Optimal Subsidy Level and Innovation Investment in the Presence of Innovation Spillover: A Perspective of Social Welfare

Abstract

We consider the effect of subsidy level and innovation spillover on the production quantity and social welfare in a mixed duopoly market with one private enterprise (PE) and one state-own enterprise (SOE). The government may subsidize the SOE or PE. We derive the equilibrium production quantity, innovation investment level and sub- sidy level. Our results show that, given the exogenously subsidy level, social welfare is concave in subsidy level and whether the SOE’s utility is monotonic in subsidy level depends on the subsidy policy and the innovation investment. When the government endogenously determines the subsidy level, the subsidy policy is equivalent no matter which enterprise is subsidized if innovation investment is not implemented. When in- novation investment is implemented, government prefers to subsidize the SOE. Both government subsidy and innovation investment can improve social welfare and these two strategies are complementary.