Production and Cost Functions

Specification, Measurement and Applications

Erkin Bairam, Erkin Bairam

• Publisher: Routledge
• Year: 2018
• ISBN:
  9781351768900
• Edition: 1
• Topic: Betriebswirtschaft
• Subtopic: Business allgemein

This title was first published in 2001. The objective of this book is to discuss specification and applications of new production, cost and profit functions. It is aimed at specialists in production, economic growth, costs, profits and applied econometrics in particular.

1 The Popular and Some New Non-Homogeneous Production Functions

Erkin I. Bairam

I. Introduction

In the production literature, it is well known that functions used in applied research are, without a priori tests, assumed to be not only homogeneous but linear homogeneous. Unfortunately, it is not generally known that the homogeneity (and hence, the constant scale elasticity) assumption is not appropriate for some aspects of the production theory.

Ringstad (1974) and Bairam (1991b) have shown that much of the theoretical work is based on production functions with a scale elasticity which decreases with increase in output. This contrasts with many popular production functions used in applied studies which assume the same returns to scale at all levels of output.

The following quotation eloquently summarises the main limitations of the homogeneity assumptions:

Production functions most commonly used in empirical research are homogeneous i.e., they have constant scale elasticity [see section II], like the Cobb-Douglas and CES production functions. On the other hand much of the theoretical work is based on production functions with a scale elasticity which is decreasing when at least one factor is increasing and none is decreasing. The difference between scale elasticities can be illustrated many ways. In Figure 1 we illustrate how the average cost curve may look when we have: i) a homogeneous production function with scale elasticity above one, ii) the same type of production function with a scale elasticity below one, and iii) an inhomogeneous production function with a scale elasticity decreasing from values above one to values below one. (Ringstad (1974, p.88)).

Consequently, as early as 1973, Christensen et al. argued that it is important to develop tests of the theory of production that do not employ homogeneity as part of the maintained hypothesis. More recently Fuss et al. (1978) went even further and emphasised that flexible functional forms, embodying few maintained hypotheses, should be used to test fundamental hypotheses of the production theory. Given this background, it is important to examine such new and not-so-new production functions in some detail and this will be the main objective of this paper.

Consequently, in this chapter new non-homogeneous functions by the present author, as well as, the popular non-homogeneous production functions developed in the late 1960’s and early 1970’s are examined and discussed. In section II important properties of the neo-classical production function, which are relevant for the discussion here, are briefly discussed. In section III, the new non-homogen...