Innovation, decentralization, and planning in a multi-region model of Schumpeterian economic growth

We study innovation and the resulting Schumpeterian economic growth that this innovation gives rise to in a model with N heterogeneous regions. For each region i where i=1,...,N, our analysis leads to five findings. First, we define the balanced growth path (BGP) allocations and the equilibrium of interest. Second, we stipulate the form of the innovation possibilities frontier that is consistent with balanced economic growth. Third, we derive the growth rate of the ith region in the decentralized equilibrium and show that there are no transitional dynamics. Fourth, we solve the social planner's problem and derive the Pareto optimal growth rate for the ith region. Fifth, we compare the two preceding growth rates and then discuss the circumstances in which there is either too much or too little innovation in (i) the ith region, (ii) the aggregate economy of N>2 regions and (iii) the specific case of an aggregate economy of N=2 regions. Finally, we conclude and then offer suggestions for extending the research described here.