Economic Models with Infinitely Many Commodities

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This project develops new economic models of markets with an infinite number of commodities. These models are used to study monopolistic competition with large numbers of firms, the dynamics of financial markets under uncertainty, the foundations of mathematical models of markets and other difficult problems in mathematical economic theory. More specifically, in the first part of the project a model is developed in which firms are sufficiently small so that each firm's effect on other firms is negligible, yet in equilibrium, active firms charge more than the perfectly competitive price and may make positive monopoly profits. This model would be more realistic than existing economic models in which the monopoly power of firms disappears as they become small in comparison to the market. The second part consists of the development of continuous time stochastic models of incomplete markets. Stochastic models with incomplete markets are useful because in the real world it is impossible to completely insure against uncertainty because many futures and contingent claims markets are in fact missing. The continuous time framework allows the investigator to relate his work to financial models and to address such questions as: does frequent trading lead to efficiency?