Economics Dictionary of ArgumentsHome
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| Aggregate Production Function: The Aggregate Production Function represents the relationship between total output and inputs like capital and labor in an economy. It is used to analyze productivity, growth, and income distribution. Criticized in capital theory debates, it assumes homogeneous capital and smooth substitution, which may not reflect real-world complexities. See also Production function, CES production function, Cobb-Douglas production function, Capital._____________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. | |||
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David Gawen Champernowne on Aggregate Production Function - Dictionary of Arguments
Harcourt I 29 Aggregate production function/equilibrium/CampernowneVsRobinson/Campernowne/Harcourt: Champernowne [1953-4] accepted the logic of Joan Robinson's approach and measure but objected to the possibility that the same physical capital could have a different value as between two situations 'merely' because it was associated with a different set of equilibrium rates of wages and profits. >Aggregate production function/Robinson, >Aggregate production function/Solow. Harcourt I 30 HarcourtVsChampernowne: This objection is valid from the point of view of the theory of production, i.e. the ability to predict the rate of flow of output from a knowledge of factor supplies, but it is neither valid nor relevant for 'capital' viewed as value property, i.e. as reflecting the institutions of capitalist society. There is a real difference between the two situations and value capital ought to reflect it. The economic significance of a given plant may vary from one economic environment to another. Harcourt: Nevertheless Champernowne appears to have been searching for a unit which could do both tricks at the same time. Measure of capital: Thus he further felt it would be convenient - and more in keeping with the orthodox neoclassical tradition - to have a measure of capital such that the rewards to the factors of production could be obtained by partial differentiation of the relationship between output and capital (so measured), on the one hand, and labour, on the other. Comparability: Furthermore, despite the strictures on using comparisons to analyse processes, he was keen to analyse the process of accumulation and deepening, tracing the development of capitalism over time, approaching its 'crisis' as real wages rose and rates of profits fell. Even if, in fact, equilibrium were ruptured repeatedly, Champernowne hoped to make the process slow enough to proceed as if this had not occurred, to measure capital each step on the way and to provide a means of comparing capital stocks over time as well as between different situations of stationary equilibrium. Measurements: Such an all-purpose measure is provided in a chain index whereby the 'normal' concave relationship between output per head of a constant labour force and capital per head would be established, provided that any one technique, having been the most profitable or equi-so at a given rate or range of interest rates, could never reappear again at another rate or range of rates, and that, of two techniques which are equi-profitable at a given rate of interest, it is the one with the higher output per head and higher value of capital per head that is the more profitable at a lower rate of interest. Harcourt I 32 Formalization/indexes: This series of index numbers shows the changes in the 'quantity' of capital after the effects on the value of capital of different rates of wages and profits have been removed. Output/labour: Output may now be expressed as a unique function of labour and chain index capital and the rewards of the factors of production correspond to the partial derivatives of the appropriate branches of the function. In the 'pure' cases, the coefficients of the production function set the upper or lower limits to the factor prices: see Champernowne [1953-4](1), p. 127.) Equilibrium wage rate: The partial derivative of output with respect to labour equals the equilibrium wage rate and the partial derivative of output with respect to capital equals the equilibrium rate of profits multiplied by the 'price' of 'capital'. Price: The price itself is a chain index price since the chain index removes, as it were, the 'quantity' of capital from the coefficient of the capital term. Capital/ChampernowneVsRobinson/Harcourt: In effect Champernowne has removed the 'zigs' - the horizontal stretches - from Joan Robinson's real-factor-ratio curve (…) and changed the slopes of the 'zags' - the upward-sloping stretches - so that they now equal the relevant equilibrium values of the 'price' of 'capital'. >Method/Champernowne. 1. Champernowne, D. G. [1953-4] 'The Production Function and the Theory of Capital: A Comment', Review of Economic Studies, xxi, pp. 112-35._____________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. |
Champernowne I David Gawen Champernowne Uncertainty and estimation in economics (Mathematical economics texts) Edinburgh 1969 Harcourt I Geoffrey C. Harcourt Some Cambridge controversies in the theory of capital Cambridge 1972 |
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