This paper compares the social welfare of a simple economy with asymmetric information under two different exchange market structures, Walrasian and the monopolistic, price-setting schemes. It is found that the relative efficiency depends on the nature of uncertainties in the economy. For some environments, the price-setting allocation with a market maker Pareto dominates the rational expectations equilibrium allocation in a competitive market. This finding provides a justification for the existence of the market maker system, which is the predominant institutional arrangement in many exchange markets.