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Capital theory controversies

3.1 Introduction

The focus of our analysis now is on the famous Cambridge Capital Controversies (CCC) that involved economists of the caliber of Piero Sraffa and his followers Joan Robinson, Piero Garegnani, Luigi Pasinetti and Geoffrey Harcourt at the University of Cambridge in England and Paul Samuelson and Robert Solow along with their students at the Massachusetts Institute of Technology in Cambridge, Massachusetts. The debates were about the consistency of the neoclassical theory of value measurement of capital goods. As we have already indicated, there is a problem arising from the dual nature of capital goods of being both produced goods and means of production at the same time. The dual nature of capital goods imposes two ways for their evaluation: first, as produced goods by their cost of production as is the case with consumer goods and second, as produced means of production by their expected returns during their useful life, exactly as is the case with the non-produced means of production (land or labor).

The structure of the remainder of the chapter is as follows: Section 3.2 provides a summary of a historical account of the debate and deals with the essence of the debate, which is more about the theoretical consistency of the neoclassical theory and less about the measurement of capital goods. Section 3.3 discusses the derivation of the wage rates of profit (WRP) curves and the associated WRP frontiers. Section 3.4 applies the WRP curves and frontiers in the context of one commodity world. Section 3.5 continues with Samuelson’s surrogate production function and derives the demand schedules for capital. Section 3.6 brings into discussion the possibility of reswitching of techniques. Section 3.7 concludes the discussion of this not necessarily a long-lasting but a very intense debate. In the Appendix, Samuelson’s and Pasinetti’s numerical examples of double switching are presented and critically evaluated.

Cambridge capital theory controversies

The neoclassical theory of value is based on marginal productivity theory according to which the incomes of factors of production are determined by their marginal contribution to production. In particular, the marginal product of labor is equal to the wage rate, the marginal product of capital is equal to the rate of profit (or interest rate) and the marginal product of land is equal to the rent. In all cases, the logical consistency of the theory compels that the marginal products of all factors of production ought to be measured in physical terms.

This is quite plausible in the case of labor input, which can be homogenized and measured in terms of labor time; however, the homogenization even of this factor of production is by no means without its problems, if we think of the thorny question of differences in skills. In the classical approach, the skilled labor is reduced to simple or unskilled labor according to the labor time required for the acquisition of the necessary skills. Thus, for all practical purposes and assuming everything else equal, skilled labor is viewed as a multiple of the unskilled and so the marginal productivity of each kind of labor, skilled or unskilled is expected to be reflected in wage differentials.1 Similarly, the heterogeneous land input, in principle at least, can be homogenized and measured in cultivated areas of the same quality of land and fertility. Hence, for both labor and land, we can stipulate economically meaningful physical units of measurement, in the sense that they are amenable to cost minimization.

By contrast, the measurement of the marginal physical productivity of capital is subjected to a number of limitations. The reason is that capital as a factor of production consists of a multitude of heterogeneous goods, whose aggregation to a single entity is fraught with problems of consistency. In fact, the problem is that capital—unlike labor or land—is an amalgam of heterogeneously produced commodities, which must be added in such a way as to enable a cost-minimizing choice of technique. In other words, there is a need to devise a kind of a yardstick with the aid of which the aggregation of the different components of capital (various tools, machines and structures) to an economically meaningful entity becomes possible. In addition, the marginal product of capital must be expressed in physical and not in monetary terms, a task that becomes nearly impossible to successfully carry out.

From the various available alternatives (e.g., labor time, market prices), neoclassical theory from J.B. Clark and Wicksell and others opts to measure capital goods in terms of values; in particular, the capital goods in terms of physical units (buildings, machines, etc.) times their respective market prices (MP). Hence, the neoclassical theory is in the logic and spirit of business- people, who evaluate every component of their entire endowment of capital stock by assigning to it a MP and arrive at a single value by summing them up, thereby expressing their capital stock in market value terms. The trouble, however, in expressing capital in monetary terms, is its dependence on the interest rate through which future revenues are discounted to the present. In this way, the value of capital is derived on the ever-fluctuating MP, which by their very nature are disequilibrium prices and as such cannot be the foundation of neoclassical or any economic theory. Moreover, if for a moment assume away the long-run character of economic analysis and the associated natural or equilibrium prices and like businesspeople use MP for the measurement of capital, we are definitely subjected to circularity issues. The idea is that there is no discounting and measurement of capital without knowing the rate of interest; therefore, it is odd to use the value of capital in a production function to determine the interest rate. Simply put, the interest rate cannot be determined from capital measured in MP because the value of capital has been previously determined based on the already known interest rate. In addition, the valuation of capital in terms of any kind of prices (equilibrium or market) is not really an option to the neoclassical theory of income distribution, whose consistency to its own premises requires the quantification of the endowment of capital goods without resorting to any value measure. This is equivalent to saying that we need firstly to measure capital goods in physical terms such that to derive their marginal productivity and the associated equilibrium prices and secondly, by assigning these prices to each and every one of the components of the entire capital stock, to arrive finally at an estimate of its total value.

