Discriminating Monopoly

Abstract

In The Wealth of Nations, Adam Smith refers to two instances of price discrimination. In Book V, Chapter I, Part III, he ruminates on the problem of finding the best set of levies for toll roads and commends the practice of charging for luxurious carriages more than for working men’s wagons even though the vehicles are of the same weight. He suggests that the rich can subsidize the poor by this tariff scheme. In Book IV, Chapter V, he notes that some groups of producers have sold their produce abroad at lower prices than at home. He views this as cross-subsidization and deplores the high prices which he sees as resulting in the domestic market. Smith’s first problem, how to set tolls, has occupied economists to this day, although the solution was laid out in principle by Dupuit (1844) and with considerable precision by Edgeworth (1910): let each user’s levy in excess of his or her marginal cost of usage (which may be zero on a toll bridge) be proportional to his or her intensity of preference as expressed by his or her elasticity of demand. Edgeworth in fact worked out details of two sorts of price discrimination – that practised by a private profit-maximizing monopolist and that practised by a ‘state monopoly’ interested in raising Z dollars of profit from the users of the monopoly while at the same time reducing welfare as little as possible. The solution to this state monopoly or public utility pricing problem we refer to today as Ramsey pricing (Ramsey 1927, who attributes the idea for his paper to Pigou).