Pricing and Selection of Second-Degree Price Discrimination Menus

We study a second-degree price discrimination problem in which a monopolist must design a menu of pricing options for high and low valuation consumers, whom he cannot directly distinguish. The firm chooses between two canonical nonlinear pricing strategies: a price-quantity menu and a two-part tariff menu. We argue that, when designing each menu, the monopolist optimally balances gains from production against information rent costs. Crucially, information rents translate into fully variable costs under a price-quantity menu, but they introduce fixed costs under a two-part tariff menu. As a result, the menu choice effectively reduces to selecting a revenue structure choice involving a trade off between fixed and variable costs. We find that the monopolist strictly prefers the price-quantity menu, which avoids fixed costs. However, the efficient menu is the one that induces greater consumption by the low-valuation type, and thus might be in conflict with the monopolist's preferred option. We fully characterize the conditions under which each menu is efficient and identify which pricing strategy benefits the firm, consumers, or both.