This paper develops an equilibrium, optimizing model of currency substitution and applies it to seigniorage taxation in the presence of currency substitution. The theoretical framework is an overlapping-generations model with the finance constraint that goods must be purchased in the seller’s currency. When consumers are young they are uncertain about what their preferences will be when they are old. Thus, they must decide how much of each currency to hold without knowing their future demand for goods. Consumers may trade currencies at a cost in the spot market immediately before purchasing goods. This cost is a measure of the substitutability of currencies. When the transaction cost is infinite, the model becomes a cash-in-advance constraint model; when the transaction cost is zero, the currencies are perfect substitutes and the analysis replicates the indeterminate-exchange-rate model of Kareken and Wallace (1981).
The model is found to yield money demand functions with reasonable properties. Demand for both currencies is positive when the cost of transacting in the spot market exceeds the rate of depreciation of the weaker currency. An increase in the future price of country two’s good relative to country one’s good lowers the share of portfolios allocated to the currency of country one if and only if first- and second-period consumption are gross substitutes. If utility is log-linear, the share of portfolios allocated to the weaker (stronger) currency depends positively (negatively) upon the transaction cost. The share of portfolios allocated to either currency depends positively upon its rate of appreciation. A stationary equilibrium is shown to exist if the cost of spot market transactions is not too small and monetary policies are not too different.
Governments are assumed to finance their expenditures by levying a costly income tax or by collecting seigniorage. In deciding the optimal level of inflation, they weigh the trade-offs between the costs of administering and complying with income taxes and the distortions created by rising prices. If identical governments cooperate, then the optimal rate of money growth is strictly positive. It is decreasing in the substitutability of currencies if and only if first- and second-period consumption are gross substitutes. If governments act independently, money growth may be either too high or too low depending on the degree of currency substitution.