With some models of money and a representative-agent there is no reason for monetary trade because identical individuals can consume their own production. Lucas proposed a parable involving differentiated products in a cash-in-advance model to avoid this problem. This paper studies Lucas?s suggestion by developing a differentiated product model with money, a cash-in-advance constraint for market purchases, and endogenous specialization. Individuals who are identical ex ante choose to differ ex post in equilibrium. Monetary exchange involves differentiated goods at a point in time, so a nonzero balance of trade is not a prerequisite for a monetary equilibrium. In contrast to results in some other models, we find that consumption of goods that are not purchased with money (analogous to leisure services or credit goods) can either rise or fall with a rise in the money growth rate. Finally, we allow for costly barter and examine individuals' choices of the method of payment. We discuss the implied nominal-interest elasticities of the (real) demand for money in the general equilibrium.