Reconsidering incentive compatibility in indirect price discrimination

Indirect price discrimination assumes there are two types of consumers, interested and disinterested, but the monopolist cannot directly identify type. Relative to a simple, single price equilibrium, the monopolist would prefer to sell to the disinterested consumer at a high price for the few goods she purchases and to the interested consumer at a lower price to capitalize on his higher demand. Thus, a separating equilibrium is required such that the disinterested consumer voluntarily pays the higher price because she does not wish to purchase as much as required to obtain the discount. Implicit in the this theory is the idea that the disinterested consumer might opt to consume above her demand curve if the minimum required purchase is set too low. If the monopolist can induce one consumer to purchase above her demand - though this theory is based on avoiding that outcome - she might be able to induce the other consumer to do so as well. Under certain conditions, a separating equilibrium is still preferred by the monopolist, and relative to the original separating equilibrium that has both consumers locating on their respective demand curves, this equilibrium has them both locating above them. In comparison to the original equilibrium, the new equilibrium is welfare improving and yields greater profit for the monopolist at the expense of consumers. Beginning with simple linear demand functions and zero marginal costs for simplicity, we lay out the basics of such a solution. We then add non-linear demand functions and non-zero marginal costs to demonstrate under the same assumptions of the original theory that the monopolist can induce consumption above demand for both types of consumers.