Currency Substitution under Transaction Costs

We consider a setting where agents can choose between two currencies to conduct their goods purchases. The usage of either currency comes with currency-specific transactions costs. For example, purchasing some goods with cryptocurrencies rather than dollars is easier and may avoid taxes. We explore an extension of Schilling-Uhlig (2019), allowing for asymmetry in transaction costs as well as dollar-bitcoin exchange fees. Agents alternate in their role as buyers and sellers, necessitating currency. A central bank steers the dollar inflation path, while bitcoins are in fixed supply. We characterize the nonstochastic equilibrium and the resulting exchange rate dynamics.