On the comparative statics of the dominant-firm model

This paper examines the effect of a change in demand upon a dominant firm's share of the market. The direction of change in market share is not readily determined in the general form of the model. It depends upon the values of a number of parameters. In the linear and log-linear forms of the model, however, the number of crucial parameters reduces to two. The market share of the dominant firm varies directly (inversely) with demand when the y-intercept of its marginal cost curve is greater (less) than the y-intercept of the supply curve of the fringe in the linear model and, in the log-linear model, when the elasticity of marginal cost with respect to output is less (greater) for the dominant firm than it is for the fringe.