Monopoly Pricing with Interrelated Costs and Demands

Abstract

ONE of the great advantages of Mrs. Robinson's analysis of monopoly pricing in her book, The Economics of Imperfect Competition, was that the geometrical methods which she employed enabled those who knew little of mathematics to understand the elements of monopoly pricing. But Mrs. Robinson did not attempt to analyse the pricing problems of a producer who sells more than one product. This is, of course, in practice the usual case and many economists must have encountered the difficulty of trying to apply simple monopoly theory to problems which were more complicated than the assumptions underlying the ordinary monopoly diagram with its curves of marginal cost and marginal revenue. If several products are sold, it will usually be found either that the costs of production of the several products are interrelated or that the demands are interrelated or that both costs and demands are interrelated. The pricing problem in these cases has not been ignored by economists; but it has been left to the mathematical economists.' Edgeworth and Hotelling have both written on this subject but their treatment is one of considerable difficulty, at least to the non-mathematical reader.2 In this article, I propose to give a solution to this problem which involves simple geometrical methods only. The case I shall consider is one in which a producer is selling two products, A and B. And I shall assume that the producer aims at maximising his profits and that he has that knowledge of his demand curves and cost curves which is assumed in simple monopoly theory.3 I would add that my aim is to show the nature of the economic forces at work rather than to analyse in detail all possible cases.