Optimum supply control of a monopolist in a dynamic market

In this paper, we develop a model for a monopolist in a dynamic market who tries to maximize his overall profits over a certain planning horizon. Conditions for his optimal supply curve for both finite and infinite horizon problems are obtained and some interesting properties of the optimal paths are discussed. A special (linear-quadratic) case is then treated and explicit characterizations of the optimal supply curve and the market price-supply behaviors are obtained.