Currency Substitution and The Law of One Price

We study endogenous currency substitution in a decentralized trade environment. Sellers maximize profits from sales of imperfectly substitutable goods by posting prices in either one of two currencies. A unique symmetric equilibrium exists where goods are priced only in the local currency. This occurs if foreign trade is sporadic, there is sufficient but not excessive liquidity, and discounting is low. Excess or scarcity of liquidity, however, induces sellers to extract all surplus from buyers. This destroys the monetary equilibrium and shuts down trade. Equilibria with and without currency substitution coexist on some region of the parameter space, and may be multiple. We prove that purchasing power parity may hold even if foreign trade is costly and the currency's value differs across countries. International circulation of money may expand the extent of the market hence enhance welfare.