University of Southern California Dissertations and Theses

Essays on pricing and contracting

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Essays on pricing and contracting

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Content ESSAYS ON PRICING AND CONTRACTING by Vlad Radoias A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Economics) May 2013 Copyright 2013 Vlad Radoias For those who taught me to be free, for those who inspired, for those who said no, and for those who believed... ii Acknowledgements I would rst like to thank my wonderful parents, Doina and George Radoias, for their unconditional love and support through the years. Nothing of what I achieved would have been possible without your sacrices and encouragements through good and bad times. Completing this dissertation would never have been possible without the guidance of my academic advisors. I would like to thank Simon Wilkie, Guofu Tan, Michael Magill, and Anthony Dukes for many invaluable comments and suggestions. For all the time you invested in me, I am indebted to you all. I would also like to thank Geert Ridder and Giorgio Coricelli for being gracious and serving on my committee and for raising important questions that made me realize where I was wrong. A special thank you goes to Jason Taylor and Aydin Cecen who provided me with the rst glimpse into what it means to do economic research and with the encouragement to pursue scholarship. Without your help and support I would not be here today. I especially want to thank Jason for believing in me when no one else did and for giving me an opportunity I never thought I would get. For your continuous generosity to this day, I will always be grateful and indebted to you. Lastly, I want to thank my many good friends who made everything bearable. You provided comfort when things got tough, laughter when I needed it, and a good push whenever I got distracted. A special thanks goes to my lifetime friend Daniel Nedelescu who as a fellow Economics graduate student always understood what I was going through and with whom I have had numerous stimulating conversations. I could always share my successes and frustrations with you and I am grateful for having you as a friend. iii Table of Contents Dedication ii Acknowledgements iii List of Tables vi List of Figures vii Abstract ix Chapter 1 Introduction 1 Chapter 2 Underpricing, Excess Demand, and Secondary Markets: Ev- idence from the Entertainment Industry 6 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Pricing in the Entertainment Industry . . . . . . . . . . . . . . . . . 9 2.2.1 Scaling the House . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2 Sharing Risk with Speculators . . . . . . . . . . . . . . . . . . . . 11 2.2.3 Social Externalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 A Model of Risk Sharing with Speculators . . . . . . . . . . . . . . . 15 2.3.1 Describing the Game . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Equilibrium Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.3 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4 Complementarities and Social In uence . . . . . . . . . . . . . . . . . 32 2.4.1 A Model with Social In uence . . . . . . . . . . . . . . . . . . . . 33 2.4.2 A Model with Complementarities . . . . . . . . . . . . . . . . . . . 35 2.5 Ticket Pricing Data and Empirical Analysis . . . . . . . . . . . . . . 38 2.5.1 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.5.2 Model Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Chapter 3 When Price Discrimination Fails: A Principal Agent Prob- lem with Social In uence 59 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.2 Benchmark Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3 A Model with Social Externalities . . . . . . . . . . . . . . . . . . . . 65 3.3.1 One Price Commitment . . . . . . . . . . . . . . . . . . . . . . . . 68 iv 3.3.2 Two Prices Commitment . . . . . . . . . . . . . . . . . . . . . . . 69 3.3.3 Prot Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Chapter 4 Price Discrimination and Collusion in the Automotive In- dustries of the European Union 78 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2 The European Automobiles Market . . . . . . . . . . . . . . . . . . . 80 4.3 Basic Model and Data Description . . . . . . . . . . . . . . . . . . . 86 4.4 Estimation Results of the Basic Model . . . . . . . . . . . . . . . . . 90 4.5 Extended Model: Competition, Collusion, and other Fixed Eects . . 94 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Chapter 5 Rules of Evidence and Liability in Contract Litigation 108 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.3 Characterization of outcomes under General Dynamics . . . . . . . . 113 5.4 Characterization of outcomes under SL . . . . . . . . . . . . . . . . . 116 5.5 Strict liability or not? Discussion . . . . . . . . . . . . . . . . . . . . 118 5.6 Disclosure of Buyer's Private Cost Information . . . . . . . . . . . . 119 5.7 An Alternative Continuous Production Model . . . . . . . . . . . . . 122 5.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Bibliography 129 Appendix A 133 A.1 List of Empirical Variables . . . . . . . . . . . . . . . . . . . . . . . . 133 Appendix B 135 B.1 Magnitudes of the Country by Country Interactions . . . . . . . . . . 135 B.2 Magnitudes of the Brand by Country Interactions . . . . . . . . . . . 136 B.3 List of Empirical Variables . . . . . . . . . . . . . . . . . . . . . . . . 137 Appendix C 138 C.1 A Brief History of General Dynamics v. U.S. . . . . . . . . . . . . . 138 C.2 Derivation of the optimal bid under General Dynamics . . . . . . . . 142 C.3 Derivation of the optimal bid under SL . . . . . . . . . . . . . . . . . 