Production externalities and local dynamics in discrete‐time multi‐sector growth models with general production technologies

The present paper examines the dynamic properties of discrete‐time, multi‐sector growth models in the presence of sector‐specific externalities. It extends the literature by allowing for multiple capital good sectors with general social constant returns production technologies. We establish conditions for the steady‐state equilibrium to be locally determinate or locally indeterminate, depending crucially on the ratios of the social to private marginal products and the number of capital good sectors. We show that when the ratios of the social to private marginal products are uniform across all sectors, the steady state is always locally determinate in a two‐sector model, although local indeterminacy might still arise when the economy features more than two sectors.