This study explores the long-run effects of inflation in a two-country Schumpeterian growth model with cash-in-advance constraints on consumption and R&D investment. We find that increasing domestic inflation reduces domestic R&D investment and the growth rate of domestic technology. Given that economic growth in a country depends on both domestic and foreign technologies, increasing foreign inflation also affects the domestic economy. When each government conducts its monetary policy unilaterally to maximize the welfare of domestic households, the Nash-equilibrium inflation rates are generally higher than the optimal inflation rates chosen by cooperative governments who maximize the welfare of both domestic and foreign households. Under the CIA constraint on R&D (consumption), a larger market power of firms amplifies (mitigates) this inflationary bias. We use cross-country panel data to estimate the effects of inflation on R&D and also calibrate the two-country model to data in the Euro Area and the US to quantify the welfare effects of decreasing the inflation rates from the Nash equilibrium to the optimal level.