A dynamical model of optimal investment in R&D

We provide steps towards a welfare analysis of a two-country endogenous model where a relatively small follower absorbs part of the knowledge generated in the leading country. To solve a suitably defined dynamic optimization problem, an appropriate version of the Pontryagin maximum principle is developed. The properties of optimal controls and the corresponding optimal trajectories are characterized by the qualitative analysis of the solutions of the Hamiltonian system arising through the implementation of the Pontryagin maximum principle. We find that for a quite small follower, optimization produces the same asymptotic rate of innovation as the market. However, relative knowledge stocks and levels of productivity differ in general. Thus, policy intervention has no effect on growth rates but may affect these relative levels. The results are different for not so small follower economies.

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