Transitional dynamics and the distribution of assets

We study the evolution of the distribution of assets in a discrete time, deterministic growth model with log-utility, a minimum consumption requirement, Cobb-Douglas technology, and agents differing in initial assets. We prove that the coefficient of variation in assets across agents decreases monotonically in a transition to the steady state from below, if (i) the consumption requirement is zero, or (ii) the consumption requirement is not too big and the initial capital stock is large enough. We also show how a positive consumption requirement or a small elasticity of substitution between capital and labor can generate non-monotonic paths for inequality.