Factor Demand Functions

  • William Peterson


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.


Cost Function Production Function Demand Function Capital Good Constant Return 
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Copyright information

© William Peterson 1979

Authors and Affiliations

  • William Peterson
    • 1
  1. 1.Cambridge UniversityUK

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