Growth and distribution in a model with endogenous time preferences and borrowing constraints

This paper proposes an AK-model with endogenous time preferences and borrowing constraints. It is assumed that the subjective discount factor of a household is an increasing function of its relative income. First, we describe the structure of balanced-growth equilibrium paths, on which the population splits into two groups: the rich and the poor. Secondly, we study sliding equilibrium paths, show that they become balanced from some time onwards and that eventually all the capital is owned by those households that were the richest at the initial state. It follows that the long-run rate of growth depends on the initial distribution of wealth and income.