Timing of R&D Decisions and Output Subsidies in a Mixed Duopoly with Spillovers

This study considers a mixed duopoly with research spillovers and examines the interplay between firms’ R&D decisions and government’s output subsidies. We investigate and compare the timing of the game between ex-ante R&D and ex-post R&D decisions where the R&D decisions are chosen before the output subsidy is determined in the former case while the order is reversed in the latter case. We show that the equilibrium outcomes can be opposite between the two cases because both public and private firms have different objectives in choosing R&D investments, but the spillovers rate is a key factor that determines their incentives. In particular, we show that the output subsidy is smaller (larger) and the welfare is larger (smaller) under the ex-ante R&D decisions for a higher (lower) degree of spillovers rate. Finally, privatization increases the welfare in both cases only when spillovers rate is weak.