The Input Side of the Firm: Indirect Functions and Indices

Abstract

In this chapter it is assumed that the firm minimizes its input cost subject to the attainment of a target revenue. The input and output prices are considered as given. The theory of the revenue-constrained firm was developed by Färe and Grosskopf (1994). Sidestepping the aggregation issue, Fisher (1995) used the revenue-constrained firm as a model for a small, fully open economy which trades outputs on world markets at fixed prices. The appropriate representations of the technology are now provided by the indirect input distance function and the indirect cost function. Their properties, as well as some efficiency measures, are discussed in the first section. The second section then proceeds to the definition of indirect input price and quantity indices. We discuss their properties and establish some nonparametric approximations. Section 5.3 turns to the indirect input based productivity indices. Using some additional assumptions it appears possible to derive nonparametric approximations to specific index numbers.