Optimum Monopolist Control in a Dynamic Market

A model is developed for a monopolist, in a dynamic market, who seeks to maximize his overall profits over a certain planning horizon. Conditions for the optimal supply-price curves for both finite and infinite horizon problems are obtained and some interesting properties of the optimal paths are explored. A special (linear-demand, quadratic-cost) case of this model is then treated and explicit characterization of the market price-supply behaviors is obtained.