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Topological aspects of the study of the model of a monopolist

The application of topological methods [1] in the mathematical study of the economic model of a fc-product monopoly enables us to reduce the problem to the study of geodesic flows on Riemannian manifolds. The classical model [2] describes the strategy of a monopolist in attempting to maximize his profit for given demand and cost functions. Trofimov [3] has shown that if the demand function incorporates the dependence on the rate of change of prices, then an optimal strategy can be realized as motion along geodesies of a Lobachevskii plane. The author has generalized this result to the case of an arbitrary Riemannian manifold.