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In this paper we construct an optimal pricing strategy for a monopoly with a finite level of a resource (a supply constraint) and competition induced by monopolistic selling price (a demand constraint). The model is first formulated as a general differential game problem. Then, after assumptions regarding competitors' strategy are specified, the problem becomes and is solved as an optimal control problem. It appears that the joint effect of both constraints generates an optimal price trajectory that may only have a local minimum; that is, if it is not monotonic, it will initially decrease and eventually increase.
Lieber et al. (Mon,) studied this question.
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