The Computation of Economic Equilibria

Herbert E. Scarf
Yale University Press | June 1973 | ISBN: 0300016409

with Terje Hansen)  One of the major triumphs of mathematical economics during the past quarter of a century has been the proof of the existence of a solution for the neoclassical model of economic equilibrium. This demonstration has provided one of the rare instances in which abstract mathematical techniques are indispensable in order to solve a problem of central importance to economic theory.

When cast in a mathematical form the general equilibrium model becomes a complex system of simultaneous equations and inequalities for the determination of all prices and output levels in the economy. Aside from an occasional special case, however, the system is so complex that the existence of a solution can be guaranteed only by an appeal to fixed point theorems rather than by more elementary and constructively oriented techniques. As a consequence, general equilibrium analysis has remained at a level of abstraction and mathematical theorizing far removed from its ultimate purpose as a method for the evaluation of economic policy.

The present monograph attempts to remedy this difficulty by providing a general method for the explicit numerical solution of the neoclassical model. The method should be of interest not only to economists concerned with the techniques of economic planning, but to applied mathematicians in a variety of fields whose work requires the solution of highly- nonlinear systems of equations.