Optimal Investment in R&D with International Knowledge Spillovers

We provide steps towards a welfare analysis of a two-country endogenous growth model where a relatively small follower absorbs part of the knowledge generated in the leading country. To solve a suitably defined infinite-horizon dynamic optimization problem a specialized version of the Pontryagin maximum principle had to be applied. 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 the two solutions. Thus, optimal policy intervention has no effect on long-run growth rates but affects these relative levels.