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Turnpike Theorem in a Generalized Dynamic Input-Output System
Jinkichi Tsukui
Abstract
A strong type of turnpike theorem is proved for a planning model of a generalized dynamic Leontief system in which each industry has a polyhedral technology. Also, a dual turnpike theorem is proved for the shadow price of the original problem. This dual theorem shows the turnpike-like property of the shadow price with respect to the Neumann price ray. As a synthesis of the turnpike theorem and its dual, it is shown that all efficient paths of stocks are exactly on the so-called Neumann facet for most of the planning period in the case of polyhedral technology. McKenzie's recent results [3] are utilized in the course of the argument.
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