On the uniqueness of local equilibria.

In a pure exchange economy, we definie a new concept of local equilibria where the consumers are restricted by sale constraints. So the equilibrium consumptions are close to the initial endowments. We prove that the local equilibrium is always unique when utility functions are smooth and the constraints are sufficiently tight. We also prove that the local equilibria converge to the equilibrium of the linear tangent economy when the sale constraints converge to zero.General economic equilibrium, local equilibria, uniqueness.