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Keynes's Identity, Ricardian Virtue, and the Partial Dichotomy*

Published online by Cambridge University Press:  07 November 2014

Robert E. Kuenne*
Affiliation:
Princeton University
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Extract

Ricardo offers us the supreme intellectual achievement, unattainable by weaker spirits, of adopting a hypothetical world remote from experience as though it were the world of experience and then living in it consistently. With most of his successors common sense cannot help breaking in—with injury to their logical consistency. (J. M. Keynes, The General Theory, p. 192.)

What was the contribution of Lord Keynes to the development of general equilibrium theory? It is becoming possible now, with the passage of a quarter-century, to view Keynes's General Theory as an (important) episode in the continuous development of general neo-classical systems. From one vantage point, it is paradoxical that his work should have been accepted as the Grand Departure from its neo-classical progenitors—even though Keynes presented it in that light—since his interpretations of these systems are almost always kept visible for purposes of comparison. On the other hand, Keynes's impact on economic policy, on the methodology and analytics of quantitative economics, and on the working economist's “vision” of reality, may be seen even today to be of that order of power rightfully termed “revolutionary.”

Type
Articles
Copyright
Copyright © Canadian Political Science Association 1961

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Footnotes

*

I am indebted to Professors W. J. Baumol, L. V. Chandler, and R. E. Quandt for valuable criticism and to the Ford Foundation whose funds financed this study in part.

References

1 In this sense, Chapter 19 is the most important chapter of The General Theory of Employment, Interest, and Money (New York, 1936)Google Scholar, for it deals with the effects upon the Keynesian model of changes in the wage rate most explicitly (but unsatisfactorily).

2 Becker, G. and Baumol, W., “The Classical Monetary Theory: The Outcome of the Discussion,” Economica, NS, XIX, 1952, 356–7.Google Scholar

3 Cf. Haberler, G., “The General Theory,” in Harris, S., ed., The New Economics (New York, 1948), 173–5.Google Scholar For a recent contrary view, see Edwards, E. O., “Classical and Keynesian Employment Theories: A Reconciliation,” Quarterly Journal of Economics, LXXIII, 1959, 420.Google Scholar Professor Edwards asserts that Keynes's major contribution was to emphasize the aggregate demand curve, although, in retrospect, he neglected factors which would eliminate excess demand for money at full employment. But to say this is to imply that a distinctively Keynesian static theory does not exist, and that Keynesian unemployment was due to the slowness of adjustments in a neo-classical world. In short, something more than the possibility of an excess demand for money is needed: namely, a set of postulates providing for its perpetuation.

4 Lange, O., “Say's Law: A Restatement and Criticism,” in Lange, O., ed., Studies in Mathmatical Economics and Econometrics (Chicago, 1942), 4968 Google Scholar, and Price Flexibility and Employment (Bloomington, Ind., 1944)Google Scholar; and Patinkin, D., Money, Interest, and Prices (Evanston, Ill., 1956), 119–21.Google Scholar See especially p. 119, where Patinkin explicitly sides with “those who deny that [Say's Identity] is a basic component of the classical and neoclassical position.”

5 Kuenne, R., “Patinkin on Neoclassical Monetary Theory: A Critique in Walrasian Specifics,” Southern Economic Journal, XXVI, 1959, 119–24.CrossRefGoogle Scholar

6 To choose another illustration of our point: even though Patinkin's hypothesis were proved that Keynes's speculative money holdings were not a function of the price level, not only is such a postulate unnecessary for his system, but it violates the logic of the system. Its removal cannot but improve the model and may constitute an important preliminary, if indeed the postulate is present at all. But such removal cannot be a major disturbance to the Keynesian model. Cf. Patinkin, , Money, Interest, and Prices, 173–4.Google Scholar (However, the equations on p. 173 have been reversed in their numbering through typographical error).

7 Cf. Harrod, R., “Keynes, the Economist,” in Harris, , ed., The New Economics, 69 Google Scholar: “No one had a greater sense than he of the complexity of economic adjustments and of the numerous reservations that had to be made to a generalization. In his case these reservations always sprang from a strong sense of their importance and not in the least, as in some writers, merely to safeguard himself from criticism—for on the latter point he was notoriously and signally indifferent.”

