General Equilibrium Theory with Imperfect Competition

This survey is organized as follows. l. lntroduction. Il. The main issues. IIl. Negishi's model. IV. Objective demand in the Cournot-Nash framework. V. Objective demand in the Bertrand-Nash framework. VI. The assumption of quasi-concavity of the profit functions. VII. Compromises between the conjectural and the objective approach. VIIL Insights into the notion of perfect competition. IX. Conclusion. The flrst rigorous analysis of the behaviour of irms which do not treat prices as exogenous parameters is due to Cournot (1838), whose book preceded Walras's (1874) by thirty-six years. Cournot studied the case of a homogeneous-product industry where each irm knows the inverse demand function which associates with every value of industry output the common price at which every firm is able to sell. Each trm independently chooses its own output level. The notion of equilibrium put forward by Cournot is a special case of the more general notion of Nash equilibrium introduced later (Nash, 1950, 1951). lt consists of a list of output levels, one for each flrm, with the property that no irm can increase its profits by unilaterqlb) changing its output. We shall refer to this notion of equilibrium as Cournot-Nqsh. On the other hand, when the decision variable of a firm is the price it charges-rather than its own output level-the corresponding notion of equilibrium will be referred to as Bertrand-Nash.2 The 1930s saw, with the publication of the books by Chamberlin (1933) and Robinson (1933), an upsurge of interest in the theory of imperfect comperirion. The approach, however, remained one of partial equilibrium and some authors (e.g. Triffin, 1940) expressed the hope that a general theory of monopolistic competition could be developed that would match the scope of the Walrasian theory of general equilibrium with perfect competition. While the latter was fully developed and systematized in the 1950s (Arrow and Debreu, 1954, Debreu, 1959), the lirst attempt to introduce imperfect competition in a general equilibrium model was made as late as 1961 by Negishi. Since then a large number of contributions have appeared, but unfortunately we are still far from a satisfactory theory of general equilibrium with imperfect competition.