The theoretically consistent measurement of capital, as being of cardinal importance, was pointed out from the first neoclassical economists, who tried to offer plausible solutions. More specifically, Jevons and Menger tried to measure capital goods in physical terms and, surprisingly enough, in terms of labor time. Walras, on the other hand, attempted to measure capital goods in terms of a vector of heterogeneous entities, however, without success (see Eatwell 1990; Garegnani 1990, 2012; Petri 2020 and the literature cited). Finally, Wicksell, who fully understood the problem of specifying the endowment of capital goods in a way consistent with the requirements of neoclassical theory, gave up after a long intellectual struggle and, in his search for scientific truth and intellectual honesty, he proposed to measure the endowment of capital goods as a given quantity of value. In Chapter 2, we argued that these first neoclassical economists went through an intellectual struggle, on the one hand, to arrive at a new theory of value and distribution and in so doing to discard the labor theory of value for its explicit or implicit social implications threatening the status quo of the system. On the other hand, regarding the notion of capital to device a common substance, other than labor time, characterizing all capital goods to aggregate them in an economically meaningful manner. Surprisingly enough in the measurement of capital, they utilized labor time and the evaluation of capital became possible through the use of turnover time; a concept of minor importance in Ricardo’s numerical examples (see Tsoulfidis and Tsaliki 2019, ch. 1).

The problem of consistent evaluation of capital goods does not appear in the classical approach because in the estimation of equilibrium prices and rate of profit, it is assumed that the size and composition of output are given together with the real wage and the state of technology. In other words, the classical analysis assumes one of the distributive variables, usually the real wage, as given and determines the other distributive variable, the rate profit.

Alternatively, we could hold as given the rate of profit and the money wage and through them to determine the relative prices as well as the price level (Leontief 1986). Thus, the evaluation of capital goods (assuming them in physical terms in an input—output setting) can be made without the consistency problems of the neoclassical theory. By contrast, in the neoclassical approach, by determining the profit rate and equilibrium prices through the forces of demand and supply, theoretical concerns arise about the logical consistency and the analytical structure of the neoclassical theory, known as logical or internal critique. This logical critique arises because of the heterogeneity of the endowment of capital goods and the lack of a single physical measure that rules out the assessment of the marginal physical productivity and the associated with it rate of profit.

The issue of capital and its measurement in a way consistent with long-run equilibrium prices resurfaced in Robinson’s (1953—1954) important article inspired by the teaching and writings of Piero Sraffa, especially by his introduction in Ricardo’s Principles. In this seminal article, Robinson raised three interrelated issues: first, the meaning of capital within the neoclassical theory of income distribution; second, the measurement units of the entity capital such that to be independent of equilibrium prices; and third, the existence of long-run equilibrium position of the economy and its attainment. Robinson was particularly interested in the theoretically consistent measurement of capital goods as to whether and to what extent it is possible to employ capital as a pure physical magnitude in a production function and in particular to be used in a theory of value and income distribution. Robinson notes,

|T|he production function has been a powerful instrument of mised- ucation. The student of economic theory is taught to write Q = / (L, C) where L is a quantity of labor, C a quantity of capital and Q a rate of output of commodities. He is instructed to assume all workers alike, and to measure L in man-hours of labor; he is told something about the index number problem involved in choosing a unit of output; and then he is hurried on to the next question, in the hope that he will forget to ask in what units C is measured. Before ever he does ask, he has become a professor, and so sloppy habits of thought are handed on from one generation to the next.

(Robinson 1953—1954, p. 81)

The background of all these discussions on capital theory is Piero Sraffa and his path-breaking book (1960) that made more explicit the internal consistency problems in the measurement of capital within the neoclassical framework and gave a much deeper content and perspective in the debates that followed. In particular, Sraffa argued that within the neoclassical theory, it is not possible to obtain a relationship between wage and profit rate (interest), described by the WRP frontier, with negative and simultaneously monotonic or even better constant slope, as required by the neoclassical production function. Hence, it is not possible to rank the different techniques according to their capital intensity, simply because capital intensity is not constant, but it varies with changes in income distribution in ways impossible to theorize and, therefore, predict. Moreover, if the characterization of an industry as capital- or labor-intensive changes with income distribution, it follows that the edifice of neoclassical theory of value is not based on solid foundations.

