Investments in R&D and Production Capacity with Uncertain Breakthrough Time: Private versus Social Incentives

The article considers a sequential investment project which starts with a product innovation phase, and subsequently, once R&D is completed, a production phase. The investment decision of the R&D phase involves choosing the time and the size of the R&D investment. The time to breakthrough is stochastic in which the instantaneous probability of innovation is increasing in the R&D investment size. Once R&D is completed the firm starts producing the new product. To do so, the firm first needs to invest in production capacity, the size of which must be determined. We compare the optimal investment decisions of the firm with those of the social planner and conclude that the firm invests too late in R&D and not enough in production capacity. We find that a proper subsidy policy, consisting of an R&D investment and a productive investment subsidy can make up for that. However, taking into account a budget constraint such that subsidy expenses cannot exceed the resulting increase in total surplus, learns that a first-best solution can only be reached if the demand situation is relatively stable, i.e., when growth and demand uncertainty are limited, or when the price elasticity of demand is low.