144 C.4 Derivation of the optimal bid under DPI . . . . . . . . . . . . . . . . 146 v List of Tables 2.1 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2 Summary Statistics - Price Dierences . . . . . . . . . . . . . . . . . . . . 40 2.3 Price Regression { Dependent Variable: Price . . . . . . . . . . . . . . . . 42 2.4 Price Segmentation Regression { Dependent Variable: Price Levels . . . . 44 2.5 3SLS Regression Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.6 Theoretical Predictions vs. Empirical Evidence { Speculators Model . . . 52 2.7 Theoretical Predictions vs. Empirical Evidence { Social In uence Model . 54 2.8 Theoretical Predictions vs. Empirical Evidence { Complementarities Model 56 4.1 Price Dierences in the Euro Zone . . . . . . . . . . . . . . . . . . . . . . 83 4.2 Regression Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.3 Regression with no Collinear Variables . . . . . . . . . . . . . . . . . . . . 93 4.4 The Eects of a Domestic Producer . . . . . . . . . . . . . . . . . . . . . 96 4.5 Country by Country Interactions . . . . . . . . . . . . . . . . . . . . . . . 100 4.6 Brand by Country Interactions . . . . . . . . . . . . . . . . . . . . . . . . 104 B1 Magnitudes of the Country by Country Interactions . . . . . . . . . . . . 135 B2 Magnitudes of the Brand by Country Interactions . . . . . . . . . . . . . . 136 B3 Relevant Empirical Variables . . . . . . . . . . . . . . . . . . . . . . . . . 137 vi List of Figures 3.1 The Incidence of Price Discrimination . . . . . . . . . . . . . . . . . . . 75 vii Abstract This dissertation is concerned with studying certain pricing and contracting issues that are motivated by real problems. The second chapter is focused on determining why persistent excess demand is pervasive on certain markets. The focus is on the markets for popular concert tickets which present a number of viable theoretical issues to consider and also allow us to assemble a unique data set of prices from both primary and secondary markets that we can use to test the alternative theories. We nd that secondary markets emerge not because promoters fail to price or price discriminate optimally, but because they have strong incentives to either underprice or articially maintain shortages on the market. These incentives are provided by their desire to share risk with speculators when demand is uncertain, by the presence of complementary products, and by social in uence. Continuing to study the eects of social in uence, the third chapter builds a theoretical model of price discrimination under social in uence. We show that when consumers are uninformed about a product they can be persuaded through social in uence to update their preferences. Under these conditions social in uence reduces the protability and incidence of price discrimination. We show that sellers that are more sensitive to social in uence price discriminate less and oer less product variety. We also show that rationing occurs mainly at the low end and it can be severe. All these results are consistent with the empirical evidence from the entertainment industry and also with other observations from certain fashion and cult product industries. The fourth chapter considers a long studied pricing problem in both the Industrial Organization and International Trade literature. We try to shed light on why the law viii of one price does not always hold. The focus is on the automotive industry inside the European Union. We show that prices for identical models failed to converged in spite of the elimination of virtually all trade barriers and the adoption of the common currency. We argue that the exclusive dealership system allows for successful market segmentation and price discrimination based on purchasing power. We also point to pricing patterns that are consistent with collusive agreements among the three major manufacturing groups in Italy, France, and Germany. The nal chapter of this thesis analyzes the eciency implications of dierent sets of legal rules in contract litigation. When contracts are aected by asymmetric information, litigation often occurs. The legal rules under which the contracts are being written aect the incentives of both contracting parties and therefore the prices and eciency of these contracts. We show that a non interference rule that allows the parties to settle the dispute on their own is more preferable to a strict liability rule that forces the contractor to fulll his obligations regardless of the cost, and also to a rule that allows the private information to be made public and awards damages based on this information. ix Chapter 1 Introduction This thesis contributes to the way we understand certain pricing and contracting issues that aect economic agents in a multitude of settings. The major focus is placed on per- sistent underpricing and excess demand, price discrimination, and pricing and contracting under asymmetric information when default and litigation occur. We oer a balanced mix of theory and empirical evidence that convincingly provides explanations for some real world phenomena. The second and third chapters tackle the issue of underpricing and excess demand maintenance. Contrary to the common assumption of market clearing, we can often observe markets that do not clear for long periods of time. A natural consequence is that, when this happens, secondary markets emerge where resellers can extract additional prots. The question that we ask is why sellers do not produce more or simply increase their price to a level that would clear the market? Why do they leave money on the table for secondary market speculators? The industry most commonly aected by excess demand is the entertainment industry. Consumers generally have a hard time procuring tickets for popular music or sporting events directly from the box oce. There is an abundance of literature at the theoretical level that tries to explain why sellers underprice their tickets and why secondary markets emerge, but very little empirical evidence. Chapter 2 makes a contribution on this front. 