Linear Programming Problems Representing Dorfman’s Model of Monopoly

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.