Capital Theory 1873–2019 and the State of Macroeconomics

Abstract

The current understanding of capital theory suffers from insufficient clarity about the logic of the marginal/neoclassical approach. A central point remained unclear throughout the Cambridge controversies: the traditional versions of that approach needed a given ‘quantity of capital’ not because assuming an aggregate production function ‒ they were fully disaggregated ‒ but because aiming to determine long-period equilibria, centres of gravitation of time-consuming adjustments, and accordingly left the relative endowments of the several capital goods to be determined endogenously, but then needed a given ‘quantity of capital’ to render the equilibrium determinate. A simple model confirms this fact.

This clarification allows further insights. Walras was simply contradictory because aiming at determining a long-period equilibrium while taking the endowments of the several capital goods as given. The derivation of the traditional interest-elastic investment function from the demand-for-‘capital’ function needs the continuous full employment of labour; without this assumption investment is indeterminate. The current reference to intertemporal equilibria as the microfoundation of mainstream macro is a smokescreen, hiding a continuing faith in the traditional marginalist adjustments refuted by reswitching. Finally, the neoclassical approach operates as blinkers, blinding mainstream economists to the adaptability of production to demand, which makes it obvious that output and growth are governed by aggregate demand.

Keywords:

• Capital theory
• macroeconomics
• investment
• Garegnani

Acknowledgements

This is a revised version of the talk with the same title delivered on 4 October at the 2019 HETSA Conference in Sydney. I am greatly honoured for having been given the opportunity to speak at that Conference. I would like to extend heartfelt thanks to Professor Aspromourgos, to the administrative personnel who helped him, and to the University of Sydney, for making my visit possible. I thank the editorial staff of HER for helpful linguistic corrections.

Disclosure statement

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

Notes

1 I must leave aside the debate on the relevance of reswitching and reverse capital deepening, recently enriched by numerous contributions by Professor Bertram Schefold, not so much because of time constraints as because few firm conclusions have been reached so far.

2 It would seem that in this article Joan Robinson did not consider the notion of production function Q = f(L,C) logically untenable, otherwise she would not have written: ‘The production function, it seems, has a very limited relevance to actual problems’ (1953–54, 100). Her problem was rather to find out how to measure C and its changes connected with changes in distribution and with accumulation; and her conclusions were very traditional, the lower the real wage, the less ‘mechanized’ (that is, using less capital per unit of labour) are the techniques imposed by competition, and, given the ‘quantity of capital’, a higher real wage determines a lower level of employment (see e.g. p. 97 of the article). Little wonder that the neoclassicals did not feel greatly threatened by this article.

3 For completeness, it must be added that in order for the Leontief separability condition to authorize aggregating all capital goods into an economy-wide scalar C, it is necessary that the condition holds for the economy’s net product vector, but since the latter consists of separately produced goods, what is required is that Leontief separability holds in the production of each final good and that the function C(k₁,…,k_h) is the same in all of them, so that the several C’s ‘produced’ in the course of the production of each final good can be all summed up because homogeneous. Which implies that the proportions among heterogeneous capital goods must be the same in the production of each final good.

4 This notion of a variable ‘form’ of a given quantity of capital is present in all traditional marginalist authors; let me mention here a less frequently cited instance, Pigou (1935) who speaks of capital as ‘capable of maintaining its quantity while altering its form’ (239).

5 I did not discover the point; I learnt it from Garegnani’s writings and in conversations with him, but I realized that few other persons were clear about it because it was not explicitly made in any contribution to the controversy, and not many people had access to Garegnani’s PhD dissertation.

6 The demand for ‘capital’ must be persistent if the equilibrium is to be persistent. If net savings are only a small portion of total savings, the rate of interest will be nearly the (static) stationary one and the demand for capital for investment in new plants will be nearly the stationary one: the static stationary assumption is legitimate. An equality between supply of, and demand for, capital conceived as a single factor implies that firms are satisfied with the amount of capital they are using and therefore have no reason to change it; so as long as prices and income distribution do not change and labour supply does not change, firms want only to replace the used-up capital goods; hence equations 11 and 12. In this way the equilibrium is persistent, as required by its role as indicator of the averages of day-by-day prices and quantities. If consumer decisions to perform net savings cause a small decrease of the rate of interest, then – the marginalist implicit argument goes ‒ firms will desire to employ more capital per unit of labour in the new plants that re-employ the labour ‘freed’ by the gradual closing down of the plants that reach the end of their economic life. As years pass, the new K/L ratio gradually extends itself to more and more durable plants, the economy is on the way to a new static equilibrium with the stock of ‘capital’ that makes depreciation equal to the current flow of gross savings. See Petri (2004, ch. 4) and Dvoskin and Petri (2017) for a discussion of this slow adjustment process.

7 This is a truly striking paper, a supposed overview of the theory of capital in which no attempt is made to summarize the anti-neoclassical claims, and none of the critics’ contributions are cited apart from Sraffa’s book.

8 The editorial introduction by professors Cohen and Harcourt to the 2005 Edward Elgar three-volume collection of papers on capital theory makes much the same mistake.

9 In what I call a marginalist secularly stationary equilibrium, i.e. an equilibrium which is stationary because the rate of interest has become so low that net savings become zero (which can only result from very slow processes taking even a century), the data determining the equilibrium do not include a given ‘quantity of capital’, the latter is endogenously determined by the condition that the rate of interest must be so low as to induce zero net savings.

