Limit pricing in a Cournot-Stackelberg market

Abstract

Consider a monopolist that in any discrete-time decision period is faced with the market demand curve P = l+a bQ and the average cost curve C = 0 are constants. A ř-denotes-time subscript is suppressed. When & = ( ) 1, the producer has constant (increasing, decreasing) average costs. The profit-maximizing monopolist's period t output and profit rates of qi = l/2 and 7Zi = l/4, respectively, are independent of b. Following Cournot (1897), suppose that a second profit-maximizing producer employing the same technology enters the market producing at a rate of q 2, and that each duopolist naively assumes that the other's output rate will be unaltered from one decision period to the next. In equilibrium, each duopolist's output rate will be 1/(2 + b) yielding a profit of 1/(2 + b) 2. 1 Alternatively, in somewhat more sophisticated fashion, uncertainty can be incor-