1 We collect pricing data for a sample of 45 popular music concerts from both primary and secondary markets and test the alternative theories. Of particular interest, and to my knowledge this is the rst eort done in this regard, is to study the protability of secondary markets, namely the dierence between face value prices and secondary market prices. We test four theories that can potentially explain the underpricing and persistence of excess demand. The rst theory argues that the main reason for the emergence of secondary markets is that sellers do not price discriminate optimally. As consumers are generally willing to spend more money on better seats that are closer to the stage, promoters should scale the house and price accordingly. There are obvious logistic limitation to how nely this can be done in practice and there is also a large number of events that, surprisingly enough, are priced uniformly. These facts have led some to argue that, since this kind of price discrimination cannot be employed optimally, speculators can take advantage and arbitrage away the better seats in the house. If that was the case we should expect a negative correlation between the level of price discrimination and the leftover prots generated by resellers. We nd this not to be the case and therefore reject this theory. Alternative theories deal with complementarities, social in uence, and risk sharing when demand is uncertain. We nd that these theories are consistent with the empirical evidence. Artists sell not only live events, but also albums and merchandise. To stimu- late the sales of these complementary products, they lower their ticket prices to attract a larger audience. Promoters might also have incentives to lower their prices and attract speculators on the market if demand is uncertain, essentially transferring all the demand associated risk away. This incentive is even stronger if we consider merchandise sales during the event which is often the case. In those cases, the goal might be maximizing 2 attendance rather than ticket revenue. Finally, social in uence plays an extremely impor- tant role. Consumers' preferences might not be rigid or pre-determined, they might be in uenced by other consumers to value the event dierently, according to the perceived popularity. In such cases, promoters have the direct incentive to articially create short- ages and create a \buzz" around the product. Excess demand acts as a form of cheap advertising. All these theories are arguably valid in the entertainment industry, since entertainment has a strong social component, complementary products are present, and also demand uctuates from event to event. We present simplied models that are them tested against the available data and are found to be valid explanations. Chapter 3 continues investigating the role of social in uence on prices and on the protability of price discrimination specically. The puzzling empirical results of the previous chapter are fully explained by a simple price discrimination model to which we add social in uence. We show that social in uence reduces the protability and incidence of price discrimination. Under social in uence sellers have the incentive to ration the market, at least temporarily, in order to signal their quality to uninformed customers. Some customers will update their beliefs and will shift from the low end of the market to the high end. This reduces the protability of price discrimination and, if social in uence is strong enough, can render it unprotable and completely eliminate it. These predictions are consistent with the empirical ndings from the music industry and also with other observations from other markets. Firms that produce cult or fashion products that are trendy and very sensitive to social in uence oer less product variety and use less price discrimination than rms that produce generic goods. They are also the ones that usually ration the supply during so called \pre-sale" periods whenever a new product 3 enters the market. This rationing of consumers occurs mainly at the low end, which is again consistent with what we observe. In Chapter 4 we study the apparent failure of the law of one price in the European automotive industry. There has been a long persistent and documented price dispersion across European Union member states for identical, or nearly identical models for the past 2-3 decades. Some of the previous literature focused product dierentiation, trade liberalization, exchange rates uctuations, and more recently strategic pricing. Histori- cally prices have converged some due to market integration and the elimination of trade restrictions in the EU, but still signicant dierences persist. We analyze a panel data set of prices for dierent car models across 21 EU member states and nd that international price discrimination and possible collusive agreements between the major manufacturing groups lead to price dierences that are not likely to fully converge as long as the exclu- sive dealership system that prevents arbitrage is in place. Our data structure allows us to analyze country specic eects and point to the signicant demand side dierences that exist across countries and also to the country specic market structures. One particu- lar result that contradicts previous studies is that the cheapest market, once we control for purchasing power, is the UK market which was previously thought to be the most expensive. From a market structure point of view the UK is actually the most competi- tive market which is consistent with having the lowest overall prices. In Germany, Italy, and France on the other hand, markets are highly concentrated and dominated by three major manufacturing groups. The pricing patterns observed are consistent with collusive behavior among these groups and cars are more expensive on average in these countries, even after controlling for income and physical characteristics. 