Growth and Distribution in a Model with Endogenous Time Peferences 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. Then we study sliding equilibrium paths. They become balanced from some time onwards and eventually all the capital is owned by the household that is the richest at the initial state. Finally, we consider time consistent equilibrium paths and prove their existence.