General competetive equilibrium of the spatial economy

The spatial economy is analyzed in the general equilibrium framework by considering the production and the utility functions depending on spatial distribution and sets. The geometric constraint between the location and the extension of goods supplies the equilibrium condition for space. The existence of an equilibrium is demonstrated by extending the Gale-Nikaido theorem to the case under examination. Consequently, the competetive equilibrium exists, under the assumptions of the theorem, although each point of space is heterogeneous with any other point (because of the different location): the existence is allowed by the perfect partibility of space.