Heterogeneity of marginal shipping costs leads to persistent and volatile deviations in real exchange rate. In a two-country, three-good endowment general equilibrium model, arbitrage firms use a transportation technology which depends positively on distance and physical mass of goods. The model exhibits endogenous tradability, non-linearity of law of one price deviations and trade-inducing and suppressing substitution effects due to heterogeneity in trade costs. When endowments follow an AR(1) process that matches quarterly HP-filtered US and EU GDPs, and the aggregate trade costs consume 1.7% of GDP, persistence of real exchange rate matches the data. A model with quadratic adjustment costs also induces sufficient real exchange rate volatility.