4 Lastly, Chapter 5 deals with pricing of contracts under asymmetric information. When rms contract under asymmetric information there is always the risk of default and liti- gation rising from under-estimating the costs or over-evaluating the benets on the unin- formed side. These information asymmetries can result in large ineciencies. The existent legal rules play major roles in providing the right incentives to the contracting parties and minimizing these ineciencies. We focus on a contracting auction where the buyer has private information regarding the true cost of the project. We study the bidding process, the arrival of con icts, the litigation process, and the eciency implications of three dif- ferent rules of liability. We nd that a non interference rule that leaves both parties where they were at the time of litigation is more preferable from an eciency standpoint to both a strict liability rule and to an evidentiary rules that allows for the private information to be made public and awards damages based on this private information. The simple intu- ition of this result is that, by non-interfering, the court allows the parties to internalize these ineciencies. The informed party has the incentive to make his private information public while the uninformed party has the incentive to bid and price competitively. On the other hand, awarding any kind of damages to the informed party gives the wrong incentives to both parties: it gives the buyer the incentive to withhold his private infor- mation and it gives the seller the incentive to over-bid in order to insure against future losses rising from litigation. This over-bidding leads to large eciency losses. 5 Chapter 2 Underpricing, Excess Demand, and Secondary Markets: Evidence from the Entertainment Industry 2.1 Introduction Much traditional economic literature assumes that markets always clear. In such a set- ting, secondary speculative markets will not exist, since producers extract all possible prots, and nothing is left on the table for resellers. Persistent excess demand and sec- ondary markets are however frequently observed phenomena. Dierent brokers, usually not associated with the producer, operate on these markets selling goods at prices sig- nicantly higher than the original face value price. This phenomenon is especially true today, with the development of online marketplaces. We observe an explosion of sec- ondary marketplaces where anybody can trade goods on websites such as Ebay, Stubhub or Craigslist. A recent example is the popular video gaming console Wii, produced by Nintendo. The Wii has been constantly under-supplied for almost three years since its launching. During all this time, it has been sold at exactly the same price of 250 dollars, while resellers were able to generate signicant markups on secondary markets. Avid customers were 6 searching for days for an available console, web trackers were created so that people could track their local stores for in-stock items, and it was common to see Nintendo Wii consoles, sealed in their original packaging, auctioned on Ebay for up to 450 dollars. Additional examples can be found in the entertainment industry, where tickets for popular events are often traded on secondary markets. How do we explain such a marketing strategy? Why do producers maintain excess demand on the market and leave prots on the table? Why do they not increase prices to a level that would clear the market, and capture all the prots for themselves? Nintendo is well known for such rationing strategies. Nintendo's vice president of marketing, Peter Main, started his career by studying the rise and fall of Atari, another video games producer with great market success. He was convinced that scarcity sustains demand. He started employing a successful marketing strategy of both stimulating demand and rationing supply, in order to keep consumers' interest high 1 . Mr. Main was reported stating that "with demand projected at 43 million units, ideally we would like to produce 40 million" 2 . In fact, in 1988, with demand projected at 45 million game cartridges, and retailers requesting 110 million cartridges, Nintendo only shipped 33 million - an even lower fraction than what Mr. Main admitted. Capacity constraints, mistakes in estimating demand or sub-optimal pricing are often cited as explanations for excess demand. However, when excess demand persists for many years, one needs to question the validity of such arguments. Rather it seems likely that we are dealing with an optimal strategy designed for a more complex, dynamic world. Maintaining shortages on the market can serve to create a "buzz" around a product, which like advertising, serves to bring attention to the product. Producers may also be 1 The Games Played for Nintendo's Sales - NY Times 1989 2 Adweek's Marketing Week 1989 7 interested in selling complementary products whose demand can be stimulated by the perceived popularity of the principal product. Sometimes, when large initial investments are made, sellers are extremely averse to demand uncertainties and are eager to shift part of the risk to speculators. This chapter presents several theoretical models, and assembles a unique data set of both primary market prices and secondary market markups, for a sample of 45 popular music concerts. The data explains