COMPETITIVE GROWTH IN A LIFE‐CYCLE MODEL: EXISTENCE AND DYNAMICS*

Abstract

The dynamic behavior of the capital growth rate is analyzed using an overlapping‐generations model with continuous trading. Assuming a technology satisfying constant social returns to capital, the equilibrium growth rate is piecewise‐defined by functional differential equations with both delayed and advanced terms. The main result concerns the existence of a solution expressed as a series of exponentials, which is shown to crucially depend on the initial wealth distribution among cohorts. Upon existence, the dynamics of the capital growth rate has a saddle‐point trajectory that converges to a unique steady state. Along the transition path, the growth rate exhibits exponentially decreasing oscillations.