Asymptotic growth rates in knowledge-exchanging economies

Two ODE models of innovation dynamics based on Grossman and Helpman's endogenous growth model with horizontal product differentiation are coupled through knowledge exchange. It is shown that in the coupled model, the steady rates of innovation are asymptotically stabilized at a unique level higher than the autarky growth rate in each economy. The steady rate of innovation common to both countries is positively related to each country's ability to absorb knowledge from abroad. Conditions sufficient for the existence of a steady trajectory are provided.