We study the nature of appropriate domestic R\&D policy in an imperfectly competitive world, where both the R\&D rivalry among firms and the presence of technological spillovers from a superior foreign technology play a crucial role.There are two firms (a foreign and a domestic firm) that are located in the domestic country, produce a commodity that is sold overseas and compete both in an output and an R\&D stage. We use the basic Spencer and Brander (1983) model with three modifications. First, we introduce R\&D dynamics by considering both an initial R\&D investment and a subsequent improvement. Firms invest in R\&D in period one and can make further improvements in period two. Second, we introduce an asymmetry between the two firms: the foreign firm is more advanced -so it has to invest fewer resources to achieve a given technological level. Third, we consider technological spillovers between firms. We find that the appropriate R&D policy balances the strategic incentive to induce a reduction in foreign initial R&D with the spillover incentive to induce the foreign firm to invest more. If initial foreign R &D increases the present value of domestic profits (i.e., the spillover effect dominates), either a tax to first period domestic R&D or a subsidy to domestic imitation is appropriate. If instead improvements in first period foreign technology have a negative effect on the present value of domestic profits (i.e., the strategic effect dominates) a subsidy to first period domestic R\&D is appropriate.In this case, the nature of the optimal policy on imitation will depend on the relative importance of first and second period effects.