10 It seems impossible that Hicks was not aware of the distinction clearly pointed out by Robbins (1930) between static and secular stationary states.

11 The quantity of capital in Solow’s 1956 growth model is persistent enough to allow for time-consuming disequilibrium adjustments. So the ‘momentary equilibrium’ of Solow’s model has no need for the auctioneer or instantaneous adjustments in order for the economy to gravitate towards it; it is in fact a slowly shifting long-period equilibrium, a centre of gravitation of time-consuming adjustments. Because of this, it is not so illegitimate to modify the model by making the propensity to save depend on expectations as to future income and income distribution, expectations that have plenty of time to be corrected; in this way one passes, without much loss of credibility, to Ramsey-type descriptive models, whose ‘momentary equilibria’ can again be seen as centres of gravitation of time-consuming adjustments. No doubt some intuitive perception of all this is one reason for the popularity of these models. Of course these models can be interpreted as applying to real economies only if one believes in ‘capital’.

12 Walras (1954, 380; Walras, Dockès, et al. 1988, 580).

13 ‘Capital goods proper are artificial capital goods; they are products and their prices are subject to the law of cost of production. If their selling price is greater than their cost of production, the quantity produced will increase and their selling price will fall; if their selling price is lower than their cost of production the quantity produced will diminish and their selling price will rise. In equilibrium their selling price and their cost of production are equal’ (Walras 1954, §238, 271; Walras, Dockès, et al. 1988, 353; unchanged from the second to the last edition of the Eléments).

14 This determination of income distribution has relevant supply-side problems too, which I must leave aside for lack of time. I have discussed them in Petri (2004, ch. 8, 298–303) in the form of obstacles to the determination of the labour demand curve in a Marshallian-Keynesian short period.

15 ‘Under conditions of perfect competition, or in an economic system in the position of the theoretical equilibrium (stationary or moving), all sources would yield a uniform rate of return on their cost of production, which would be equal both to their cost of reproduction and their market value … Under real conditions, this rate “tends” to be approximated at the margin of new investment (or disinvestment), with allowance for the uncertainties and errors of prediction’ (Knight 1946, 396).

16 Given the essentially rigid technical coefficients in already existing plants, the gross investment needed to replace intermediate goods is very rigid, so investment can be a function of the rate of interest only in new plants. This by itself suggests a low short-period sensitivity of gross investment to the rate of interest.

17 In most contributions in this approach the absurd assumption is made that the firm treats the price of output as given and unchanging over the entire infinite horizon even when this price is greater than average cost. Imagine the effect this must have on students, who have learnt in microeconomics courses that price tends to minimum average cost in the long run, and now are faced with a denial of this conclusion, supported by no justification. Also, the number of firms is taken as given, as if investment were not often aimed at creating new firms: but if one admits the possibility of appearance of new firms, the approach becomes totally indeterminate. See Petri (2015; also 2004, ch. 7). The popularity of the approach is truly disconcerting.

18 I think it will not be difficult formally to prove that if a wage reduction brings no increase in employment (Keynesian theory implies it can easily have the opposite effect!), then it is rational for unemployed workers not to offer to work for a lower wage. The employed workers would have to accept the lower wage themselves, in order not to be replaced. The cost of firing and hiring would then induce firms to maintain the old workforce, now paid less. So the unemployed workers’ attempt to get a job by accepting a lower wage would produce lower wages for the employed workers, while the unemployed would remain unemployed. Cumulated historical experience, crystallized in popular culture, will teach new generations that this is how things work.

19 The legitimacy of the assumption of continuous equilibrium for a Solow-type model does not derive from intertemporal equilibrium theory, where this assumption is an unfortunate necessity, but from the long-period nature of the ‘momentary’ equilibrium of a Solow-type model; see note 11.

20 Imprecise, because it is not really the Solow model but rather long-period marginalist analysis that one is accepting. Solow’s model is only accepted as representing the latter in simplified form, neglecting consumer and consumption-goods heterogeneity, and land. The aggregate-production-function models are the way the traditional notion of long-period general equilibrium currently survives in neoclassical theory (see Dvoskin and Petri 2017, in particular p. 639, fn. 13; and Petri 2004, appendix to chapter 9). Given the illegitimacy of traditional marginalist adjustments, not only because of reverse capital deepening but also because of the problem remembered in section 9, mainstream macroeconomics is nowadays a fairy-tale that survives only because of a convention to remain blind to its lack of foundations and to prevent by all means the access of the heterodox to the editorial boards of the so-called ‘top’ journals.

21 This is accepted by neoclassical theory too, where each given real wage determines the corresponding factor proportions; the direction of causality is from (full-employment) marginal products to factor rentals only when one adds the full employment of given factor endowments. In actual economies the flexibility of production and the role of new plants in determining prices implies that marginal products in new plants (when there is enough substitutability to determine them) are endogenously determined.

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Fabio Petri

Fabio Petri studied in Napoli, Siena, and Cambridge; he was until 2014 Professor of Istituzioni di Economia (Foundations of Economics) at the Department of Political Economy and Statistics (DEPS), Università di Siena. He continues to teach there in the Economics PhD program. His scientific interests are in the theories of value, distribution, capital and employment. He is an admirer of Piero Sraffa and Pierangelo Garegnani.