A Note on Shadow Prices in Linear Programming

Abstract

Using convex analysis and a characterization of the entire family of optimal solutions to an L.P., we show that in order to obtain shadow prices, one has to solve a much smaller L.P. derived from any optimal tableau. We then show that positive as well as negative shadow prices for any constraint or for any combination of constraints can easily be computed by parametric linear programming. Some examples exhibiting the method are also included.