Rethinking Profit-Maximization in Second-Degree Price Discriminating Markets

Standard models of indirect price discrimination generate a separating equilibrium in which all consumers choose bundles on their demand curves. Low-demand consumers voluntarily choose to pay a higher unit price for small quantities because the discount is offered by the monopolist at prohibitively high quantity. These models implicitly assume the low-demand consumer would purchase the higher quantity at the discounted price if the quantity requirement were set at a low quantity, but rational monopoly pricing avoids this. We show that it is possible for a monopolist to offer price/quantity bundles that induce each consumer to choose voluntarily the one preferred by the monopolist for her where each bundle is above the respective consumer’s demand curve. The primary theoretical results include greater profits for the firm and greater total efficiency as output more closely approaches the socially optimal level in both market segments. Resolving an ambiguity from earlier research on price discrimination, the model also unequivocally demonstrates that consumer surplus is reduced. An important implication of the monopolist constraining consumption to be above the demand curve for her product is that she has effectively reduced the demand for some subset of other goods and services the consumers purchase.