Market Equilibrium in Exchange Economies with Some Families of Concave Utility Functions

We consider the problem of computing equilibrium prices for exchange economies. We tackle this problem under the assumption that the traders have either CES (constant elasticity of substitution) utility functions or a subfamily of ASC (additively separable concave) utilities. For the subfamily of ASC functions, and for a range of CES functions which include some CES functions that do not satisfy weak gross substitutability, we translate the equilibrium conditions into a convex feasibility problem. This enables us to obtain new, polynomial time algorithms for computing the equilibrium. As a byproduct of our work, we prove the uniqueness of equilibrium in an interesting setting where such a result was not known.