The Dual of Duopoly Is Complementary Monopoly: or, Two of Cournot's Theories Are One

Abstract

The observation that two theories share the same formal structure, that is, differ only in the interpretation placed on symbols, can almost always be used to simplify a body of knowledge. The purpose of this communication is to demonstrate that Cournot's theories of duopoly and complementary monopoly are formally identical; furthermore, a precise statement of the correspondence which identifies them serves to extend a famous criticism of the duopoly theory. Cournot's duopoly theory (Cournot, 1963, chap. vii) applies to a market situation in which two producers sell identical products, and his complementary monopoly theory (Cournot, 1963, chap. ix) to a market situation in which two producers sell products which are of no use unless combined in a fixed ratio (say 1:1) to form a composite commodity. Edgeworth observed that, in the former case, "there cannot well be supposed two prices; and [in the latter case] . .. there cannot be supposed two (independent variations of the) quantities" (Edgeworth, 1925, p. 122). For two producers (A and B) this suggests a formal definition of duopoly as a situation in which the sum of the producers' outputs (denoted by