Existence of competitive equilibria with externalities: A differential viewpoint
We consider a class of pure exchange economies with externalities. The consumption set and the preferences of each household depend on his initial endowment and on the actions of the other households. We give a definition of competitive equilibrium with externalities which includes as particular case the classical definition. Under differentiability and boundary conditions, we show that for all economies there exist competitive equilibria with strictly positive consumptions and prices. Our approach is based on homotopy arguments in differential topology, where it is possible describe equilibria in terms of first order conditions and market clearing conditions.
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