Optimal Provision of Costly Currency

Items of currency wear out and must be replaced. In The Mechanism of Exchange, Jevons recommended that the government bear the cost of replacing worn gold coins with new coins instead of having the holders of worn coins bear the cost. We study the optima of a minimally interesting model: money is essential and indivisible so that physical depreciation is not neutral; and there are alternative ways of financing the costly replacement of worn currency. The optima contradict the Jevons proposal. People with worn currency bear a cost that makes them indifferent between getting a new unit and discarding the useless worn unit, a cost that exceeds the physical cost of replacement.