Optimal R&D Subsidies with Heterogeneous Firms in a Dynamic Setting

When firms engaged in R&D are observably heterogenous (in size) and policymakers are able to condition policy on the observed heterogeneity, what is the optimal policy? This paper starts with a static two-stage duopoly model of R&D competition with uncertainty and finds it welfare enhancing to subsidize the larger firms, with no subsidies for (or taxes on) the smaller firm (extending existing results, Lahiri and Ono, 1999). This result follows because marginal cost reductions by the largest firm have larger net effects on consumer and producer surplus. The policymaker's goal is effectively to minimize the average cost of production. However, when we move to a dynamic setting, the optimal policy is less clear. When firms compete repeatedly, the degree of competition becomes an endogenous variable over the in finite horizon. The optimal policy depends on the nature of long-run competition. In some situations, the optimal policy remains the same, subsidize the larger rm. However, in other scenarios, the policymaker optimally chooses to subsidize the smaller firm more heavily to promote more intense competition which lowers the long-run deadweight loss and long run costs through increased R&D competition.