the determining factors of both primary market pricing, and observed price dierences, and ts the theory well. The focus is on the ticketing markets, since data is richer and easier to collect and much of the theoretical literature focuses on ticketing markets since they have unique characteristics not present elsewhere. However, important insights can be extrapolated to other markets with persistent excess demand. The results show that secondary markets do not emerge because of the inability of the promoters to price discriminate eciently. The main factors that drive both pricing on the primary market and secondary market markups are the band- and location-specic variables. More experienced and successful artists price higher, price discriminate better, but also leave more money on the table. Also bands with more studio albums, and bands with more recent albums price lower, and use less price discrimination. This supports theories of risk sharing, social externalities, and complementarities. Social in uence in particular plays a major role: low valuation customers can be in uenced by social pressure to update their valuations and, under such conditions, sellers nd incentives to articially maintain excess demand. While risk sharing and complementarities can explain excess demand in the presence of capacity constraints, social in uence is virtually the only possible explanation in the absence of such constraints. 8 2.2 Pricing in the Entertainment Industry The markets for concert tickets present a number of interesting pricing issues. Prices vary because events take place in dierent locations and on dierent dates, because seats are of dierent qualities or located in dierent places, because complementary goods are sold at the venue, or because discounts are oered for season tickets. A major issue is that seats are not perfectly homogenous products. The location of the seat matters for the overall satisfaction obtained from attending a concert. Since it takes time to attend a certain event, the exact day of the event matters as well. There is also a strong social element to entertainment events. People attend such events for a socializing experience, because others are going too. Finally, live events are experience goods, with the exact quality unknown before consumption. A few of the major literature strands that try to explain why under-pricing and excess demand occur are presented in the following paragraphs. 2.2.1 Scaling the House One of the most important issues, specic to live entertainment events, has to do with taking advantage of the dierences in seat location and quality. A oor seat at a basketball game is not only closer to the action, but at the same time it is usually much larger and more comfortable than a seat in the nose-bleed section. The same is true for music concerts, or any other entertainment event. People prefer, and they are willing to spend more money for seats that are closer to the stage, or for seats that are larger and more comfortable. Generally speaking, promoters take advantage of this, and price accordingly. The front rows are usually priced higher, and the price is reduced progressively all the way 9 to the last rows. This practice is commonly referred to as \scaling the house". It is essentially a price discrimination strategy which varies greatly from event to event - from a uniform pricing strategy, where all tickets in the house sell at exactly the same price, to a very ne scaling. From a purely theoretical perspective, no two seats oer the same experience, and they should therefore be priced dierently. However, in practice, it is almost impossible to price each individual seat as a distinct good, and hence, groups of similar seats are usually sorted into categories that are priced dierently. Most live events usually have anywhere between one and ve pricing zones, with two or three being the most common numbers. A theoretical framework for dealing with this issue has been oered by Rosen and Roseneld (1997). Huntington (1993) provides empirical evidence that shows that, com- pared to uniform pricing, revenues are increased by scaling the house. His study on the theater industry shows that scaling the house could increase revenues by an estimated 24 percent after controlling for seat capacity and number of performances. Papers by Leslie (2004), and Courty and Pagliero (2012) are also providing more recent evidence that scaling the house does increase revenues and should be preferred to a uniform pricing scheme. Surprisingly though, this practice is somehow underused in the industry. In a 2003 survey, 43% of all live events were found to use uniform pricing. I will test empirically whether a poor use of this strategy is to be blamed for the emergence of secondary markets. According to theory, if the house is scaled and priced optimally, there should be no left-over prots for brokers. On the other hand, if a less than optimal segmentation is used, brokers can arbitrage the better seats in the house to customers willing to pay the premium. They will buy good seats at the average value and resell them at their true market value, thus making a prot. One should expect that 10 a ner scaling will result in smaller secondary market markups. Another conclusion that arrives from this theory is that better seats, generally yield a higher price dierence. 