SHADOW PRICES FOR INFINITE GROWTH PROGRAMS: THE FUNCTIONAL ANALYSIS APPROACH

Abstract

This paper summarizes some recent results on price systems characterizing efficient or optimal programs in economic models for which the commodity space can be represented as a subset of l_∞. In general, a price system is represented as a continuous linear function on l_∞. An efficient program is called regular if there is an associated price system of the form P(y) = ∫gy, where g is in l_1. Various conditions are given under which efficient programs can be approximated by regular programs. The approach is illustrated by examples of economic optimization problems involving time and uncertainty.