In this work, we study the complexity of finding a Walrasian equilibrium. Our main result gives an algorithm which can compute an approximate Walrasian equilibrium in an exchange economy with general, but wellbehaved, utility functions in time that is polynomial in the number of goods when the number of agents is held constant. This result has applications to macroeconomics and finance, where applications of Walrasian equilibrium theory tend to deal with many goods but a fixed number of agents.