The Marginal Unit Shadow Price and its relationship to the Average Shadow Price

Saral Mukherjee and Chatterjee Ashis K

No WP2003-06-02, IIMA Working Papers from Indian Institute of Management Ahmedabad, Research and Publication Department

Abstract: The economic significance of the average shadow price for integer and mixed integer programming problems has been established by researchers (Kim and Cho 1988), (Crema 1995). In this paper we introduce the concept of the marginal unit shadow price to deal with the integer programs where the right hand side resource availability can only be varied in discrete steps. We show that for integer programs, a sufficient condition for the marginal unit shadow price to equal the average shadow price is that the Law of Diminishing Returns should hold. The polyhedral structures that will guarantee this equivalence have been explored. Identification of the problem classes for which the equivalence holds greatly simplifies the existing procedure for determining shadow price for such integer programs.

Date: 2003-06-02
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