Market Structure and Schumpeterian Growth

We present a discrete-time version of an otherwise standard Schumpeterian growth model. Discrete time exhibits two important differences from continuous time. First, the probability of successful innovation cannot be homogeneous of degree one in inputs. A natural R&D analogue to constant returns to scale implies a Poisson production function with diminishing marginal product of inputs. Second, R&D firms sometimes innovate simultaneously. The resulting market conduct is critical. We consider both Bertrand competition and collusion among successful innovators. Surprisingly, the industry demand for R&D inputs does not depend on the number of firms in the R&D sector if Bertrand competition ensues following ties. In contrast, demand for R&D inputs is higher if ties are expected to result in collusion. In general equilibrium, Bertrand competition leads to random switching between monopoly and competitive production. Under collusion, production is always at the monopoly level, but there is faster growth. Numerical simulations suggest that this also leads to higher welfare.