Pricing in multiproduct firms - Armstrong, M; Mark Armstrong (1993)
﻿ This thesis is a theoretical analysis of optimal pricing by firms when consumer demands are uncertain. The purpose is to extend the familiar literature on single-product nonlinear pricing in two directions: to cases where the firm is regulated and to the case where the firm produces several products. Chapter 1 embeds these problems into the general setting of models of asymmetric information and, as well as covering existing work on the pricing decisions of firms facing adverse selection, discusses other areas including repeated contracts, auctions, signalling and the uses of what is known as the 'first-order approach'. Chapter 2 analyzes nonlinear pricing by a regulated single-product firm. As an alternative to requiring the firm to offer a given linear tariff two different types of regulation which allow nonlinear pricing are considered, namely, average revenue regulation and optional tariff regulation. Chapter 3 introduces the topic of multiproduct pricing when consumers have differing tastes for the various goods. The important simplifying assumption is that consumers wish to buy either one unit of a good or none at all. There are three main results: if consumers' taste parameters are continuously distributed then the firm will not offer all goods to all consumers; in the symmetric two-good case it is shown that (subject to a kind of 'hazard rate' condition) the firm will offer the bundle of two goods at a discount compared with the charge for the two goods separately; and the pricing strategy when the number of goods becomes large is solved approximately. Chapter 4 relaxes the assumption of unit demands and uses differential methods to analyze the multiproduct nonlinear pricing problem. In the symmetric case when taste parameters are continuously distributed the firm will choose to exclude some low-demand consumers from the market. It is shown that when parameters are independently distributed the firm will wish to introduce a degree of cross-dependence into its tariff. Sufficient conditions for a tariff to be optimal are derived and any tariff which satisfies these conditions necessarily will induce 'pure bundling', so that once a consumer decides to participate in the market at all she will choose to buy all goods. A class of cases is solved explicitly using these sufficient conditions. Since other solutions may be hard to solve analytically, a procedure for numerically generating solutions for the two-good case is described and two more solutions are described.