This paper deals with the evolution of the literature on the problem of population and growth from the classical period to the recent literature on endogenous growth and development. The 'problem' concerns two distinct issues: 1. how to explain the observed covariation of the levels and rates of...

We study general dynamic programming problems with continuous and discrete choices and general constraints. The value functions may have kinks arising (1) at indifference points between discrete choices and (2) at constraint boundaries. Nevertheless, we establish a general envelope theorem:...

In this paper we develop a framework to analyze stochastic dynamic optimization problems in discrete time. We obtain new results about the existence and uniqueness of solutions to the Bellman equation through a notion of Banach contractions that generalizes known results for Banach and local...