Social Status, Reputation, Financing, and Commitment∗ Preliminary and incomplete - Please do not make it available without the authors' permission Rog´erioMazaliy Jos´eA. Rodrigues-Netoz April 25, 2016 Abstract We develop a dynamic model of a horizontally differentiated product duopoly. The purpose is to investigate the relationship between the market niche each firm targets, the social status of its brand, its project financing and ownership structure. Firms' financial decisions can be used as signals of the social status of each firm’s brand name, and thus, the market niche that is targeted. We provide conditions under which a firm is not able to produce high status goods credibly, but by restricting its ability to adopt an industrial technology it may. A firm that produces high status goods may purposely restrict its own access to capital markets, remaining private, using this decision as a commitment device. In this case the firm has the credibility it needs to convince other parties that it will keep producing a high status good and not \invade" its rival's market niche. Following a stream of literature that started with Titman (1984) and Brander and Lewis (1986), the present paper provides a novel link between financial and capital markets: concerns with \brand reputation" regarding the social status of a firm’s products. Keywords: brand, competition, reputation, commitment, status, capital structure. JEL classification: G32, C78, L13, L15. ∗We thank Steffen Lippert, Simona Fabrizi, and seminar participants at the Australasian Economic Theory Workshop, Australian National University, University of Bras´ıliaand Catholic University of Bras´ıliafor helpful comments. All remaining errors are our own responsibility. yCatholic University of Brasilia, Graduate Program in Business Economics, SGAN 916 M´oduloB, Bloco B sala A-120, Bras´ılia,DF, CEP 70790-160, Brazil. Phone: +55 (61) 3448-7192. Email: [email protected] zAustralian National University, College of Business and Economics, Research School of Economics, H.W. Arndt Building 25A, ANU, Canberra ACT - 0200, Australia. Phone: +61 (2) 612-55633. Email: [email protected] Contents 1 Introduction 1 2 Setup 7 2.1 Firms and Investors . .7 2.2 Consumers . .8 2.3 Game Dynamics . .9 2.4 Dynamic Game Setup and Equilibrium Concept . .9 3 Stage-Game Analysis 10 3.1 Consumer Demands . 10 3.2 Hotelling Equilibrium Under the Same Technology and No Status . 11 3.3 Hotelling Equilibrium Under Different Technologies and No Status . 11 3.4 Hotelling Equilibrium Under the Same Technology and Status . 12 3.5 Hotelling Equilibrium Under Different Technologies and Status . 13 3.6 Stage Game Along the Equilibrium Path . 13 3.7 One-Shot Deviation: Firm 0 . 15 3.8 One-Shot Deviation: Firm 1 . 15 3.9 No Punishment After Deviation: Hotelling Competition with Reputation Loss . 16 3.10 Punishment After Deviation: Generic Pricing . 17 3.11 Punishment After Deviation: Stackelberg Equilibrium . 18 3.12 Punishment After Deviation: Minmax Punishment . 19 3.13 Firm 0 deviates from punishing Firm 1 . 19 3.14 Firm 1 punishes Firm 0 . 20 4 Dynamic Game Equilibria 21 4.1 Equilibrium with Product Differentiation on Status . 21 4.1.1 Financial Markets . 25 4.2 Dynamic Strategy . 26 4.3 Incentive Compatibility Constraints . 28 4.4 Deviations from the Equilibrium Path: Customer Punishment Only . 29 4.5 Deviations from the Equilibrium Path: Customer and Rival Punishment . 30 4.6 Incentives for Firm 0 to Punish a Deviation from Firm 1 . 31 4.7 Incentives For Firm 1 to Return to the Equilibrium Path . 34 4.8 Incentives For Firm 1 to Punish a Deviation from Firm 0 . 35 5 Optimal Punishment 36 5.1 Case 1 (δ ≥ bδ1): \Customer punishment only" can enforce equilibrium with status goods........................................... 36 5.1.1 Comparing the two types of punishment . 37 5.2 Case 2 (δ < bδ1): \Customer punishment only" cannot enforce equilibrium with status goods . 38 2 6 Social Status, Private Firms and Commitment 39 6.1 Subgame in which Firm 1 chooses no commitment . 42 6.2 Equilibrium of the Dynamic Game with Commitment . 44 L NP 6.2.1 Effect of commitment when p0 ≥ p0 ..................... 44 L NP 6.2.2 Effect of commitment when p0 < p0 ..................... 48 7 Discussion 50 A Appendix: Proofs 51 A.1 Stage Game . 51 A.1.1 Consumer Demands . 51 A.1.2 Hotelling Equilibrium Under the Same Technology and No Status . 51 A.1.3 Hotelling Equilibrium Under Different Technologies and No Status . 52 A.1.4 Hotelling Equilibrium Under the Same Technology and Status . 53 A.1.5 Hotelling Equilibrium Under Different Technologies and Status . 54 A.1.6 Stage Game Along the Equilibrium Path . 54 A.1.7 One-Shot Deviation: Firm 0 . 56 A.1.8 One-Shot Deviation: Firm 1 . 56 A.1.9 No Punishment After Deviation: Hotelling Competition with Reputation Loss ....................................... 