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The Efficiency of Competition as an Allocator of Resources: I. External Economies of Production*

Published online by Cambridge University Press:  07 November 2014

Murray C. Kemp
Murray C. Kemp*
Affiliation:
McGill University
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Extract

Marshall and, later, Pigou were the first to question the competitive allocation of resources, arguing that “increasing-cost” industries produce beyond the optimal point and that the outputs of “decreasing-cost” industries fall short of the optimum. They proposed, on this basis, a system of taxes on the former group of industries, subsidies on the latter group. The criticism of Young, Robertson, and Knight almost completely destroyed the argument. At present, only when “external economies” (and “diseconomies”) play a part in determining the competitive supply function is it admitted that interference with the competitive allocation of resources may be justified.

Our purpose is to present diagrammatically the case for interference with the competitive allocation of resources when external economies of production are present. With the aid of three significant cross-classifications of economies we are able to arrive at several conclusions with policy implications of some importance. In particular, we seek to show that only under very special conditions will the incentive provided by subsidies restore the optimal allocation of resources. Section I is concerned with the definition of terms. Sections II to V provide the diagrammatic analysis, section VI states the policy implications of our results. Section VII briefly summarizes our earlier conclusions.

Throughout the discussion abstraction is made from any special disadvantages of government intervention. No consideration is given to the danger of bureaucratic corruption nor to the possibility that sectional interests will be advanced at the expense of the “general welfare.” Further, all problems of incentive attendant upon government intervention are neglected. Finally, the cost of collecting the revenue from which any net subsidies are to be paid is ignored.

Type
Research Article
Information
Canadian Journal of Economics and Political Science/Revue canadienne de economiques et science politique , Volume 21 , Issue 1 , February 1955 , pp. 30 - 42
Copyright
Copyright © Canadian Political Science Association 1955

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Footnotes

*

This is the first of two papers on the efficiency of competition as an allocator of resources. The second, dealing with external economies of consumption, is to appear in a later issue of this Journal.

In the preparation of this paper the advice of Professor Arnold Harberger has been invaluable, materially improving tie exposition at several points. Professors Burton Keirstead and Eugene Grasberg also have made several suggestions which have been gratefully incorporated.

References

1 Marshall, Alfred, Principles of Economics (8th ed., London, 1920), 467–70Google Scholar; Pigou, A. C., Wealth and Welfare (London, 1912), 172–9.Google Scholar Mention should be made also of Sidgwick. See Sidgwick, H., Principles of Political Economy (London, 1883), Book III, chap. II.Google Scholar

2 Young, Allyn A., “Pigou's Wealth and Welfare,” Quarterly Journal of Economics, XXVII, 1913, 672–86CrossRefGoogle Scholar; Robertson, D. H., “Those Empty Boxes,” Economic Journal, XXXIV, 1924, 16–31 Google Scholar; Knight, F. H., “Fallacies in the Interpretation of Social Cost,” Quarterly Journal of Economics, XXXVIII, 1924, 582–606 CrossRefGoogle Scholar, reprinted in The Ethics of Competition (New York, 1935), 217–36.Google Scholar

3 See Pigou, A. C., The Economics of Welfare (4th ed., London, 1938), Part II, chap, XI, and Appendix 3.Google Scholar Further contributions to the discussion were made by Sraffa, Piero, “The Laws of Returns under Competitive Conditions,” Economic Journal, XXXVII, 1926, 535–50CrossRefGoogle Scholar; Viner, Jacob, “Cost Curves and Supply Curves,” Zeitschrift für Nationalökonomie, III, 1931, 23–46 Google Scholar; Kahn, R. F., “Some Notes on Ideal Output,” Economic Journal, XLV, 1935, 1–35.CrossRefGoogle Scholar The reader may consult also Stigler, G. J., Production and Distribution Theories (New York, 1941), 68–83 Google Scholar; Hicks, J. R., “The Rehabilitation of Consumers' Surplus,” Review of Economic Studies, VIII, 1940–1941, 108–16Google Scholar; Ellis, Howard S. and Fellner, William, “External Economies and Diseconomies,” American Economic Review, XXXIII, 1943, 493–511 Google Scholar; Samuelson, Paul Anthony, Foundations of Economic Analysis (Cambridge, 1948), chap, VIII, especially 207–8Google Scholar; Ruggles, Nancy, “The Welfare Basis of the Marginal Cost Pricing Principle,” Review of Economic Studies, XVII, 1949–1950, 29–46.CrossRefGoogle Scholar The problem of specifying cases in which interference (by taxes and subsidies) with the competitive allocation of resources may be justified has been the subject of a considerable literature in the theory of international trade, dating from the publication of Graham's views in the early twenties. See Graham, F. D., “Some Aspects of Protection Further Considered,” Quarterly Journal of Economics, XXXVII, 1923, 199–216.CrossRefGoogle Scholar The literature is reviewed by Viner in his Studies in the Theory of International Trade (New York, 1937), 475–82.Google Scholar

4 Throughout the paper we speak of economies and subsidies rather than of diseconomies and taxes. After obvious adjustments, the argument becomes equally applicable to diseconomies and taxes.

