Are Dual Variables Prices. If Not, How to Make Them More So
Abstract
Actual prices in an economy reflect a number of institutional arrangements -- salaries, savings, taxes, loans, interest, transfer payments, profits, rents, and investment credits. These can be quite different from prices generated by a L.P. (Linear Program). The price of an item in the L.P. is the change in the objective value if an additional unit of the item is made available to the system. An unfortunate consequence is that any capacity (or labor) not fully used gets a zero price. The purpose of this paper is to show how to make a simple perturbation to the linear program, after it has been solved, so that the new dual variables behave more like actual prices. To do this we will need three assumptions: (a) the unused part of capacity is worth zero and can be deleted from the system; (b) an infinitesimal epsilon part of the used capacity is malleable; (c) the value of capacity can be measured by deleting the malleable epsilon part and seeing what it is worth to put it back. We shall show that it is possible to associate new prices with the optimal solution to the perturbed linear program without changing the original optimal primal solution. The new prices remain invariant as the malleable epsilon part of used capacity tends to zero.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1978
- Accession Number
- ADA060819
Entities
People
- George Bernard Dantzig
Organizations
- Stanford University