2.2.2 Sharing Risk with Speculators Another theory that tries to explain the emergence of secondary markets, stems from the idea that demand is uncertain, and most times, dynamic pricing cannot be employed. Many times, promoters invest large amounts of money in securing a venue or an artist. For instance opera houses contract with the main performers years in advance of the show and sports franchises write multimillion dollars contracts with star players that last multiple years. This might make the promoters extremely risk averse with respect to demand uncertainties. A possible solution is to oer the product at a low enough price to attract both regular customers and speculators. The promoter will thus transfer some of the risk to speculators who can charge a higher price if demand turns out to be high, but also incur losses if demand turns out to be low. The presence of complementary products further skews the promoter's incentives, and provides support to this theory. Tickets related revenue might be one of the many ways a certain producer can generate prots. Consider for instance that when people attend a live event, they buy snacks and drinks at the venue, that often amount to more than the price of the ticket itself. Therefore, promoters might have a strong incentive to maximize attendance, rather than ticket revenue. A theoretical model of risk sharing will be presented, following Su (2010), which shows the incentives of producers to underprice and attract speculators, the speculators' incentives to enter the market, and the incentives of certain consumers to wait and buy from speculators. The model will also be empirically tested using the available data on ticket prices. 11 2.2.3 Social Externalities A critical aspect of ticket pricing is the social dimension associated with live entertain- ment. Consumers often make their decisions to attend a certain event after being rec- ommended to do so by friends, and they often attend the event in groups. Live events are also experience goods, with the exact quality of the show ex ante unknown. Under such circumstances, people often consider to attend only the more popular events, with a certain success history that signals good quality. Social interactions could potentially explain why producers deliberately underprice and ration supply. Under-pricing guarantees a sellout, and maintaining excess demand generates a certain hype and prestige. In a way, it is a cheap form of advertising. Social externalities are not only present in the entertainment industry, but also for popular electronics, like the Apple Ipad and Iphone, or video-gaming consoles such as Nintendo Wii, Sony Playstation and Microsoft Xbox360. By rationing supply, at least during the market introduction period, producers might extract more prots in the long run by attracting those customers who might otherwise not buy the product if it was readily available to everyone. We can observe this kind of behavior virtually with every popular electronic gadget that is being launched on the market. Fans line up in front of the stores days in advance of the launching date, and they put their names on pre-order lists. This generates hype and brings in new customers. Becker (1991) and a following paper by Karni and Levin (1994) are among the few who tried explaining how social interactions might aect the pricing decision of rms, specically why rms with popular products do not raise prices even when confronted with persistent excess demand. These types of social interactions are extremely hard to 12 quantify and test empirically, but we can still argue their presence and eects on prices. This chapter develops a simple theoretical model of social in uence, that can explain excess demand, and ts well some of the observed empirical evidence from secondary markets. Another type of social externality is the in uence that a popular product has on the demand for its complements, and pricing complementary products is a common issue in these industries. It can take many forms, from pricing tickets alongside food and beverages at a sports event, to pricing albums and live events, in the case of musicians. Hendricks and Sorensen (2009) show how releasing a new successful album generates an externality and increases sales of previously released albums for musical artists. When a relatively unknown band releases an album that turns out to be successful, the new album acts as an information transmission device, and customers go back to purchase the band's past albums, that were previously unknown to them. Traditionally, musicians have been going on tours to promote studio albums, and judg- ing from that perspective, one would think that another reason to underprice live events is to generate popularity and promote album sales. This is however not always true, as the opposite can also happen. A recent trend shows old bands reuniting, recording a single, and using that as a device to promote a tour. Small and up-and-coming artists usually use the same strategy. With the recent technological boom, and the advent of le-sharing technologies, album sales do not seem to be regarded as well as they used to be. Revenues from album sales have been plummeting during recent years and many artists, especially the smaller and less successful ones, prefer allowing consumers to download their music for free, just for advertising purposes. Mortimer, Nosko and Sorensen (2010) empirically tested for this, and found that the introduction of le-sharing technologies reduces album 13 sales and increases live performance sales for small artists, while the eect for more pop- ular artists is not signicant. To account for complementarity externalities, this chapter presents a simple theoretical model which shows that when certain complementarities are present, producers change their pricing strategies in a way that is fairly consistent with the observed pricing data on the primary markets. Scaling the house, sharing risk with speculators, social externalities, and complemen- tary goods are the main issues I address in this chapter. There are other pricing issues to be considered when dealing with ticket pricing in a more