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… (More)
This paper analyses the optimal timing of switching between alternative and consecutive regimes in optimal growth models. We derive the appropriate necessary conditions for such problems by means of the standard techniques from calculus of variations and some basic properties of Sobolev spaces.
This paper studies the optimal growth of a developing non-renewable natural resource producer, which extracts the resource from its soil, and produces a single consumption good with man-made capital. Moreover, it can sell the extracted resource abroad and use the revenues to buy an imported good, which is a perfect substitute of the domestic consumption… (More)
In this paper we propose a unifying approach to the study of recursive economic problems. Postulating an aggregator function as the fundamental expression of tastes, we explore conditions under which a utility function can be constructed. We also modify the usual dynamic programming arguments to include this class of models. We show that Bellman's equation… (More)