Returns to scale in a spatial Solow–Swan economic growth model

Abstract

In this work we add decreasing and increasing returns to scale in a unidimensional spatial Solow–Swan economic growth model, considering capital-induced labor migration, capital transport cost, a Cobb–Douglas production function, and a logistic organic growth for the labor force. Stability analysis results of the spatially homogeneous equilibrium of the model show that higher returns to scale ease the formation of economic agglomerations and/or cycles in the economy. Besides, through numerical simulations, we confirm the stability analysis results, and obtain the interesting result that the presence of increasing returns to scale seems to be a key factor in order to cause that economic agglomerations – which are regions with higher levels of capital and labor than their neighbors – also show a higher per capita output. This helps to explain the observed positive correlation between population and per capita GDP distributions in Brazil, suggesting the presence of increasing returns to scale in the empirical data. Finally, higher returns to scale also imply a higher aggregate per capita output for the economy as a whole.