Dynamic Monopoly with Demand Delay

Abstract

This study analyses the dynamics of nonlinear monopoly. To this end, the conventional assumptions in the text-book monopoly are modified; first, the complete information on the market is replaced with the partial information; second, the instantaneous information is substituted by the delay information. As a result, since such a monopoly is unable to jump, with one shot, to the optimal point for which the profit is maximized, the monopoly has to search for it. In a continuoustime framework, the delay destabilizes the otherwise stable monopoly model and generates cyclic oscillations via a Hopf bifurcation. In a discrete-time framework, the steady state bifurcates to a bounded oscillation via a Neimark-Sacker bifurcation. Although this has been only an introduction of delay into the traditional monopoly model, it is clear that the delay can be a source of essentially different behavior from those of the nondelay model.