Introduction

Speculation about the selling behavior (revenue side) of multi-product firms may be traced to Pigou and Mrs Robinson and, more recently, to Reder, Coase, Gordon, Clemens, Weldon, Simkin, Edwards, and Bailey. Taking some liberties, one may say that these writers viewed the pricing process in a multi-product firm as an extended application of the Pigou– Robinson theory of price discrimination (Pigou's ‘discrimination of the third degree’).

Subsequent to this original start, the multi-product firm was given a more thorough and conventional treatment by Hicks, whose approach was later extended by Allen, Samuelson, Dorfman, and Kuenne. Basically, Hicks and his followers used conventional marginal methods to analyze the profit-maximizing behavior of a firm that produces a variety of products by means of a variety of variable inputs. Fixed inputs were occasionally introduced; but their important role was not analyzed.

To be sure, it was recognized that the existence of fixed inputs is more significant in the theory of the multi-product firm than in the theory of the single-product firm, even when the latter practices price discrimination. However, it was Pfouts who first realized the crucial difference and constructed a model of the multi-product firm that permitted switching of fixed inputs among various outputs. Pfouts' model, and subsequent ones based upon it, cannot be solved by the usual methods of the calculus. The introduction of a variety of fixed inputs leads to a set of linear inequalities as constraints in the maximization process. As a result, the model must be analyzed by means of the Kuhn–Tucker theorems.