Economic Theories on Reswitching - Dictionary of Arguments

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Reswitching: Reswitching is a concept in capital theory where a particular production technique, abandoned at one interest rate, becomes optimal again at a different, lower rate. It challenges the idea of a simple relationship between capital intensity and interest rates, undermining neoclassical theories of capital and distribution. See also Capital, Capital theory, Cambridge Capital Controversy. _____________ 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	> Reswitching	Economic Theories on Reswitching - Dictionary of Arguments Harcourt I 124 Reswitching/reverse capital/Economic theories/Harcourt: The phenomena of double- (or re-) switching and capital-reversing were first noticed in the literature by Joan Robinson [1953-4⁽¹⁾,1956⁽²⁾], Champernowne [1953-4]⁽³⁾ and Sraffa [1960]⁽⁴⁾ (whose book, it will be remembered, though published in 1960, had an enormously long gestation period dating back at least to the mid-1920s). >D. G. Champernowne, >Joan Robinson, >Piero Sraffa. Double-switching is associated essentially with the possibility that the same method of production may be the most profitable of a number of methods of production at more than one rate of profits (r) even though other methods are more profitable at rates in between. Capital-reversing is the value of capital moving in the same direction, when alternative rates of interest are considered, so that a technique with a lower degree of mechanization, as measured, for example, by its level of output per head and value of capital per head, is associated with a lower rate of profits. That is to say, it is the most profitable technique at this rate of profits and, in particular, is more profitable than a more mechanized technique (in the two senses above) which was either equi-profitable or more profitable than this one at higher rates of profits. (All these comparisons must be taken to occur in the neighbourhood of a switch point.) Joan Robinson [1956⁽²⁾], pp. 109- 10, called this a 'perverse' relationship, a curiosum, and acknowledged Ruth Cohen for pointing out the possibility to her, so that it has become known in the literature as the Ruth Cohen curiosum (RCC). Harcourt I 125 In the same passages she describes (but does not name) double-switching (which is not the same thing as capital-reversing) but the implications of the phenomena were neither realized nor spelt out: see Robinson [1970a]⁽⁵⁾, pp. 309-10. Both phenomena imply that the same physical capital goods may have more than one value, because a different real-wage rate and set of relative prices will be associated with each rate of profits and the capital goods associated with the method have to be valued at their appropriate set of prices. Double-switching and capital-reversing may occur in an industry (Sraffa's example in Sraffa [1960]⁽⁴⁾, chapter xn) and in an economy (the original cases discussed by Joan Robinson [1953-4⁽¹⁾, 1956⁽²⁾] and Champernowne [1953-4]⁽³⁾ in a context, one ought to add, that goes back at least to Wicksell and probably to Ricardo: see Sraffa [1960]⁽⁴⁾). Before entering the realm of controversy, it may clarify the subsequent arguments if we give now some very simple examples of the two phenomena. >Wicksell effects, >David Ricardo. (…) we show the w-r relationships of two techniques, one of which is a straight line (bb), the other, concave to the origin {ad). Technique b has a higher output per man than technique a, i.e. qb{= wbmax)>qa{ = wamax). It will be recalled that the value of kb is constant (the price Wicksell effect is neutral), no matter what are the values of r and w, and that ka is smaller, the smaller is the value of r (a negative price Wicksell effect). At a rate of profits greater than rba technique b is the more profitable; at rba the two are equi-profitable, while below rba (and above rab) technique a is the more profitable. In the lower half of the figure we plot in an unbroken line the values of capital per head (in terms of the consumption good) of the technique that would actually be in use at each value of r. Harcourt I 127 We repeat the analysis, this time measuring capital in terms of labour time per head, i.e. as real capital per head, kx. With our present assumptions, the value of kx of any given technique, no matter what is the shape of its w-r relationship, is smaller, the smaller is the value of r. Harcourt I 128 Reverse capital/double switching: When only two techniques are considered, and we are comparing stationary states, capital-reversing implies double-switching and vice versa. However, when more than two are considered, it is possible to have capital-reversing without double-switching, i.e. any one technique is the most profitable of all for a self-contained range of values of r and once it retires it never makes a comeback. Def Ruth Cohen curiosum: This refers to the possibility that as we change the interest rate producers switch the process of production from a to ft, but as we change it further in the same direction they return to a. Harcourt I 129 This would have the unfortunate consequence that we could no longer say that the lowering of the interest rate brings about a process