Government Subsidy Strategy for Innovative Drug R&D Based on the Inter-Firm Spillovers

Government subsidies can supplement R&D investment within pharmaceutical firms and strengthen industry knowledge spillovers effectively. Based on the inter-firm spillovers, a differential game model is established to investigate the government subsidy strategies under the different innovative drug R&D strategies of pharmaceutical firms. With the Hamilton-Jacobi-Bellman equitation, the optimal R&D investment, the pharmaceutical technical levels, and the optimal benefits are obtained under the strategies of no pharmaceutical firms conduct R&D innovation, one side innovates alone and R&D cooperation. It can be concluded that the R&D investment of pharmaceutical firms and the effort level of the government is positively related to the technical level and their comprehensive benefits, while it is a negative correlation to the cost coefficient. In addition, an increase in spillover coefficient produces an increase in government subsidy. Furthermore, when the spillovers are low, the government should give a higher subsidy to the strategy of R&D cooperation. As the spillovers increase, the government should allocate more subsidies to pharmaceutical firm who conduct independent R&D of innovative drugs.