We augment a Schumpeterian growth model with a public basic-research sector to examine how much a country should invest in basic research. We find that the closer the country is to the world's technological frontier the more the government should invest in basic research. Basic-research expenditures are increasing with a country's degree of openness as long as innovation sizes are small. We provide possible explanations for the empirical evidence available on basic-research expenditures across countries.