The debate started in the early 1960s, when Samuelson (1962) presented a model based on the heroic assumption that capital intensity is uniform across sectors, which is no different to saying that there is a one-commodity world. In such an economy, as income distribution varies, the subsequent revaluation of capital gives rise to results that are absolutely consistent with the requirements of neoclassical theory. In fact, Samuelson derived a straight-line WRP frontier or in Samuelson’s terminology factor-price frontier, the mirror image of the usual convex isoquant curves, which enables the derivation of a well-behaved demand-for-capital schedule. It is important to point out that Samuelson (1971) attacked Marxian value theory for its alleged inability to explain relative prices. However, if one applies Samuelson’s heroic assumption of an equal capital intensity across all industries to Marx’s labor theory of value, then the labor values become equal to prices of production (PP) and profits to surplus values. Consequently, all of Samuelson’s (1971) criticisms of Marx on the so-called transformation problem become untenable.

The Cambridge UK participants in the capital debates noticed this irony. Samuelson’s assumption was criticized for its simplicity and, above all, for the lack of realism by Garegnani (1970, 1990) and Pasinetti (1966, 1977), among others, who showed that once we hypothesize different capital intensities across industries, the neoclassical results do not necessarily hold. The idea is that as relative prices change, the revaluation of capital can go either way. Thus, it is possible for an industry to begin as capital intensive in one income distribution and to become labor intensive in another. Consequently, we no longer derive Samuelson’s straight-line WRP frontiers, which are absolutely required for the cost-minimizing choice of technique and give rise to well-behaved demand-for-capital schedules.

Samuelson’s doctorate student and research associate Levhari (1965) opined that reswitching is not possible in an indecomposable production system and, therefore, reswitching is only applicable to a single industry and not to the totality of the economy. The article stimulated a debate and a symposium organized by the Quarterly Journal of Economics. Among those that refuted Levhari’s claim were after Sraffa’s encouragement his student Pasinetti (1966). Samuelson (1966) conceded that his one-commodity-world description of the operation of the economy, the only way that one may derive consistent demand schedule for capital, was patently unrealistic. The Sraffian economists of the UK Cambridge with Samuelson (1966), this time on their side, claimed using numerical examples that the neoclassical demand and supply schedules determining equilibrium prices for goods and produced factors of production may not hold.

The internal theoretical inconsistencies of the neoclassical theory in its long-period method of analysis that were revealed in the CCC led to the development of its new variant known as intertemporal equilibrium approach. The new variant of neoclassical theory surpasses the problem of inconsistency in the measurement of capital at the expense of spiriting away the long-run character of the analysis associated with the equalization of the rate of profit and, therefore, equilibrium prices. That is, this strand of the neoclassical theory has abandoned the long-period natural price concept as a center of gravity and it deploys the concept of intertemporal equilibria, where future prices are determined simultaneously with relative current prices, through an assumption either of the existence of complete markets for all future goods, or of perfect foresight."

It is important to stress that Sraffa’s primary interest was in the price movement induced by changes in income distribution and the subsequent reordering of techniques. In effect, the standard commodity, a major Sraffa’s innovation, was designed to shed light and settle the very old question that troubled Ricardo. That is, the discovery of an industry, theoretically or practically, whose price is not affected by changes in income distribution, and therefore it can be used as a reference or standard for the evaluation of changes in relative prices of all other industries. Hence, Sraffa’s primary concern was on the shape of the price rate of profit (PRP) trajectories and not the shape of WRP curves. Nevertheless, the latter, which are the mirror image of isoquant curves through which the neoclassical demand schedules of capital and labor are derived, attracted most of the attention of Sraffian economists. The idea was to bring neoclassical economists on their own playfleld by invoking production functions and the isoquants associated with them and by applying their logical critique to reveal the internal inconsistencies of the neoclassical theory. The trouble with the logical critique, however, is that once one makes-believe that accepts, as if they were realistic, assumptions such as perfect substitutability and perfect competition, may end up entrapped in the framework of the theory whose internal inconsistencies seeks to reveal. While neoclassical theory may be criticized for many unrealistic assumptions, such as perfect foresight and perfect rationality, there is a more fundamental critique, and this is its inability to deal consistently with a world that contains heterogeneous capital goods.

In conclusion, economists of the Cambridge University in the UK adopted Sraffa’s work and insights. Among his many students in the 1960s, we distinguish Joan Robinson, Pierangelo Garegnani, Geoffrey Harcourt and Luigi Pasinetti. On the other side of the Atlantic Ocean, in Cambridge Massachusetts, top neoclassical economists, like Paul Samuelson, Robert Solow, and many others, defended the neoclassical theory and, as we will argue, without success. The exchange of views on this issue has been established in the literature as the famous Capital Theory Controversy between Cambridge University in England and the MIT in the Cambridge region of Massachusetts. We now turn to CCC and we bring the internal theoretical inconsistency of neoclassical economics to deal with capital as a means of production in the framework of the production function.

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