Economic equilibria are usually solutions to fixed point problems rather than solutions to convex optimization problems. This leads to two difficulties that are closely related: First, equilibria may be difficult to compute. Second, a model economy may have more than one equilibrium. This paper explores these issues for a number of stylized economies, including static economies that involve both pure exchange and production, economies that have infinite numbers of goods because of time and uncertainty, and economies with distortionary taxes and externalities. There are numerous numerical examples that illustrate the theory and could serve as test problems for algorithms.