OPTIMAL GROWTH, EQUILIBRIUM AND RECURSIVE UTILITY.

摘要

The purpose of this thesis is to demonstrate the equivalence principle for one- and two-sector neoclassical models of capital accumulation with a flexible rate of time preference, perfect foresight, and an infinite horizon in continuous time. The equivalence principle asserts that when each agent in the decentralized economy pursues his economic objective subject to the given constraints, a perfect foresight competitive equilibrium is equivalent to an optimal growth solution.; Previously, Becker (1981, 1983) developed these principles in the context of the time additive utility function with multisector heterogeneous capital goods and a one-sector model with adjustment costs, respectively. The equivalence principle simplifies the analyses of equilibrium properties such as the existence, uniqueness, stability, and comparative dynamics by reducing them to the related problem in the corresponding optimal growth model. This principle solves the so-called Hahn's (1966) saddlepoint instability problem.; To this end, recursive competitive one- and two-sector dynamic equilibrium models are defined by a representative consumer who owns the capital stock and a representative firm which produces goods by renting the services of capital from the consumer at each time in a competitive market. A corresponding optimal growth model is defined by identifying the planner's objective with that of the consumer. The proof of the equivalence principle follows by matching the first-order necessary condition for optimality and the appropriate transversality condition for the infinite horizon problems. Benveniste and Scheinkman (1982) proved the existence of absolutely continuous dual variables for the optimal growth problem with a time additive utility function. However, their theorem is not directly applicable to the recursive model addressed in this study. The first-order necessary condition is therefore derived as an Euler equation in terms of the Volterra variational derivative. The transversality condition is also demonstrated for each agents' problem.; An application of the equivalence principle shows that equilibrium trajectories exist. Local asymptotic stability of the steady state in one- and two-sector models is proven. The hypothesis of increasing marginal impatience is a crucial element in the stability theory. This condition is also the basis for deriving the incomplete specialization of production in the two-sector model.