Markets for Goods with Externalities

43 Pages Posted: 22 May 2020

Date Written: April 26, 2020


I consider the welfare and profit maximization problems in markets with externalities. I show that when externalities depend generally on allocation, a Pigouvian tax is often suboptimal. Instead, the optimal mechanism has a simple form: a finite menu of rationing options with corresponding prices. I derive sufficient conditions for a single price to be optimal. I show that a monopolist may ration less relative to a social planner when externalities are present, in contrast to the standard intuition that non-competitive pricing is indicative of market power. My characterization of optimal mechanisms uses a new methodological tool—the constrained maximum principle—which leverages the combined mathematical theorems of Bauer (1958) and Szapiel (1975). This tool generalizes the concavification technique of Aumann and Maschler (1995) and Kamenica and Gentzkow (2011), and has broad applications in economics.

Keywords: externalities, Pigouvian tax, mechanism design, constrained maximum principle, nonconvexities

JEL Classification: C61, D47, D61, D62, D82

Suggested Citation

Kang, Zi Yang, Markets for Goods with Externalities (April 26, 2020). Available at SSRN: or

Zi Yang Kang (Contact Author)

Stanford University ( email )

Stanford, CA 94305
United States

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