Linear Programming Problems Representing Dorfman’s Model of Monopoly

[somdeb...@gmail.com]

At the link below is a discussion of chapter 3 of Robert Dorfman's 1951 dissertation, from the perspective of linear programming.

https://doi.org/10.31224/5347

It is well known that monopoly pricing requires solving a "non-linear programming" problem.

Abstract

In a model similar to the one discussed in chapter 3 of Robert Dorfman’s dissertation on production theory we formulate the problem faced by a profit maximizing multi-product firm that is a uniform-price monopolist in the market for a single product, as a linear programming problem. Subsequently we formulate the problem faced by the same profit maximizing firm if it is a price-discriminating monopolist in the market for a single product, as a linear programming problem. We require the Marshallian market demand curve faced by the firm to be a non-increasing step function with a finite number of points of discontinuity, for the product that the firm is a monopolist.

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Thanks and regards.

Somdeb.