Market Equilibrium for CES Exchange Economies: Existence, Multiplicity, and Computation

We consider exchange economies where the traders’ preferences are expressed in terms of the extensively used constant elasticity of substitution (CES) utility functions. We show that for any such economy it is possible to say in polynomial time whether an equilibrium exists. We then describe a convex formulation of the equilibrium conditions, which leads to polynomial time algorithms for a wide range of the parameter defining the CES utility functions. This range includes instances that do not satisfy weak gross substitutability. As a byproduct of our work, we prove the uniqueness of equilibrium in an interesting setting where such a result was not known. The range for which we do not obtain polynomial-time algorithms coincides with the range for which the economies admit multiple disconnected equilibria.