Smoothness, Comparative Dynamics, and the Turnpike Property

A. Araujo · J. A. Scheinkman

118 citations0/0 files storedEconometrica

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Economic theories and models Economic Growth and Productivity Optimization and Variational Analysis

Abstract

This paper treats dynamic optimization problems from the point of view of programming in infinite dimensional spaces. Sufficient conditions (of a dominant diagonal nature) for smooth dependence of optimal paths on initial conditions and other parameters are given. It is also shown that the smooth dependence and the so called are very closely related. This relationship is used to prove a turnpike theorem for a model that may be interpreted as a multisectoral model of optimal growth with positive discounting and to show that the turnpike property is kept under small perturbations.

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References

1928A Mathematical Theory of Saving 1967On Optimal Development in a Multi-Sector Economy 1970On Existence of Weakly Maximal Programmes in a Multi-Sector Economy 1976On optimal steady states of n-sector growth models when utility is discounted 1956A Complete Capital Model involving Heterogeneous Capital Goods

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