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An Attempt at a Rigorous Restatement of Ricardo's Long-Run Equilibrium*

Published online by Cambridge University Press:  07 November 2014

Hans Brems
Hans Brems*
Affiliation:
University of Illinois
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Ricardo's Principles are the most difficult book on economics ever written. It is difficult enough even to understand it, more difficult to interpret it and most difficult to estimate it properly.

–Joseph A. Schumpeter

Judging the accomplishments of the past by the standards of the present, perhaps each generation must make its own attempt at understanding the great masters. It has been said that “Ricardo was the first to present a complete model—one which, for all its faults, was self-consistent and displayed the whole economy as a single interdependent system.” The present paper is an attempt to isolate that self-consistent model and to set it out rigorously. Anyone trying to isolate it must be painfully aware of the possibility that what he is removing may be more valuable than what he is preserving. However, the criterion of consistency leaves him little choice. Having isolated the self-consistent model, he must relate it to our own thinking. The latter emphasizes aggregation, occupies itself increasingly with the underdeveloped two-thirds of the world, and sees no “law” of diminishing returns outside agriculture. In these three senses it is becoming more Ricardian.

Consider three sectors, each producing a homogeneous product or service, that is, a consumers' goods industry, a producers' goods industry, and a labour household sector. The subscripts used to designate the three sectors are c, p, and l, respectively. The consumers' goods industry is facing a production function having one output and three inputs in it. The output consists of consumers' goods, the inputs consist of labour services, services rendered by durable man-made producers' goods, and services rendered by indestructible nature-given land.

Type
Articles
Information
Canadian Journal of Economics and Political Science/Revue canadienne de economiques et science politique , Volume 26 , Issue 1 , February 1960 , pp. 74 - 86
Copyright
Copyright © Canadian Political Science Association 1960

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Footnotes

*

The writer wishes to acknowledge the influence of Carl Iversen's brilliantly clear teaching of Ricardo's Principles at Copenhagen twenty years ago. For helpful criticism he is indebted to Irma Adelman, Alfred F. Chalk, and Knud Erik Svendsen.

The present article was completed before the publication of Paul A.Samuelson's “A Modern Treatment of the Ricardian Economy,” Quarterly Journal of Economics, LXXIII, nos. 1 and 2, Feb. and May, 1959, 1–35 and 217–31. Samuelson is primarily interested in the demolishing of the labour theory of relative prices. Only sections XII–XIV of the present article are devoted to the subject of relative prices and are entirely consistent with Samuelson's findings. The present article is primarily interested in Ricardo's aggregates and is believed to say something new about the two kinds of technological progress discussed in section VIII. Except for the inclusion of three references to Samuelson's work, no changes seemed called for.

References

1 Harrod, R. F., “Walras: A Re-appraisal,” Economic Journal, LXVI, no. 262, 06, 1956, 308.Google Scholar

2 Chap. ii, passim. The term “capital” is also used. All quotations and page numbers refer to The Works and Correspondence of David Ricardo, I, ed. Sraffa, Piero, with the collaboration of Dobb, M. H. (New York, 1951).Google Scholar

3 Chap. v, first par. (p. 93).

4 Edelberg, Victor. “The Ricardian Theory of Profits,” Economica, XIII, no. 39, Feb., 1933, 61.Google Scholar Samuelson, , “A Modern Treatment of the Ricardian Economy,” 5 Google Scholar, agrees that Ricardo's system has a long-run horizontal supply curve of labour (“reproducibility-at-constant-returns of people”).

5 Chap, vi (p. 122). Samuelson, , “A Modern Treatment of the Ricardian Economy,” 227 Google Scholar also interprets Ricardo's system as “literally having a long-run [horizontal supply] schedule for interest.”

6 Chap, vi (p. 122).

7 Schumpeter, J. A., History of Economic Analysis (New York, 1954), 653 n. and 660Google Scholar, considers the minimum supply price of entrepreneurship as one among several alternative profit theories found in Ricardo's Principles. In his earlier work, translated as Economic Doctrine and Method (New York, 1954), 137, and 147 Google Scholar, Schumpeter had been unwilling to consider it as such: he refused to date this notion farther back than to Senior.

8 Therefore, taking derivatives of the wage share, the rent share, and the profit share with respect to the labour force to see what happens to these shares under an autonomously growing labour force is alien to Ricardo's long-run equilibrium system. This is done by Davidson, Paul, “A Clarification of the Ricardian Rent Share,” this Journal, XXV, no. 2, 05, 1959, 190–5.Google Scholar Needless to say, taking such derivatives may illuminate the path that leads toward long-run equilibrium.

9 Chap, ii (p. 80).

10 Ibid. (p. 82).

11 Stigler, George J., “The Ricardian Theory of Value and Distribution,” Journal of Political Economy, LX, no. 3, 06, 1952, 206.Google Scholar

12 As we know, the first and second editions did not contain this chapter. Schumpeter, J. A., Economic Doctrine and Method, 149 Google Scholar, considers this chapter as standing “entirely outside the remaining context of the book.” If our interpretation of it is accepted, it is part and parcel of the Ricardian model.

13 Chap. xxxi (p. 390).

14 Chap. i, sec. iv (p. 31).

15 Chap. ii (p. 74).

16 Chap. i, sec. iv (p. 30).

17 Ibid., sec. v (p. 38).

18 Wicksell, Knut, Lectures on Political Economy, I (London, 1949), 101–33.Google Scholar Sections XII-XIV of the present article are devoted to the same problem as Samuelson is concerned with in “A Modern Treatment of the Ricardian Economy,” and are entirely consistent with the latter's findings. See particularly Samuelson's pp. 16–18 and his n. 4 on page 19.

19 Chap. i, sec. iv (p. 30).

20 Ibid., (p. 30).

21 Ibid. (pp. 36–7).

22 Walras, Léon, Elements of Pure Economics (Homewood, Ill., 1954), 318.Google Scholar

23 Blaug, Mark, “The Empirical Content of Ricardian Economics,” Journal of Political Economy, LXIV, no. 1, Feb., 1956, 41–58.CrossRefGoogle Scholar

24 Frisch, Ragnar, “Propagation and Impulse Problems in Dynamic Economics” in Economic Essays in Honour of Gustav Cassel (London, 1933), 171.Google Scholar

25 Bö̠hm-Bawerk, Eugen Von, Positive Theorie des Kapitales (Innsbruck, 1888)Google Scholar, translated by Smart as Positive Theory of Capital (New York, 1891), Book VII, chaps, II–VGoogle Scholar, “The Rate in Market Transactions” and “The Market for Capital in Its Full Development,” 381–424.Google Scholar

26 Akerman, Gustaf, Realkapital und Kapitalzins (Stockholm, 1923)Google Scholar, examined the case where durable producers' goods and free uninvested labour co-operate. The Akerman model was summarized in rigorous form and further extended by Wicksell, Knut in his long review article, “Realkapital och kapitalranta,” Ekonomisk Tidskrift, XXV, nos. 5–6, 1923, 145–80CrossRefGoogle Scholar, now translated into English as the second appendix to his Lectures, I (London, 1934), 258–99.Google Scholar

27 Economic Doctrine and Method, 132.

28 Empirical studies of the relation between variations in output and costs … indicate with few exceptions a linear covariation.… This conclusion certainly does not justify the statement that all cost functions are linear, but it does suggest that the conditions underlying discussions of ‘diminishing returns’ not only need to be reexamined, but may not be as typical as presumed.” Cost Behavior and Price Policy (New York, 1943), 109, 111.Google Scholar