Return on Commodity Money, Small Change Problems, and Fiat Money

We construct a search-theoretic model of commodity money where a penny is an indivisible silver coin that can be either melted into a silver bar yielding a positive return or used as a medium of exchange. In equilibria where the rate of return on silver is sufficiently high, small change problems arise in the form of too-much-trade inefficiency because of a too-high value of a penny and no-trade inefficiency because of a shortage of coins in circulation. In the fiat money system, however, trades are not affected at all by the rate of return on silver and the value of a penny is determined by its medium-of-exchange role without incurring the loss in efficiency due to small change problems.