Competitive Growth in a Life-cycle Model: Existence and Dynamics

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.