Investment function in Marshall, Fisher and Keynes: a critique of the neoclassical theory of investment in light of the capital theory controversy

Abstract

An overwhelming majority of the economics profession is taught that there is an inverse relationship between interest rate and investment expenditures. In the light of the controversies in the theory of capital, we analyse in this article the way in which Marshall, Fisher and Keynes have constructed this inverse relationship. All three were aware of the problems associated with this construction and tried—albeit unsuccessfully—different ways to get around them. This implies that within the neoclassical analysis there does not exist a theoretically consistent conceptualisation of an investment demand function inversely responsive to the rate of interest.

Keywords:

• Capital controversy
• investment theory
• Marshall
• Fisher
• Keynes

JEL CODES:

• B22
• B31
• B51
• E11
• E22

Acknowledgement

This article is a substantially revised version of a part of my Ph.D. dissertation written some time ago for the University of Cambridge under the supervision of Professor Lord Eatwell. I would like to thank him for his guidance and help during the initial construction of the argument. I also would like to thank Prof. Franklin Serrano of the Federal University of Rio de Janeiro, and Professor Emeritus Paul Christensen of Hofstra University for their comments on this earlier draft. Finally, I thank the two anonymous referees of this journal whose comments have greatly improved the argument. Needless to say, all remaining errors are mine.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 See Petri (2004, Ch. 7) for a review and detailed critique of the various alternative approaches developed in the post-War period based on the inverse relationship between the rate of interest and investment.

2 Wicksell’s Lectures on Political Economy was originally published in Swedish 1901 and, hence, it was unavailable to all three, but its German translation came out in 1913. Fisher knew German (Hagemann 2013, 324), but neither in The Theory of Interest (1930) nor, of course, in The Rate of Interest published earlier in 1907, he refers to the Lectures. On the other hand, the English translation of the Lectures was not available to Marshall who had already passed away. However, Keynes had seen the translation in 1932 when it was initially submitted for publication to Macmillan (Keynes [1983] 2013, 865), but he does not seem to be apprehensive of its importance.

3 See Garegnani (1976), Milgate (1979) and Gherke (2003).

4 This was a possibility that could not be ignored, since it had happened in the past, after the decline of the “wage fund” theories (Garegnani 2012, 1424).

5 The initial controversy in the theory of capital took place in the first decade of the twentieth century between J.B. Clark and Eugen von Böhm-Bawerk in the pages of the Quarterly Journal of Economics and in private correspondence between the two (see Kurz 1990, 84 and Cohen and Drost 1996), with Irving Fisher participating at different points and Thorstein Veblen attacking both Clark and Fisher. There was a revival of the controversy in the 1930s, this time mainly between Frank Knight and Friedrich von Hayek with the participation of Nicholas Kaldor, as Knight launched an attack on the Austrian concept of the “period of production,” which was recently revived by Hayek (Kurz 1990, 85). The third round, known as the “Capital Controversy” or the “Controversy between the two Cambridges,” began with Joan Robinson’s (1953) article, culminated in the 1960s and 1970s and, at least from the viewpoint of the critics, still continues today, entering a new phase with Garegnani’s (1976) article, focusing on the criticism of the neo-Walrasian intertemporal versions of the neoclassical theory (see Cohen 2014 for a review of the first round, and Milgate (1979) and Kurz (1990) for the second).

6 It should be noted that Marshall waters down this distinction that he makes between the rate of interest and quasi-rent, arguing that “interest on free capital and quasi-rent on an old investment of capital shade into one another gradually” (cited in Kurz and Salvadori 1995, 370). However, he does not specify the demarcation lines in this gradual shading.

7 For “free” or “floating capital,” Marshall also uses the terms “capital in general”, “capital for any use”, “circulating capital” or, referring to J. B. Clark’s conception, “pure capital” (Clark [1899] 1965, 9).

8 The “normal” degree of capacity utilization associated with a long-run position can be defined as the degree of capacity utilization consistent with the demand expectations of entrepreneurs (with respect to the peaks, troughs and the average level of the demand) at the time of installing their capacities (Ciccone 1986, 26–27).

9 In real life, this new set of machines will, obviously, incorporate the advances in technology and will not be of the same technological vintage. However, for the purposes of this discussion, technology is assumed to be unchanging.

10 As is well known by now, this long-run solution of Walras, with a uniform rate of net income over the supply prices of capital goods, was inconsistent (see Garegnani (1990) and Eatwell (1987) for a critique of Walras’ analysis).

11 Fisher (op. cit. 131n). In comparing his analysis with that of Walras and Pareto, Fisher expresses the same idea on p. 519 of The Theory of Interest.

12 Strictly speaking, this is the variation in net investment. Not to further complicate the expression, we have implicitly assumed the prior net investment to be equal to zero.

13 Since (R_β - R_α)/(R_ξ – R_α) gives the slope of the line αβ, (R_β - R_α)/(R_α – R_ξ) will be negative of the slope. The rate of return over cost, as described in Equation 3.3, will be the negative of the slope minus one.

14 Adapted from Fisher, The Theory of Interest (Fisher [1930] 1986, Ch. 11, 270–271).

15 Tobin has also observed that Fisher conducts his analysis assuming a one commodity world. He explains it with the complexity that a multi-commodity multi-agent world would create with inter-temporal production possibilities. “Therefore (Fisher) proceed(s) as if there (is) just one aggregate commodity to be produced and consumed at different dates” (Tobin 1990, 167).

16 We saw above that, in discussing his theory graphically, Fisher had modified his argument and assumed only two periods. In the algebraic exposition of his theory, Fisher makes yet another change in his argument and assumes a finite income flow of ‘n’ years (Fisher [1930] 1986, 293) instead of the perpetual returns ad infinitum of his intuitive exposition.

17 Formalized on the basis of the numerical examples Fisher gives in ([1930] 1986, 155–156).

18 In the numerical examples that Fisher employs, all prospective returns, except the initial cost, are assumed to be non-negative. Hence, there is only one change of sign from the initial cost, which can be seen as a negative return, to the positive prospective returns. If some returns are negative, because signs change more than once, there will be more than one real root and some of these roots may be negative. To avoid this outcome and guarantee the uniqueness of roots, the process must be truncated in the period before the negative return, corresponding to Fisher’s nth period. Imaginary roots, which can be determined by subtracting the total number of positive and negative roots from the number indicating the degree of the polynomial, are assumed away. See Karmel (1959, 430) and Soper (1959, 177) for a discussion of truncation within a partial equilibrium framework; Arrow and Levhari (1969), Hicks (1970, 1973) and Nuti (1973) for the attempts to generalize the idea of truncation to the economy as a whole. See also, however, Eatwell (1975) and Kurz and Hagemann (1976) for a critique of these generalizations.

19 Net return is defined here as the difference between the returns expected from the sale of the output produced and the running expenses incurred during the process of production (i.e., the current costs of production, administrative and distributive costs, interest costs and taxes). The supply price, by contrast, is “the price which would just induce a manufacturer to produce an additional unit of such assets” (Keynes [1936] 1964, 135).

20 The name “array of opportunities approach” was first used by Witte, as he concisely criticized the approach by saying that “[i]f one way of using capital goods is more profitable than others, why employ the other methods at all” (Witte 1963, 445).