Note--Computation of Particular Economic Equilibria

The computation of economic equilibria, given specific supply and demand functions, is a well-established problem normally treated by fixed point methods or other iterative schemes which converge to a point satisfying the equilibrium criteria. In cases where there are several points which satisfy the equilibrium criteria, these methods will produce a solution distinguished only by the characteristics of the method itself and the starting point used. For some applications, it is desirable to characterize a particular equilibrium point in the presence of multiple equilibria. We consider here economies with demand and supply characteristics which can be described in terms of separable functions (i.e., functions which are sums of functions, each of a single variable) or in terms of functions which can be made separable by introducing new variables and equations. We apply a recently developed branch and bound algorithm to the problem of maximizing any one of several separable objective functions subject to the equilibrium criteria, thus producing a particular equilibrium point. If there is more than one equilibrium point solution for a particular objective function, the branch and bound procedure will produce all such solutions. We present an example with three commodities to show that economic equilibrium models can have different solutions depending on which objective function is used. We briefly discuss other examples with up to 30 commodities.