We examine the use of subsidies to research and development (R&D) in a mixed and a private duopoly
market. We show that the socially optimal R&D subsidy is increasing in the degree of spillovers, but it is
lower in the private duopoly. The optimal R&D subsidy leads to an increase in total R&D and production;
however, it does not lead to the equalization of per firm output and therefore to an efficient distribution
of production costs. We also find that privatization of the public firm reduces R&D activity and welfare in
the duopoly market. This result stands even when optimal R&D subsidies are provided.