Spillovers, subsidies, and second-best socially optimal R&D

This paper provides a thorough second-best welfare analysis of the standard two-stage model of R&D/product market competition with R&D spillovers. The planner's solution is compared to the standard non-cooperative scenario, the R&D cartel, and the cartelized research joint venture (or joint lab). We introduce the notion of a social joint lab, as a way for the planner to avoid wasteful R&D duplication. With no spillovers, the non-cooperative scenario, the joint lab, and the second-best planner's solutions coincide. However, with spillovers, all three scenarios yield R&D investments that fall short of the socially optimal level. To shed light on the role of the spillover level on these comparisons, we observe that the gaps between the market outcomes and the planners solutions widen as the spillover parameter increases. Finally, we establish that a social planner and a social joint lab solutions may be achieved starting from any of the three scenarios by offering firms respective suitably weighted quadratic R&D subsidization schedules.