Strong Currency and Weak Currency

This paper presents a two-country model in which two currencies compete with each other. There exists an equilibrium in which the two currencies with different rates of inflation circulate as media of exchange despite that neither currency is forced to be used for transactions. Taxes payable in local currency and asymmetric injection of fiat money by government through purchases of a certain good generate demands even for the currency with a higher inflation rate. In such an equilibrium, the government that issues the currency with a lower rate of inflation collects seigniorage not only from its own residents but from the residents of the other country provided that the rate of inflation is positive. The strong currency in the sense of a low inflation rate becomes an international medium of exchange. Policy games, in which two governments simultaneously choose and commit to tax rates and inflation rates, are also examined. We show, among other things, that the equilibrium rate of inflation is zero in this policy game. In other words, unlike a common argument, the rate of inflation does not go below zero. This result is due to the fact that a negative rate of inflation induces a negative amount of seigniorage and vice versa. Some alternative currency regimes are examined. Even for a country with a weak currency, abandonment of its currency leads to a lower level of welfare. Monetary unions are briefly discussed as well.