
The proof is as follows. Let people's judgment concerning the value of the marginal net product of resources invested at B be correct, but let their estimate of the corresponding value at A differ from fact by a defined quantity k. Let the costs of movement between A and B be equated to an annual sum spread over the period during which the unit of resources that has moved may be expected to find profit in staying in its new place. This annual sum is not necessarily the same in respect of movements from A to B and movements from B to A. Transport, for example, "acts more easily down than up hill or stream [and]...the barrier of language acts more strongly from England to Germany than vice versa" (Macgregor, Industrial Combination, p. 24). For the present purpose, however, we may ignore this complication and represent costs in either direction by an annual sum equal to n. Construct a figure in which positive values are marked off to the right of O and negative values to the left. Mark off OM equal to k; and MQ, MP on either side of M each equal to n. It is then evident that the excess of the value of the marginal net product of resources at B over that at A—let this excess be known as h—is indeterminate and may lie anywhere between a value OQ, which may be either positive or negative, and a value OP which may also be either positive or negative. A diminution in the value of n is represented by movements on the part of the two points P and Q towards M. So long as the values

of k and n are such that P and Q lie on opposite sides of O, it is obvious that these movements make impossible the largest positive and the largest negative values of h that were possible before, and have no other effect. When, however, P and Q lie on the same side of O—in which case, of course, all possible values of h are of the same sign—they make impossible both the largest values of h that were possible before and also the smallest values. This double change seems equally likely to increase or to diminish the value of h. Hence, if it were the fact that the points P and Q always lay on the same side of O, we could not infer that diminutions of the value of n would be likely to affect the value of h either way. In fact, however, it must often happen that P and Q lie on opposite sides of O. When account is taken of these cases as well as of the others, we can infer that, over the mass of many cases, diminutions in the value of n are likely to reduce the value of h. In other words, diminutions in the costs of movement are likely, in general, to make the values of the marginal net products of resources at A and B less unequal. Furthermore, it is evident that, when the distances MP and MQ are given, the probability that P and Q will both lie on the same side of O and, therefore, the probability that a diminution in the distances MP and MQ will be associated with an increase in the value of h, is smaller the smaller is the value of k.

20.
Cf. Cournot, Mathematical Theory of Wealth, ch. xi., and Edgeworth, "Theory of International Values," Economic Journal, 1894, p. 625.
21.
Cf. post, Part III. Ch. IX. §§ 11-14.
22.
To obviate misunderstanding two modifying considerations should be added. First, the presumption just established against the grant of a bounty to the industry of promoting mobility is merely a special case of the general presumption against the grant of a bounty to any industry. It may, therefore, be overthrown if there is special reason to believe that, in the absence of a bounty, investment in the industry in question would not be carried so far as is desirable. Secondly, when the State takes over the work of providing either information or the means of movement, and elects for any reason to sell the result of its efforts either for nothing or below cost price, we have, in general, to do, not merely with the grant of a bounty on these things, but at the same time with a real cheapening due to the introduction of large-scale methods. Even, therefore, though the bounty element in the new arrangement were proved to be injurious, it might still happen that that arrangement as a whole was beneficial.

Part II, Chapter VI

End of Notes


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