Catch-up and fall-back through innovation and imitation

Will fast growing emerging economies sustain rapid growth rates until they "catch-up" to the technology frontier? Are there incentives for some developed countries to free-ride off of innovators and optimally "fall-back" relative to the frontier? This paper models agents growing as a result of investments in innovation and imitation. Imitation facilitates technology diffusion, with the productivity of imitation modeled by a catch-up function that increases with distance to the frontier. The resulting equilibrium is an endogenous segmentation between innovators and imitators, where imitating agents optimally choose to "catch-up" or "fall-back" to a productivity ratio below the frontier.