Optimal innovation and optimal imitation: an integrated analysis

When assessing the role that technology plays in fostering economic growth, it is usual to conceive a technology frontier, where the most research advanced economy is placed, and relatively to which all the other economies, the followers, will want to catch-up. Catching-up is typically feasible through imitation; economies that do not possess conditions to undertake cutting-edge research will want to adopt the technology that the technological leader has already tested and successfully implemented. The study of technology creation and how it diffuses has a long tradition in economics, that goes back to Nelson and Phelps and that has counted with a large number of seminal contributions (among many others, Jovanovic and Rob, Segerstrom, Parente and Prescott, Mukoyama, Peyton-Young). A recent contribution relating the subject under discussion, which is analyzed in this paper, is the one by Benhabib, Perla and Tonetti, henceforth BPT. In BPT a fully deterministic model is designed to address the optimal decisions of the economies on whether to innovate or imitate the leader. A single optimal control problem allows to address both the challenge of the country in the technology frontier and the behavior of all the followers, and it is precisely this ability to integrate innovation and technology adoption under the same simple modeling structure that makes this an appealing framework upon which to think about how knowledge creation and knowledge diffusion take place in the world we live in.