8 Cf. Smithies, A., “Effective Demand and Employment,” in Harris, , ed., The New Economics, 563.Google Scholar

9 Lange, , “Say's Law,” 50.Google Scholar

10 Hicks, J. R., Value and Capital (2nd ed., Oxford, 1946) 315–9, 325.Google Scholar The literary statement, pp. 62–77, contains an ambiguity which can be misleading. See Kuenne, R., “On Hicks's Concept of Perfect Stability in Multiple Exchange,” Quarterly Journal of Economics, LXXIII, 1959, 309–15.CrossRefGoogle Scholar

11 Except for those cases where the conditions for Hicksian perfect stability are necessary and sufficient for true dynamic stability—when only two goods exist in the economy, when the matrix [E] is negative definite, when all goods are gross substitutes—we cannot derive the condition that principal minors of ∣E∣ must be opposite in sign to the latter. Only the sign of ∣E∣ is derivable from the Routhian conditions, which are necessary and sufficient for the real parts of the latent roots of the characteristic equation of a linear dynamic system to be negative.

12 Kuenne, , “Patinkin on Neoclassical Monetary Theory,” 120–1.Google Scholar

13 Cf. Lange, “Say's Law,” and Modigliani, F., “Liquidity Preference and the Theory of Interest and Money,” reprinted in Lutz, F. and Mints, L., eds., Readings in Monetary Theory (Philadelphia, 1951), 214–16.Google Scholar

14 This result was derived explicitly by Lange, , Price Flexibility and Employment, 520 Google Scholar, but it was stated clearly by Keynes, , General Theory, 259–60.Google Scholar Lange develops his analysis for an economy in which all real excess demands are homogeneous of degree zero in all prices but P e (the price of securities), the supply of money, and the supply of securities, which is the homogeneity postulate implicit in neo-classical systems not characterized by Say's Identity.

15 Price Flexibility and Employment, 5–20. The terminology in this area has become a bit overextended, so that a glossary may prove helpful. Let us postulate a k per cent fall in all prices but P e (i.e., all prices but the rate of interest, i). Then:

1. Lange, beginning from a position of disequilibrium in two markets, defines a “monetary effect of the price change” in terms of changes in the excess demands of the two markets out of equilibrium. Since the excess demand for money reflects the second disequilibrated market perfectly, he needs only to concentrate upon changes in the money market. This latter market must therefore register any changes in the amounts demanded in the equilibrium position of goods other than money. If dEu /Eu is equal to –k, none of the amounts demanded of the goods whose markets are once more in equilibrium can have changed, and the monetary effect is defined to be zero. If dEu /Eu is negative and greater than k in absolute value, some of the amounts demanded of these goods must have increased, and if dEu /Eu is negative and less than k in absolute value, some of these amounts demanded must have decreased. Lange speaks of a “positive monetary effect” in the first case and a “negative monetary effect” in the second.

2. Patinkin, beginning and ending with all markets in equilibrium, defines a “real-balance effect of the price change” in terms of changes in the amounts demanded of goods and of money balances. This definition is for a subcase of Lange's: where the excess demands in the money market and the market for the second good are zero.

16 Ibid., 14. With a fixed supply of money, Su , the demand for money, Du must expand by only k(l–Su /Du ) if the excess demand for money is to fall by k per cent.

17 This work is, of course, that of Patinkin. See Money, Interest, and Prices, 39–45.

18 This effect was discussed by Pigou, A. C. in “The Classical Stationary State,” Economic Journal, LIII, 1943, 343–51CrossRefGoogle Scholar; Economic Progress in a Stable Environment”, Economica, XIV, 1947 Google Scholar, as reprinted in Lutz, and Mints, , eds., Readings in Monetary Theory, 241–51Google Scholar; and in chap. IX, 123–34, of Pigou's, Employment and Equilibrium (2nd ed., London, 1949).Google Scholar Pigou's analysis originally was stated in terms of the long run and for the effect of a drop in prices on the supply of money wealth. Kalecki pointed out that the effect could only operate on that portion of the money supply which was not offset by private indebtedness to the banking system. See his Professor Pigou on the ‘Classical Stationary State’—A Comment,” Economic Journal, LIV, 1944, 131–2.Google Scholar Pigou changed his concept in his later work to one of the effect of a fall in prices on physical as well as money wealth, but the concept remained a long-run concept.