of 'deepening' and each process is more capital-intensive than its predecessors. Harcourt I 130 This curiosum is also discussed by Piero Sraffa in chapter 12 of his book⁽⁴⁾. He shows that producers may shift from one activity to another as the interest rate changes but return to the first activity as it changes further in the same direction. The phenomenon may indeed be observed in the production of a single good. But (…) it is impossible with the whole basis of production. Levhari: We cannot switch from one matrix to another in response to a change in the interest rate and then return to the first matrix in response to further changes in the same direction. So even though we cannot order the activities according to 'degree of mechanization', we can do so with the matrices. (Levhari [1965]⁽⁶⁾, p. 99 HarcourtVsLevhari: That is to say, Levhari claimed to have shown that double-switching was impossible in an 'indecomposable' or 'irreducible' technology, 'a situation in which every single output requires, directly or indirectly as input for its production something .. . of every single other output'. (Levhari and Samuelson [1966]⁽⁷⁾, pp. 518-19.) This proposition was shown conclusively to be false (except under very special conditions) in a series of papers in the 1966, 1967 and 1968 issues of the Quarterly Journal of Economics by Pasinetti [1966a]⁽⁸⁾, Morishima [1966]⁽⁹⁾, Bruno, Burmeister and Sheshinski [1966]⁽¹⁰⁾, Garegnani [1966]⁽¹¹⁾, Samuelson [1966a]⁽¹²⁾, Robinson and Naqvi [1967]⁽¹³⁾, Bruno, Burmeister and Sheshinski [1968]⁽¹⁴⁾. >P.A. Samuelson. Harcourt I 131 Production: Suppose that there is more than one method available for producing directly or indirectly a commodity which will be in surplus and therefore part (or even the whole) of the net product of the year's production, after account has been taken of the amount of commodities used up as means of production in the production process. The forces of competition are assumed to ensure that the same rates of profits and wages will be paid in all industries. (Samuelson [1966a]⁽¹²⁾, p. 575, attributes this result to the workings of ruthless competition, allied with geometry.) Notice that this implies nothing about what determines their actual sizes or the distribution of income. Neoclassical theory: Then the neoclassical parables (>Neoclassicals/Samuelson) lead us to believe that as we arbitrarily consider lower rates of profits, methods associated with higher outputs per head become eligible, values of capital per head and per unit of output become greater and the distribution of income may be obtained by multiplying the quantities of factors by their respective marginal products which may be treated as if they were equal to the equilibrium real wage and rate of profits. Or, rather, the distribution of income, which, under very special circumstances, equals the simple Marshallian elasticity of the factor-price frontier envelope, may be treated as equivalent to that which would be obtained by this alternative procedure. >A. Marshall, >Factor price frontier, >Equilibrium/Neoclassical economics, >Neo-neoclassicals, >Reswitching/Samuelson, >Cambridge Capital Controversy, >Reswitching/reverse capital/Neoclassical economics. 1. Robinson, Joan (1953-4). 'The Production Function and the Theory of Capital', Review of Economic Studies, xxi. 2. Robinson, Joan [1957] 'Economic Growth and Capital Accumulation - A Comment', Economic Record, xxxm, pp. 103-8. 3. Champernowne, D. G. [1953-4] 'The Production Function and the Theory of Capital: A Comment', Review of Economic Studies, xxi, pp. 112-35 4. Sraffa, Piero[1960] Production of Commodities by Means of Commodities. Prelude to a Critique of Economic Theory (Cambridge: Cambridge University Press). 5. Robinson, Joan, [1970a] 'Capital Theory Up to Date', Canadian Journal of Economics, in, pp. 309-17. 6. Levhari, D. [1965] 'A Nonsubstitution Theorem and Switching of Techniques', Quarterly Journal of Economics, LXXIX, pp. 98-105. 7. Levhari, D. and Samuelson, P. A. [1966] 'The Nonswitching Theorem is False', Quarterly Journal of Economics, LXXX, pp. 518-19. 8.Pasinetti, L.L. [1966a] 'Changes in the Rate of Profit and Switches of Techniques', Quarterly Journal of Economics, LXXX, pp. 503-17. 9. Morishima, M. [1966] 'Refutation of the Nonswitching Theorem', Quarterly Journal of Economics, LXXX, pp. 520-5. 10. Bruno, M., Burmeister, E. and Sheshinski, E. [1966] 'Nature and Implications of the Reswitching of Techniques', Quarterly Journal of Economics, LXXX, pp. 526-53. 11. Garegnani, P. [1966] 'Switching of Techniques', Quarterly Journal of Economics, LXXX, pp. 554-67. 12.Samuelson, P.A. [1966a] 'A Summing Up', Quarterly Journal of Economics, LXXX. pp. 568-83. 13. Robinson, Joan and Naqvi, K. A. [1967] 'The Badly Behaved Production Function', Quarterly Journal of Economics, LXXXI, pp. 579-91. 14. Bruno, M., Burmeister, E. and Sheshinski, E. [1968] 'The Badly Behaved Production Function: Comment', Quarterly Journal of Economics, LXXXII, pp. 524-5. Bruno, M. [1969] 'Fundamental Duality Relations in the Pure Theory of Capital and Growth', Review of Economic Studies, xxxvi, pp. 39-53. _____________ 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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