We develop a general equilibrium model of international trade with heterogeneous firms, where countries can invest into basic research to improve their technological potential. These research investments tighten firm selection and raise the average productivity of firms in the market, thereby implying lower consumer prices and higher welfare. In an open economy, there is also a strategic investment motive since a higher technological potential gives domestic firms a competitive advantage in trade. Countries tend to over-invest due to this strategic motive. There are thus welfare gains from coordinating research investments. The over-investment problem turns to an under-investment problem if there are sufficiently strong cross-country spillovers of basic research investments.