Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach

In this paper we propose a unifying approach to study optimal growth models with bounded or unbounded returns (above/below). We prove existence of optimal solutions. We prove also, without using contraction method, that the Value function is the unique solution to the Bellman equation in some classes of functions. The value function can be obtained by the usual algorithm defined by the operator provided by the Bellman equation. The well-known results, and those in Alvarez and Stokey (1998) can be obtained from this paper. ∗CERMSEM, EP 1737 du CNRS, Université de Paris I, Maison des Sciences Economiques, 106-112 Bd de l’Hôpital 75647 Paris Cedex 13, France. E-mail: [email protected], [email protected]. Tel: 33 1 44 07 83 00. Fax: 33 1 44 07 83 01. This paper was finished while Cuong Le Van visiting CORE (University Catholique de Louvain) in March, April 2000. We would like to thank Raouf Boucekkine for his remarks and suggestions.