The Invariance of R&D to the Number of Firms in the Industry : Equilibrium and Efficiency under Bertrand Competition

This paper presents certain results, of remarkable simplicity, concerning the market allocation of resources of research and development (R&D) and its comparison to socially efficient allocations. In contrast to many previous studies, we posit that a firm can undertake more than one project (at desired levels of intensity) aimed at the same innovation, if it is profitable to do so. The market is characterized by a Bertrand equilibrium in the product market. We show that the marginal private decisions are independent of the number of firms in the industry; as a result, the equilibrium R&D (that is, the number of projects undertaken in the market, and the level of effort spent on each project) is invariant to the number of firms. The equilibrium level of effort per project is also invariant to the magnitude of (appropriable) rents from successful innovation. The number of firms affects the gains from innovation to consumers and firms; for any research program, a larger number of firms entail larger gains to consumers, smaller gains to firms, and larger aggregate social benefits. While the market equilibrium level of effort per project is shown to coincide with the socially efficient level, the market undertakes fewer projects than is desirable