Dress to impress: Brands as status symbols

We analyzed the market for indivisible, pure status goods. Firms produce and sell di¤erent brands of pure status goods to a population that is willing to signal individual abilities to potential matches in another population. Individual status is determined by the most expensive status good one has. There is a strati…ed equilibrium with a …nite number of brands. Under constant tax rates, a monopoly sells di¤erent brands to social classes of equal measure, while in contestable markets, social classes have decreasing measures. Under optimal taxation, contestable markets have progressive tax rates, while a monopoly faces an adequate ‡at tax rate to all brands. In contrast with the literature, subsidies may be socially optimal, depending on the parameters, in both market structures. Keywords: brand, competition, free entry, matching, monopoly, signaling, status, tax, welfare. JEL classi…cation: C78, H23, L12, L15. We would like to thank Harold Cole, Larry Samuelson, Sheri Tice, George J. Mailath, Ken Binmore, Andrew Postlewaite, Martin Richardson, Mark Johnson, Chris Jones, Kieron Meagher, Bill Sandholm, Luciana Fiorini, Antonio Mazali, James Taylor, participants at the Public Choice Conference, VII Latin-American Workshop on Economic Theory, Public Economic Theory Conference, and seminar participants at Catholic University of Brasília and Australian National University for helpful comments. We would like to thank Judy Livingston and Merrilyn Lárusson for the English editing. All remaining errors are our own responsibility. yTulane University, A. B. Freeman School of Business, 706 Goldring/Woldenberg Hall, 7 McAlister Drive, New Orleans, LA 70118, USA. This author would like to thank CNPq for …nancial support. Phone: 1 (504) 865-5532. Email: [email protected] zResearch School of Economics, College of Business and Economics, H.W. Arndt Building 25A, Australian National University, Canberra ACT 0200, Australia. Phone: 61 (2) 612-55633. Email: [email protected] Contents 1 Introduction 1 2 Model Setup 5 3 Demand for Status Goods 8 4 Welfare 10 5 Monopoly 12 6 Contestable Markets 15 6.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 6.2 Strati…ed Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 7 Pigouvian Taxation 20 7.1 Why Should We Tax or Subsidize Status Goods? . . . . . . . . . . . . . . . 20 7.2 Optimal Taxation for a Monopoly . . . . . . . . . . . . . . . . . . . . . . . . 20 7.3 Optimal Taxation in a Contestable Market . . . . . . . . . . . . . . . . . . . 22 8 Conclusion 23 A Appendix: Proofs 24 A.1 Demand for Status Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 A.2 Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 A.3 Monopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 A.4 Contestable Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 A.5 Pigouvian Taxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B Appendix: Leontief Technology 32 B.1 Demand for Status Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 B.2 Welfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 B.3 Monopoly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 B.4 Contestable Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 B.5 Pigouvian Taxation for Monopolies . . . . . . . . . . . . . . . . . . . . . . . 36 B.6 Pigouvian Taxation in Contestable Markets . . . . . . . . . . . . . . . . . . 37 B.7 Comparing the Leontief and Cobb-Douglas Cases . . . . . . . . . . . . . . . 37