Economic Theories on Aggregate Capital - Dictionary of Arguments

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Aggregate capital: Aggregate capital refers to the total stock of physical, financial, and human capital in an economy used for production. It includes machinery, infrastructure, and investments. In capital theory debates, its measurement is controversial due to issues like heterogeneity and reswitching, challenging the validity of aggregate production functions. See also Production function, Aggregate production function. _____________ Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

> Economic Theories	> Aggregate Capital	Economic Theories on Aggregate Capital - Dictionary of Arguments Harcourt I 155 Aggregate capital/Economic theories/Harcourt: (…) once heterogeneity of capital goods is introduced, the parables based on jelly no longer necessarily apply. ((s) Here the (neoclassical) „parables“ again:) Harcourt I 122 (1) an association between lower rates of profits and higher values of capital per man employed; (2) an association between lower rates of profits and higher capital-output ratios; (3) an association between lower rates of profits and (through investment in more 'mechanized' or 'round-about' methods of production) higher sustainable steady states of consumption per head (up to a maximum); (4) that, in competitive conditions, the distribution of income between profit-receivers and wage-earners can be explained by a knowledge of marginal products and factor supplies. Harcourt I 156 In particular, it may no longer be argued that r equals the marginal product of 'capital' (even in an equilibrium situation), nor may the distribution of income be deduced from a knowledge of the elasticity of the FpF envelope alone. >Elasticity. Furthermore, we are now unable in general to start from the FpF envelope and derive an *as if, well-behaved, production function from it. This has led some writers to look elsewhere than to the concept and properties of an aggregate production function ('as if or real) and marginal productivity concepts to explain the distribution of income (…). Harcourt I 157 The backlash to this argument has been the contention that the existence or not of an aggregate production function (in the sense of a unique relationship between value capital per head and output per head) and marginal productivity relations in distribution theory are not one and the same thing, as Champernowne [1953-4]⁽¹⁾ showed long ago. Bliss [1968b]⁽²⁾, for example - but he is only the leading species of a large genus - argues that if we assume equilibrium (a most important proviso) and price-taking, cost-minimizing, profit-maximizing behaviour under perfectly competitive conditions in linear models, factors as a matter of logic must receive their marginal products, suitably defined, even though an aggregate production function may not be shown to exist. The key points of the argument are two: 1) first, that we impose strict equilibrium assumptions; 2) secondly, that businessmen are profit-maximizers and price-takers. A subsidiary point is that in linear models, marginal products at points (corners) may only be defined as lying within a range that is given by the partial derivatives that lie on either side of them. Factors/revenues/costs: Within this range of indeterminancy, it is obvious that if any factor was not paid the value of its marginal product, a change in output consequent upon using more or less of it would add more to (or subtract less from) revenues than to (from) costs, so violating the assumptions that profits are maximized and that the economy is at equilibrium. (That the economy may not in fact get to an equilibrium position even if one can be shown to exist, that these relationships do not apply in out-of-equilibrium positions and that the real world is usually in the latter state, no one would deny.) Solow: Solow makes the same point as Bliss in several of his papers cited earlier, Solow [1962a⁽³⁾, 1963b(4)] and Solow, Tobin, von Weizsacker, and Yaari [1966]⁽⁵⁾, where typical marginal productivity results are obtained without any reference to aggregate capital - or its marginal product. His latest statement may be found in his reply [1970⁽⁶⁾] to Pasinetti [1969]⁽⁷⁾. Having stated that he does not hold 'a peculiar version of "marginal-productivity" theory' - 'peculiar because it seems to insist (as a matter of principle, not of convenience) on aggregating the whole stock of capital into one number, and because it means by marginal productivity the derivative of net output with respect to the value of this stock of capital' (Solow [1970]⁽⁶⁾, p. 424) - he concludes his article as follows: Harcourt I 158 „. . . nobody is trying to slip over on [Pasinetti] a theory according to which the rate of profits is higher or lower according to whether the existing 'quantity of capital' is lower or higher, and as such represents a general technical property of the existing 'quantity of capital'. That is just what neoclassical capital theory in its full generality can do without.