This effect was stressed by Haberler, in Prosperity and Depression (3rd ed., Geneva, 1941), 242, 389, 403, 491503 Google Scholar, in the context of the short run. It was independently discovered by de Scitovzsky, T. in “Capital Accumulation, Employment, and Price Rigidity,” Review of Economic Studies, VIII, 19401941, 6988 Google Scholar, but he felt it to be of such long-run quality that it held true only of generations, not of individuals (pp. 72–3). His wealth concept is one of money balances in the special conditions of his non-capitalistic model.

The effect of wealth enhancements upon consumption has received extensive consideration since these early formulations. Patinkin has refined Pigou's “wealth” concept to one of net indebtedness of the government. See Price Flexibility and Full Employment,” reprinted with revisions in Lutz, and Mints, , eds., Readings in Monetary Theory, 252–83Google Scholar, and Tobin, J., “Asset Holdings and Spending Decisions,” American Economic Review Papers and Proceedings, XLII, 1952, 112.Google Scholar The effect of an increase in physical wealth upon consumption was noted briefly by Keynes. Cf. Ackley, G., “The Wealth-Saving Relationship,” Journal of Political Economy, LIX, 1951, 154–61CrossRefGoogle Scholar, and Patinkin, , Money, Interest, and Prices, 464.Google Scholar

19 This will be discussed extensively below. The term is Haberler's, used in “The Pigou Effect Once More,” Journal of Political Economy, LX, 1952, 240–6CrossRefGoogle Scholar, and is to be distinguished from Ackley's use of the same term for the long-run effect described in n. 18.

20 Tobin, , “Asset Holdings and Spending Decisions,” 109–23.Google Scholar Should this effect operate, as Tobin points out, the supply of labour becomes a function of the money wage, lending credence to the familiar Keynesian assumption.

21 General Theory, 259–260.

22 Ibid., 260.

23 Ibid., 261–71.

24 Cf. Modigliani, , “Liquidity Preference,” 211 Google Scholar; Pigou, , “Economic Progress in a Stable Environment,” 241–51Google Scholar; Patinkin, , “Price Flexibility and Full Employment,” 278–9Google Scholar; and Haberler, , “The General Theory,” 167.Google Scholar

25 This result springs from Kalecki's exception to Pigou's early analysis and is explicitly applied to securities by Patinkin, in Money, Interest, and Prices, 205.Google Scholar

26 Keynes, , General Theory, 167.Google Scholar

27 Metzler, L., “Wealth, Saving, and the Rate of Interest,” Journal of Political Economy, LIX, 1951, 97–8.Google Scholar

28 Patinkin, seems to have been the first to state this explicitly in Money, Interest, and Prices, 14, 163, and 463–71.Google Scholar Cf. also Metzler, , “Wealth, Saving, and the Rate of Interest,” 95.Google Scholar

29 General Theory, 191.

30 Or at least what Metzler has called the Keynesian system at its simplest. “Wealth, Saving, and the Rate of Interest,” 95–6. Cf. also Patinkin, , “Price Flexibility and Full Employment,” 257.Google Scholar

31 Haberler, , “The General Theory,” 169.Google Scholar See also “The Pigou Effect Once More.”

32 Patinkin hints at this when, after discussing Keynes's limitation of the real balance effect to securities, he says: “Looking back on the nature of these errors, we cannot but be struck by the irony that they should have emanated from the man who did most to demonstrate the fundamental inseparability of the real and monetary sectors of the economy …” See “Price Flexibility and Full Employment,” 270.

33 Money, , Interest, and Prices, 237.Google Scholar