A characterization of Ramsey equilibrium in a model with limited borrowing

This paper considers a one-sector economic growth model with several infinitely-lived heterogeneous households, who differ both in the discount factors as well as preferences over consumption. Unlike the extreme form of borrowing constraint observed in the classical Ramsey model, recently surveyed in Becker (2006), we allow limited borrowing by the households and prove the existence of a perfect foresight equilibrium. We also show that irrespective of production technology employed by the firms, the capital stock sequence converges to the steady state stock and from some time onward all impatient households are in the maximum borrowing state, whereas the most patient household owns entire capital stock and the debts of all other households.