We consider a general equilibrium model of a spatial private ownership economy with a continuum of consumers and with a finite number of producers. The space of locations is represented by a compact set and a finite number of physical goods is available at each location. The consumers haveto choose a unique place where to consume and their initial endowments is conditional to their choice of residence. This consumer behavior, a main difference with the Arrow-Debreu world, induces structural non-convexities (on the consumption sets). The notion of spatial equilibria is precisely defined and we provide an existence theorem of such equilibria.
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