We analyze the role of international market size differences in determining the investment in process R&D (and thus firms’ competitiveness) in a trade model with oligopolistic market structure, non-homothetic production technology and costly trade. We show that the R&D effort is higher (or even disproportionately so) for firms in the larger market, which causes endogenous asymmetries across countries. As a result, firms in the larger market have higher competitiveness, which increases their market shares in international markets. Furthermore, and contrary to what is predicted by Krugman (Am Econ Rev 70:950–959, 1980) “home market effect”, in equilibrium the larger country does not need to host a disproportionately higher share of the world’s industry than of the world’s demand. Despite this, the larger country can still continue to run a trade surplus in the oligopolistic sector, since it hosts firms with higher competitiveness than firms in the smaller country.