In an economy where there is no double coincidence of wants and without public record-keeping of past transactions, money is usually seen as the only mechanism that can support exchange. In this paper we show that, as long as the population is finite and agents are sufficiently patient, a social norm establishing gift-exchange can substitute for money. However, for a given discount factor, population growth eventually leads to the breakdown of the social norm. Additionally, increases in the degree of specialization in the economy can also undermine the social norm. By contrast, monetary equilibrium exists independent of the population size. We conclude that money is essential as a medium of exchange when the population is large.