Evolution of the Distribution of Assets in the Neoclassical Growth Model

We study the evolution of the distribution of assets in a deterministic version of the Neoclassical Growth Model with log-utility, a minimum consumption requirement, and Cobb-Douglas technology. Agents are heterogeneous in their initial endowment of assets only. The dynamics of the aggregate variables behaves as in a standard representative agent model. We prove that the disparity in assets decreases monotonically in a transition to the steady state from below, as long as (i) the minimum consumption requirement is zero or negative, or (ii) the consumption requirement is positive but not too large and the initial capital stock is large enough. This result is not based on a local approximation of the model around the steady state, nor on numerical computations, as it has been the case in previous literature. We also show how a positive minimum consumption requirement or a small elasticity of substitution between capital and labor can generate non-monotonic paths for the disparity in assets along a transition. Our work extends the result in Chatterjee (1994) on the evolution of the distribution of lifetime wealth (or consumption) to the evolution of the distribution of assets (or capital).