International monetary trade and the law of one price

We endogenize circulation of currencies and price formation in a decentralized trading environment with two countries and two currencies. In equilibrium sellers of homogeneous goods may post prices in the national or also in the foreign currency, given unobservable buyers' valuations. We prove that, under different monetary regimes, the absence of well integrated international goods markets doesn't necessarily imply a violation of the law of one price. We also illustrate the behavior of prices across regimes characterized by different degrees of monetary integration.