The purpose of this paper is to briefly review the applications of fixed point and path following methods to problems in economics, and to present one such application in some detail. The problem for which economists have adopted these methods is the computation of a set of goods prices which represent an economy’s equilibrium. By equilibrium prices, we mean that total market demands match total market supplies for every good, when both consumers and producers maximize their objective functions subject to these prices. Methods of the type described in the other papers in this conference volume are proving to be extremely useful for solving this difficult economic problem. Perhaps economists have accepted these techniques more rapidly than others because of the pathbreaking work in the computation of fixed points by an economist, Herbert Scarf. Scarf’s original articles [1967a, 1967b] and landmark book [1973] deal with the computation of economic equilibria.