## Abstract

Marginal productivity theory plays a central role in neoclassical growth theory. It has also been much used in empirical work to identify the factors responsible for growth, for if marginal productivity theory is accepted in its entirety, the contribution of particular factors of production to growth can be derived quite straightforwardly from published statistics.^{1} With no other theory can it be claimed that the contribution of, for instance, engineers to the growth rate can be measured. However, according to *simpliste* marginal productivity theory where perfect competition in factor and product markets is assumed, their contribution will be precisely the rate of increase in an economy’s ‘stock’ of engineers, times the share of the National Income which engineers receive. Much skill and ingenuity may be needed to estimate these, because this information may not be published in precisely the form needed for the calculation. However, this kind of calculation is relatively straightforward.

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### Notes

- 1.Perhaps the most notable uses of marginal productivity theory to explain past growth are
*Why Growth Rates Differ: Postwar Experience in Nine Western Countries*, by Edward F. Denison, assisted by Jean-Pierre Poullier (Washington, D.C.: Brookings Institution, 1967); and D. W. Jorgensen and Z. Griliches, ‘The explanation of productivity change’,*Review of Economic Studies*, vol. xxxiv (July 1967).Google Scholar - 1.This is simply a special case of Euler’s theorem which shows that total product is exhausted when all factors receive their marginal products with all production functions which are homogeneous to the first degree. See, for instance, Joan Robinson, ‘Euler’s theorem and the problem of distribution’,
*Economic Journal*, vol. XLIV (Sep 1934).Google Scholar - 2.R. M. Solow, ‘Technical change and the aggregate production function’,
*Review of Economics and Statistics*, vol. xxxix (Aug 1957).Google Scholar - 3.J. R. Hicks,
*The Theory of Wages*(Macmillan, 1932) p. 121. Here he defined technical progress as neutral where it raised the marginal products of labour and capital, the two factors he was considering, in the same proportion. The equivalent assumption with more than two factors is that the marginal product of each factor is increased in the same proportion.Google Scholar - 1.T. R. Malthus,
*Principles of Politicai Economy*(London, 1820) pp. 370, 373-4.Google Scholar - 2.See, for instance, N. Kaldor, ‘A model of economic growth’,
*Economic Journal*, vol. lxvn (Dec 1957); Joan Robinson,*Essays in the Theory of Economic Growth*(Macmillan, 1962) n, ‘A model of accumulation’; and K. J. Arrow, ‘The economic implications of learning by doing’,*Review of Economic Studies*, vol. xxix (June 1962).Google Scholar - 3.J. R. Hicks, ‘Thoughts on the theory of capital — the Corfu Conference’,
*Oxford Economic Papers*, vol. XII (June 1960).Google Scholar - 1.See, for instance, P. J. D. Wiles,
*Price, Cost and Output*, 2nd ed. (Blackwell, 1961) appendix to chap. 12; and A. A. Walters, ‘Production and cost functions’,*Econometrica*, vol. xxxi (Jan-Apr 1963).Google Scholar - 2.The Cobb-Douglas production function was first formulated independently by Knut Wicksell,
*Lectures on Political Economy*(Routledge & Kegan Paul, 1934;Google Scholar - 1.The concept of the ‘elasticity of substitution between labour and capital’ was first formulated independently by Hicks, in his
*Theory of Wages*, and Joan Robinson,*The Economics of Imperfect Competition*(Macmillan, 1933) pp. vii, 330. By Joan Robinson’s definition,*σ*is ‘the proportionate change in the ratio of the amounts of the factors divided by the proportionate change in the ratio of their marginal physical productivities’. The mathematical derivation of a formula for*a*is to be found in Hicks,*Theory of Wages*, pp. 242-5.Google Scholar - 1.Kenneth J. Arrow, H. B. Chenery, B. Minhas and R. M. Solow, ‘Capital- labour substitution and economic efficiency’,
*Review of Economics and Statistics*, vol. XLHI (Aug 1961); and Murray Brown and J. S. de Cani, ‘Technological change and the distribution of income’,*International Economic Review*, Vol. iv (Sep 1963).Google Scholar