We examine the use of subsidies to 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\ud duopoly. The optimal R&D subsidy leads to an increase in total R&D and production, however, it does not lead to the equalisation of per firm output and therefore to an efficient distribution of production\ud 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
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