Incentives of agency theory – Dupuit, Edgeworth, Pigou: Price Discrimination

When a monopolist or a government wants to extract consumers’ surpluses in the pricing of a commodity, it faces in general the problem of the heterogeneity of consumers’ tastes. Even if it knows the distribution of tastes, it does not know the type of any given consumer. By offering different menus of price-quality or price- quantity pairs, i.e., by using second-degree price discrimination, the government or monopolist can increase its objective function. Such an anonymous menu is an incentive mechanism that leads consumers to reveal their type by their self- selection in the menu.

Dupuit (1844) developed the concept of consumer surplus and used it to discuss price discrimination. Dupuit was well aware of the incentive problems faced by the pricing of infrastructures:

The best of all tariffs would be the one which would make pay those which use a way of communication a price proportional to the utility they derive from using this service. I do not have to say that I do not believe in the possible application of this voluntary tariff; it would meet an insurmountable obstacle in the universal dishonesty of passants, but it is the kind of tariff one must try to approach by a compulsory tariff.

—Dupuit (1849, p. 223)

Edgeworth (1911–13) extended the theory for price discrimination for the railways industry. Pigou (1920) characterized the different types of price discrimina- tion. Gabor (1955) discussed block tariffs or two-part tariffs that had been recently introduced in the electricity industry in England and showed that with one type of consumers two-part tariffs are equivalent to first-degree price discrimination. Oi (1971) derived an optimal two-part tariff. Mussa and Rosen (1978), Spence (1977), and Goldman, Leland, and Sibley (1984) provided the general framework to derive, for a monopolist, an optimal tariff that is nonlinear in prices or qualities, substantially later than similar work in the income tax or insurance literature.

Source: Laffont Jean-Jacques, Martimort David (2002), The Theory of Incentives: The Principal-Agent Model, Princeton University Press.

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