“ (pp. 427-8.) Garegnani/Pasinetti: Garegnani [1966⁽⁸⁾, 1970a⁽⁹⁾, 1970b]⁽¹⁰⁾ and Pasinetti [1969⁽⁷⁾, 1970⁽¹²⁾] in particular, have come back strongly on this one (no suggestion of reswitching is implied). Garegnani points out that, in their formulation of marginal productivity theory, not all the neoclassical economists (early, late, or neo-neo) were either groping for or using an aggregate production function which could be interpreted 'as if it behaved like a well-behaved, one-commodity one. Thus its destruction both at an economy and at an industry level (which he demonstrates in his paper [1970a]⁽¹⁰⁾) is not a conclusive refutation of the marginal productivity theory of value and distribution. 'Expressing the conditions of production of a commodity in terms of a production function with "capital" as a factor is a feature of only some versions of the traditional theory . . .' (Garegnani [1970a]⁽¹⁰⁾, p. 422.) He mentions Marshall and J. B. Clark 'who thought that the principle of substitution, drawn from a reformulation of the Malthusian theory of rent in terms of homogeneous land and "intensive" margins, could be applied without modification to labour and "capital".' But this transition foundered on the fact that 'capital' cannot be measured in a physical unit but must be measured as a value, one which, moreover, changes whenever r and w change, i.e. one which is not independent of distribution. Moreover, it changes in such a way as not to allow us to say that the marginal products of 'capital' and labour are equal to their respective rates of remuneration. All is not yet safe, because, Garegnani argues, 'traditional theory - reduced to its core as the explanation of distribution in terms of demand and supply-rests in fact on a single premise', what Pasinetti [1969]⁽¹²⁾, p. 519, calls 'an unobtrusive postulate': „This premise is that any change of system brought about by a fall in r must increase the ratio of 'capital' to labour in the production of the commodity: 'capital' being the value of the physical capital in terms of some unit of consumption goods, a value which is thought to measure the consumption given up or postponed in order to bring that physical capital into existence.“ (Pasinetti [1969]⁽¹²⁾, S. 519) >Capital demand/Garegnani. 1. Champernowne, D. G. [1953-4] 'The Production Function and the Theory of Capital: A Comment', Review of Economic Studies, xxi, S. 112-35 2. Bliss, C. J. [1968b] 'Rates of Return in a Linear Model', Cambridge: unpublished paper. 3. Solow, R. M. [1962a] 'Substitution and Fixed Proportions in the Theory of Capital', Review of Economic Studies, xxrx, pp. 207-18. 4. Solow, R. M. [1963b] 'Heterogeneous Capital and Smooth Production Functions: An Experimental Study', Econometrica, xxxi, pp. 623-45. 5. Solow, R. M., Tobin, J., von Weizsacker, C. C. and Yaari, M. [1966] 'Neoclassical Growth with Fixed Factor Proportions', Review of Economic Studies, xxxm, pp. 79-115. 6. Solow, R. M [1970] 'On the Rate of Return: Reply to Pasinetti. Economic Journal, LXXX, pp.423-8. 7. Pasinetti, L. L. [1969] 'Switches of Technique and the "Rate of Return" in Capital Theory', Economic Journal, LXXIX, pp. 508-31. 8. Garegnani, P. [1966] 'Switching of Techniques', Quarterly Journal of Economics,LXXX, pp. 554-67. 9. Garegnani, P. [1970a] 'Heterogeneous Capital, the Production Function and the Theory of Distribution', Review of Economic Studies, XXXVII (3), pp. 407-36. 10. Garegnani, P. [1970b] 'A Reply', Review of Economic Studies, XXXVII (3), p. 439. 11. Pasinetti, L. L. [1970] 'Again on Capital Theory and Solow's "Rate of Return" ', Economic Journal, LXXX, pp. 428-31. _____________ Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.	Economic Theories Harcourt I Geoffrey C. Harcourt Some Cambridge controversies in the theory of capital Cambridge 1972

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