57 A.1.10 Punishment After Deviation: Generic Pricing . 57 A.1.11 Punishment After Deviation: Stackelberg Equilibrium . 58 A.1.12 Punishment After Deviation: Minmax Punishment . 58 A.1.13 Firm 0 deviates from punishing Firm 1 . 58 A.1.14 Firm 1 punishes Firm 0 . 59 A.2 Dynamic Game Equilibria . 59 A.2.1 Equilibrium with Product Differentiation on Status . 59 A.2.2 Dynamic Strategy . 62 A.2.3 Incentive Compatibility Constraints . 62 A.2.4 Deviations from the Equilibrium Path: Customer Punishment Only . 62 A.2.5 Deviations from the Equilibrium Path: Customer and Rival Punishment . 63 A.2.6 Incentives for Firm 0 To Punish a Deviation from Firm 1 . 63 A.2.7 Incentives For Firm 1 to Return to the Equilibrium Path . 64 A.2.8 Incentives For Firm 1 to Punish a Deviation from Firm 0 . 65 A.3 Optimal Punishment . 65 A.3.1 Case 1 (δ ≥ bδ1): \Customer punishment only" can enforce equilibrium with status goods . 65 A.3.2 Case 2 (δ < bδ1): \Customer punishment only" cannot enforce equilibrium with status goods . 66 A.4 Social Status, Private Firms and Commitment . 67 A.4.1 Subgame in which Firm 1 chooses no commitment . 67 A.4.2 Equilibrium of the Dynamic Game with Commitment . 69 B Appendix: Diluting Share Ownership of Regular Goods Firm 70 B.1 Proofs . 71 1 Introduction In the last decades, many economists have dedicated their efforts in trying to understand the market for status or luxury goods. Unlike regular goods, these goods might have little or no intrinsic value, in the sense that their consumption provides little or no direct utility. In the terminology of Pollack (1967, 1976), Koopmans (1960), among others, these goods provide rela- tively low \cardinal utility". The main component of the value these goods provide come from their \ordinal utility", that is, the utility given by the position one occupies in a rank after its consumption. Because of this feature, Frank (1985, 2005) refers to these goods as positional goods. It is not just the positional goods themselves that have special features that characterize them. The companies that produce them also have special characteristics that go beyond the production of status goods. Firms that produce high-end status goods tend to be private. For example, most watchmakers of high status, such as Cartier, and Rolex, are also private compa- nies, as well as fashion giants such as Armani, Versace, and jewelers H. Stern and Swarovski. Of the world's top ten jeweler companies according to Luxe High Life's catalogue, only one (Tiffany & Co.) is publicly traded. Another is a subsidiary in a public conglomerate (Harry Winston, part of the Swatch Group), and the other eight are all privately held companies (Cartier, Van Cleef & Arpels, Piaget, Bvlgari, Mikimoto, Graff, Buccelati and Chopard).1 Most of the su- persport car manufacturers are completely private, 100% independent endeavors, or a part of a conglomerate with significant restrictions on access to funds from other companies in the con- glomerate. McLaren, Aston Martin, W Motors and Koenigsegg are in the first group while Bugatti and Lamborghini are in the second. Out of the top 10 world's most expensive cars of 2015, according to Digital Trends2, six are manufactured by private independent companies (Zenvo ST1, Pagani Huayra, Aston Martin One-77, Koenigsegg One:1, W Motors Lycan Hyper- sport, and Koenigsegg CCXR Trevita), while three are manufactured by private firms within public conglomerates (Mansory Vivere, Bugatti Veyron, and Lamborghini Veneno). Only two, both manufactured by Ferrari N.V., are manufacuted by a public company (Ferrari LaFerrari and Ferrari F60 America). Nevertheless, Ferrari has traded as a private company for most of its life, only announcing its intention to go public in 2015.3 The decision of Ferrari going public is part of a spin-off operation that dismembered Ferrari from the Fiat-Chrysler Automobiles conglomerate. An article published in Fortune magazine in January 2016 seems to imply that being part of the conglomerate was not beneficial for Ferrari in any way and that Ferrari was not able to obtain 1http://luxehighlife.com/jewellery/the-world-s-top-10-jewellery-brands 2http://www.digitaltrends.com/cars/the-top-ten-most-expensive-cars-in-the-world/ 3See http://fortune.com/2015/07/23/ferrari-files-for-ipo-nyse/. 1 financing from the conglomerate, given the high leverage of the conglomerate. 4 Other high-end status goods that are part of conglomerates have restrictions in obtaining financing from parent companies. Lamborghini S.p.A, for example, was acquired by the Volkswagen group in 2011. Instead of maintaining it under direct control of Volkswagen, the group's management decided to keep it under control of one of its higher luxury subsidiaries, Audi A.G.. This ownership structure made it very difficult for Lamborghini to obtain financing from Volkswagen, since it would need aproval from Audi management as well.