Structural implications of a class of flexible functional forms for profit functions

Abstract

In 1973, Diewert proposed the use of various Flexible Functional Forms (FFF) for profit functions. Since then, the use of FFF specifications for profit functions in empirical production analysis has become increasingly popular (Woodland [1977]; Kohli [1978]; Cowing [1978]; Sidhu and Baanante [1981], etc.). A number of alternative FFF specifications are available which may seem equally plausible. In fact, the choice among FFF for empirical applications is typically a purely arbitrary decision. The central problem considered in this paper is whether some FFF impose more or less a priori restrictions on the structure of production. The purpose of this note is to show that indeed an important class of FFF, when used to represent profit functions, impose quite undesirable restrictions on the production technology. These restrictions include quasi- homotheticity and certain additional separability structures of the underlying production technology. A paper by Blackorby, Primont and Russell [1977] shed some doubt on the flexibility of FFF when certain separability conditions are imposed. It proved that the flexibility of these forms rest indeed on very feeble grounds, being extremely sensitive to weak separability restrictions. These forms do not provide second order local approximations to an arbitrary weakly separable function. What we demonstrate here is that an important family of FFF does impose serious structural rigidities on the underlying production structure even if weak separability is not imposed. We first present a simple taxonomy of flexible functional forms which allows us to classify them into two major families according to certain key differences. Next, we show that one of these families imposes quasi-homotheticity and certain separability conditions on the underlying production technology. In section 3, we provide some general comments concerning the implications of these results as a potential basis for discriminating among FFF in empirical analysis. We end this note with a summary of the major conclusions.