Technological opportunity, long-run growth, and convergence

We derive a R&D-based growth model where the rate of technological progress depends, inter alia, on the amount of technological opportunity. Incremental innovations provide direct increases to the knowledge stock but they reduce technological opportunity and thus the potential for further improvements. Technological opportunity is renewed by radical innovations, which have no direct impact on factor productivity. We study both the market equilibrium and the social planner allocation in this economy. Investigating the model for its implications on economic growth we find: (i) in the long run, a balanced growth path requires that the returns to radical innovations are at least as large as those of the incremental ones; (ii) the transition need not be monotonic. We show under which conditions our model generates endogenous cycles via complex dynamics without resorting to uncertainty; (iii) the calibrated model exhibits substantial quantitative differences between the market outcome and the social planner allocation.