Market structure and Schumpeterian growth

We present a discrete-time version of a Schumpeterian growth model. A natural R&D analogue to constant returns to scale implies a Poisson production function with diminishing marginal product. 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 is higher if ties 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 leads to higher welfare.