## Abstract

This paper sets out the theoretical derivation of a system of demand equations for productive inputs using the hypothesis of cost minimisation by producers, and tests the validity of this hypothesis using disaggregated data for two important UK manufacturing industries. The paper makes use of the methodology and results of consumer demand analysis to establish the restrictions which are implied for the demand functions by the cost minimisation hypothesis, and the additional restrictions which can be imposed if it is assumed that the production function is homothetic. These additional restrictions can often be imposed unintentionally by an inappropriate parameterisation of the demand functions or choice of functional form. In view of this problem, and of the limited range of production functions for which the demand functions can be expressed in explicit form, the system of demand functions used in this paper is derived by direct differentiation of a cost function, and the production function is not used in estimation. The system of demand functions is estimated under a variety of assumptions about substitution possibilities and the embodiment of technical progress. The results show that there is no need to adopt a vintage model of technology, but also that the evidence does not support the basic hypothesis of cost-minimisation.

## Keywords

Cost Function Production Function Demand Function Capital Good Constant Return## Preview

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## References

- Allen, R. G. D. (1938),
*Mathematical Analysis for Economists*(London: Macmillan).Google Scholar - Anderson, T. W. (1958),
*An Introduction to Multivariate Statistical Analysis*(New York: John Wiley & Sons).Google Scholar - Armstrong, A.G. (1974),
*Structural Change in the British Economy**1948–68*, Vol. 12 of Stone, R. (ed.),*A Programme for Growth*, (London: Chapman and Hall).Google Scholar - Atkinson, A.B. and Stiglitz, J. E. (1969), ‘A New View of Technological Change’,
*Economic Journal*, September, pp. 573–8.Google Scholar - Barker, T. S. (1972),
*Updated Social Accounting Matrices: U.K. Commodity Accounts 1954–68*, Growth Project Paper 363, Department of Applied Economics, University of Cambridge.Google Scholar - Barten, A. P., Kloek, T. and Lempers, F. B. (1969), ‘A Note on a Class of Utility and Production Functions Yielding Everywhere Differentiable Demand Functions’,
*Review of Economic Studies*, January, pp. 109–11.Google Scholar - Berndt, E. R. and Christensen L. R. (1973), ‘The Internal Structure of Functional Relationships: Separability, Substitution and Aggregation’,
*Review of Economic Studies*, July, pp. 403–10.Google Scholar - Christensen, L. R., Jorgenson D. W. and Lau, L. J. (1973), ‘Transcendental Logarithmic Production Frontiers’,
*Review of Economics and Statistics*, February, pp. 28–45.Google Scholar - Deaton, A. S. (1974), ‘A Reconsideration of the Empirical Implications of Additive Preferences’,
*Economic Journal*, June, pp. 338–49.Google Scholar - Denny, M. (1974), ‘The Relationship between Functional Forms for the Production System’,
*Canadian Journal of Economics*, February, pp. 21–31.Google Scholar - Diewert, W. E. (1971), ‘An Application of the Shephard Duality Theorem: a Generalised Leontief Production Function’,
*Journal of Political Economy*, pp. 481–507.Google Scholar - Geary, P. T. and M. Morishima (1973), ‘Demand and Supply under Separability’ in Morishima, M. (ed.) Theory of Demand, (Oxford University Press).Google Scholar
- Goldman, S. M. and Uzawa, H. (1964), ‘A Note on Separability in Demand Analysis’,
*Econometrica*July, pp. 387–98.Google Scholar - Gorman, W. M. (1959), ‘Separable Utility and Aggregation’,
*Econometrica*, July, pp. 469–81.Google Scholar - Greub, W. H. (1963),
*Linear Algebra*(Berlin: Springer-Verlag).CrossRefGoogle Scholar - Hotelling, H. (1932), ‘Edgeworth’s Taxation Paradox and the Nature of Demand and Supply Functions’,
*Journals of Political Economy*, October, pp. 577–616.Google Scholar - Kiefer, N. H. (1975),
*Quadratic Utility, Labor Supply and Commodity Demand*Paper presented to 3rd World Congress of the Econometric Society, Toronto.Google Scholar - Morishima, M. (1964),
*Equilibrium, Stability and Growth*(Oxford University Press).Google Scholar - Parks, R. W. (1971), ‘Price Responsiveness of Factor Utilisation in Swedish Manufacturing, 1870–1950’.
*Review of Economics and Statistics*, May, pp. 129–39.Google Scholar - Peterson, A. W. A. (1974),
*Factor Demand Equations and Input-Output Analysis*, Paper presented to Sixth International Conference on Input-Output Techniques, Vienna, April.Google Scholar - Sato, K. (1967), ‘A Two-Level Constant Elasticity of Substitution Production Function’,
*Review of Economic Studies*, April, pp. 201–18.Google Scholar - Shephard, R. W. (1970),
*Theory of Cost and Production Functions*Princeton Studies in Mathematical Economics 4 (Princeton University Press).Google Scholar - Theil, H. (1975),
*Theory and Measurement of Consumer Demand*(Amsterdam: North Holland).Google Scholar - Uzawa, H. (1962), ‘Production Functions with Constant Elasticities of Substitution’,
*Review of Economic Studies*, October, pp. 291–9.Google Scholar