The discrete solow model with time-to-build

Abstract

This study reformulates the discrete-time Solow economic growth model by incorporating time delays and re-evaluates capital accumulation in two distinct frameworks: one in which the population growth rate is constant (either positive or negative) and another in which it varies over time. The analysis demonstrates that: (i) the stability conditions under delay remain valid; (ii) the delayed Solow model exhibits cyclic fluctuation through a Neimark-Sacker bifurcation when the time delay is sufficiently long and the labor force growth rate is low, including cases of negative growth; and (iii) the stability of the system is highly sensitive to the specification of the labor force dynamics. As a direction for future research, it would be interesting to replace the Cobb-Doglas production function with a Constant Elasticity of Substitution (CES) production function as empirical evidence suggests that the elasticity of substitution is typically less than one.