5 These assumptions are roughly those employed by Sidgwick in his original discussion of the problem. Sidgwick, , Principles of Political Economy, 419–20.Google Scholar

6 Marshall, Alfred, Principles of Economics, 266.Google Scholar

7 Ibid., 441. See also Ibid., 266.

8 Marshall has a second cross-classification of external economies based on the area over which the economy-producing expansion of output takes place: there are those dependent on expansion in the immediate neighbourhood (Ibid., 166; 265, 277) and those dependent upon expansion of the world economy (Ibid., 266).

9 Knight, (“Fallacies in the Interpretation of Social Cost,” 229)Google Scholar pointed out that internal economies result in the expansion of the output of the firm until the economies disappear or the firm becomes a monopoly.

10 Marshall's own examples are singularly unconvincing. Some involve economies arising in auxiliary or subsidiary industries (Principles of Economics, 271). Others arise only in essentially “dynamic” situations. The word “dynamic” is used in two senses: to denote changing technology (cross-fertilization of ideas, development of a skilled labour force, etc.); and to denote non-stationariness (ability to combat business fluctuations). (Ibid., 271, 273.)

11 Pigou, , Economics of Welfare, 134–5.Google Scholar

12 Ibid., 175–7, 184; Sidgwick, , Principles of Political Economy, 412–14.Google Scholar As Professor Elliott has pointed out to me, these are examples of a wide range of cases where it is difficult to make property rights effective. Fisheries, oyster beds, and weed control have often been discussed.

13 If neighbouring coal-mining firms simultaneously expand production, the average pumping cost of each firm will decline, i.e., the industry will become more efficient, because the amount of seepage from unused areas will decrease; the diseconomies of “mining” oil fields are analogous. These familiar examples would appear to be members of a rather large genus.

14 Rosenstein-Rodan, P. N., “The Industrialization of South-East Europe,” Economic Journal, LIII, 205.Google Scholar See also Reder, M. W., Studies in the Theory of Welfare Economics (New York, 1947), 63, n. 2.Google Scholar The point was first made by Sidgwick, , Principles of Political Economy, 411–12.Google Scholar This type of external economy involves the application, rather than the discovery of knowledge. Hence its occurrence is not confined to dynamic” situations. See footnote 10.

15 von Mises, Ludwig, Human Action (London, 1949), 657–9.Google Scholar See also Sidgwick, , Principles of Political Economy, 413.Google Scholar

16 By “no entry” we mean not only that the number of firms in an industry cannot be expanded but also that it cannot be contracted. The M n -curve is a marginal social cost curve only if this restriction is accepted (see below).

17 These statements are not accurate. Under competitive conditions business men seek to establish certain inequalities between the marginal magnitudes. If the total cost and the total revenue functions are differentiable at the relevant outputs, then the price-marginal cost equality may be deduced from the inequalities. See Bishop, R. L., “Cost Discontinuities, Declining Costs, and Marginal Analysis,” American Economic Review, XXXVIII, 1948, 607–17.Google Scholar

Similarly, it is not necessary that price and marginal social cost be equated. Rather, it is necessary only that price be greater than marginal social cost for outputs less than the optimum, and that price be less than marginal social cost for outputs greater than the optimum. When the total social cost curves are differentiable, then the price-marginal social cost equality may be deduced. For this point I am indebted to Professor J. Tobin. For the remainder of this article differentiability will be assumed and the more familiar, if less general, formulation of the optimum pricing rule will be used.

18 This argument is always true only of industries which generate economies “greater” than the “average” for the whole economy. See Pigou, , The Economics of Welfare, 225 Google Scholar; Kahn, “Some Notes on Ideal Output.”

The following argument has been made to the author: if a single firm expands, it incurs marginal private costs MCi . But its expansion results in lower costs to other firms in the industry. These other firms therefore expand too. This secondary expansion results in economies to the firm which first expanded. That firm as a result finds that its marginal costs are not MCi , but are less than MCi ; in fact they are equal to Mn . Hence single firms' will in fact use Mn as their guide in the regulation of output. This conclusion does not depend on the possession of any special foresight, nor on collusion in any respect. However, the argument does depend on the unwarranted assumption that other firms will expand when their total costs are reduced (i.e., that their total and marginal costs move together over the relevant output range), and that they will expand by the appropriate amount.

19 This measure is reasonably accurate only on the assumption of an elastic factor supply to the industry. See introduction.

20 Cf. Sidgwick, , Principles of Political Economy, 414.Google Scholar

21 We assume a perfectly elastic supply of all factors of production to the industry. See introduction.

22 If P were not the envelope of the Ci -curves then it would follow that for some outputs the identical firms would produce unequal outputs. This, however, would imply unequal marginal costs, and this, in turn, would permit of a lowering of total cost for the industry by a reallocation of output in favour of those firms with the lower marginal costs.

23 In this section we consider only economies and subsidies. An easy translation into the language of diseconomies and taxes is possible (see footnote 4). The application of the conclusions to the theory of international trade is left to the reader (see footnote 3).