Limit policies in n-sector dynamic growth games with externalities

We examine an economy with n production sectors that interact via a production externality. We find a solution to the resulting dynamic differential game between sectors and compare it with the cooperative solution. As the number of sectors increases, the limiting policy is the optimal policy without a production externality. This policy is inefficient and, depending on the sign of the externality between sectors, the inefficiency is due to over- (or under-) consumption.