On Rivalry, Variety and Spillovers in Endogenous Growth

Evidence shows that firms build their market position by consistently investing in R&D over time and accumulating knowledge protected by secrecy, patents and other appropriability devices. To explore the macroeconomic implications of this fact, I construct an economy where oligopolistic firms establish in- house R&D programs to produce a continuous flow of cost-reducing (incremental) innovations. Firms compete for sales and resources. In symmetric equilibrium, the number of firms determines concentration and firm size. These determine the scale and the efficiency of R&D operations and the (average) rate of innovation. If the number of firms is exogenous, one can study the relationship between the number of firms and the rate of growth of the economy. This exercise gives a first intuition about the forces at work. Static economies of scale due to product and knowledge variety yield increasing returns to the number of firms. A large number of firms leads to high output, high (aggregate) R&D, and fast growth. Offsetting this force, market fragmentation leads to small firms, small R&D programs, and slow growth. The number of firms, in addition, must be endogenous and determined jointly with the rate of growth by the zero-profit condition. Price, investment, entry, and exit decisions are now interdependent. In particular, R&D is a fixed (sunk) cost and is negatively related to the number of firms. This feed-back reinforces the market fragmentation effect and yields additional interactions. Many parameters no longer have the effects predicted by standard models. For example, the scale effect of population size is negative. The intuition is simple. Large markets have many firms, high output, and high aggregate R&D. Market fragmentation offsets this force and results in small firms and slow growth. These interactions generate a market allocation of resources that is not Pareto optimal. I discuss the nature of this distortion.