Econometrica: Apr, 1977, Volume 45, Issue 3

Smoothness, Comparative Dynamics, and the Turnpike Property

https://doi.org/0012-9682(197704)45:3<601:SCDATT>2.0.CO;2-F
p. 601-620

A. Araujo, J. A. Scheinkman

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 "turnpike property" 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.