Stackelberg versus Cournot duopoly with asymmetric costs: primary markups, entry deterrence, and a comparison of social welfare and industry profits

In a linear Stackelberg (S) and Cournot (C) duopoly model with homogeneous product, it is well known that S yields higher consumer surplus than C. The comparison of social welfare (or industry profit), however, can go both ways if costs are asymmetric. We show that a remarkably simple characterization can be obtained in terms of the ratio of the leader’s and the follower’s primary markup: social welfare (industry profit) is greater in C than in S if and only if this ratio is between 1/2 and 31/38 (between 1/2 and 19/14). Furthermore, this ratio also determines the qualitative type of equilibrium: Monopoly is reinstalled from both S and C if and only if the ratio lies outside the interval (1/2, 2); for values between 3/2 and 2, the Stackelberg leader deters entry of an inefficient follower while producing more than a monopolist would.