Dynamic Structure, Exogeneity, Phase Portraits, Growth Paths, and Scale and Substitution Elasticities

The paper studies autonomous dynamic systems that allow for the existence of economic growth per capita without dynamically generating explosive solutions. The implications of any degree of homogeneity, including increasing returns to scale in production, must be carefully examined in two and higher dimensions. The necessity of introducing some exogenous state variables is demonstrated within homogeneous dynamic systems. The authors solve and demonstrate the dynamic implications of scale and the substitution elasticities in various basic (two-factor) and augmented (multifactor) aggregate growth models