Multiproduct Pricing Made Simple

Armstrong, Mark and Vickers, John (2016): Multiproduct Pricing Made Simple.

Abstract

We study pricing by multiproduct firms in the context of unregulated monopoly, regulated monopoly and Cournot oligopoly. Using the concept of consumer surplus as a function of quantities (rather than prices), we present simple formulas for optimal prices and show that Cournot equilibrium exists and corresponds to a Ramsey optimum. We then present a tractable class of demand systems that involve a generalized form of homothetic preferences. As well as standard homothetic preferences, this class includes linear and logit demand. Within the class, profit-maximizing quantities are proportional to efficient quantities. We discuss cost-passthrough, including cases where optimal prices do not depend on other products' costs. Finally, we discuss optimal monopoly regulation when the firm has private information about its vector of marginal costs, and show that if the probability distribution over costs satisfies an independence property, then optimal regulation leaves relative price decisions to the firm.

• Item Type: MPRA Paper
• Language: English
• Keywords: Multiproduct pricing, homothetic preferences, Cournot oligopoly, monopoly regulation, Ramsey pricing, cost passthrough, multidimensional screening
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D42 - Monopoly; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L12 - Monopoly ; Monopolization Strategies; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets; L - Industrial Organization > L5 - Regulation and Industrial Policy > L51 - Economics of Regulation

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