STABILITY ANALYSIS OF COURNOT'S DUOPOLY MARKET WITH RESPECT TO INVESTMENT DECISION

Abstract

In this paper we will consider the problem of maximizing the duopolist's net cash flow over infinite horizon, on the assumption that each rival will assume the other's output as given. This is known as the dynamic duopoly model of Cournot. In this context, we will present the optimal capital policy reduced from it for the duopolist. Then, we will examine existence and uniqueness of the optimal capital path and derive an adjustment function with respect to the output from the optimal path. As each rival successively adjusts his own output according to the other's output under the adjustment function, it may be regarded as a reaction function. Therefore, in our model, we will investigate how the duopoly equilibrium will be established.
In Section 2, the optimization problem of dynamic duopoly is introduced. The necessary and sufficient conditions for the optimization are derived by“Pontryagin-Arrow Method”in Section 3. In Section 4, the existence and uniqueness of the optimal capital path is analysed and the adjustment function with respect to the output is derived from the path. In Section 5, the stability of duopoly market is examined. Findings of this paper are summarized in the last section.