Endogenous currency substitution
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We introduce a simple two-country exchange model with money introduced via a cash-in-advance constraint with a variable money velocity. Currency substitution is endogenous to this model. While all purchases must be made in local currency, foreign exchange can be traded for local currency within a transactions period while other nonmonetary assets, bonds and equalities, cannot. We find that consumers only hold foreign exchange when the local inflation rate is high enough to induce a sufficient desire to reduce the holding of real domestic money balances below the level required to facilitate purchases during the exogenously determined pay period. Foreign exchange holding allows the consumer to reduce the initial level of real balances below the level required to facilitate purchases until the next pay period. In general equilibrium allowing consumers to hold foreign exchange reduces the amount of resources dedicated to transacting, the shoe leather cost. As a result, currency substitution reduces the velocity of money, increasing the level of real domestic money balances. Therefore currency substitution increases seigniorage revenue in the home country as well as in the country providing foreign exchange. Given these results, foreign exchange holding is complementary to, rather than a substitute of, domestic real balances. Currency substitution can enhance efficiency. We find that currency substitution can increase utility by reducing shoe-leather expense. The country supplying foreign exchange can appropriate this gain by increasing its own inflation rate.