general context. They are however, more suitable for other industries such as sporting events, where bundling and pricing multiple events is a common issue, or the transportation industry, where seat quality and advance sales play a much bigger role. The main goal of the chapter is to provide the empirical evidence needed to support or disprove the theories existent in the literature. There is a direct empirical test that can be employed to verify the validity of the scaling the house hypothesis since the level of house scaling can be measurable. The risk sharing theory and the theories dealing with social externalities are not as easy to test since the sensitivity to social in uence or the strength of complementarity are not directly measurable. The methodological approach in these cases is building simplied theoretical models based on the existing literature and try to test the predictions of these models using available data. It is, in essence, an eort to falsify these theories. The main shortcoming of this approach is that it is rather hard to dierentiate between the dierent channels through which prices are aected. However, the results are still highly suggestive and, at least for the entertainment industries which we study, it is arguably true that all these causes are at work simultaneously. 14 2.3 A Model of Risk Sharing with Speculators This section presents a model with speculators and random demand, which is a simpli- cation of a model following Su (2010). I account for the possible rationing of consumers during periods of high demand and also, in order to better re ect the reality of the enter- taining events, I introduce the idea of complementary merchandise purchases. 2.3.1 Describing the Game There is one capacity constrained seller who sells tickets to an event. The capacity of the venue is denoted by K and is exogenously given. The seller also sells complementary merchandise that enhances the attendees' experience. I assume, without loss of generality, that both the cost of the tickets and the merchandise are negligible, and attendees buy merchandise according to their left over consumer surplus after buying tickets. I also assume that merchandise purchases convert into utility at a one to one ratio. Hence, from a consumer's perspective, utility maximization means surplus maximization, and the merchandise purchase decision simply results in consumers spending their entire surplus on merchandise. From the seller's perspective, it does not matter whether consumer surplus is extracted through a higher ticket price or through merchandise sales. We often observe unpopular events being severely under-priced in order to generate a big turnout that can still be protable given the large markups of food, drinks, and merchandise being sold. On the demand side, I assume two types of consumers: high type and low type consumers. The low type consumers have low valuation for the event, denoted by V L . I assume there are enough low valuation consumers on any given market, at any given time, 15 to completely sell out the event. One can think of the low type consumers as being the general population of any given event location. On the other hand, any sports franchise, or any rock band has devoted fans who are willing to pay a higher price. These are the high type customers, with valuation denoted byV H . I assume this segment of the demand to have a random component. More specically, there is a deterministic component of the high type demand, which we denote by W , and a random component, denoted by X. In the rst period, after the seller announces the event and the ticket prices, there are W high value customers arriving on the market. A portion of these customers are \fanatic" or \myopic" customers, while the remaining are \strategic". Fanatic consumers buy tickets whenever they are available at a price below their reservation price, while strategic consumers are forward looking, and they only buy tickets when it is optimal to do so. Denote the fraction of strategic customers with . The stochastic part of the high valuation demand consists of a random number of customers, X, who arrive on the market in period 2. I assume X to be uniformly distributed between 0 and K. The specic distributional assumptions ease the calculations, but one could easily extend the model to other types of distributions without aecting the qualitative implications. The next segment of the market consists of speculators. Speculators do not have any valuation for the event itself, they buy tickets only to resell them for a prot. I assume the number of speculators to be exogenously determined and market specic, rather than event specic. Let S be the number of speculators active on any given market. Each speculator can buy only one ticket. The decision to buy will depend on the face value price set by the seller. Speculators will only buy if it is protable to do so (i.e. if the expected price on the secondary market exceeds the face value of the ticket). A very important thing to note is that the seller cannot use dynamic pricing. If it could, there would be 16 no reason to allow speculators on the market, since the seller could essentially fulll the same role in the second stage of the game, after the random demand is realized. This phenomenon is quite common in the entertainment industry, especially in those markets with a repeat player, such as sports franchises or touring bands. A sports franchise who operates year after year in the same market, or a rock band who is touring the country, usually refrains from using dynamic pricing, although that might increase revenue, at least in the short run. A likely explanation is that repeat players do not want to create a bad precedent, nor do they want to alienate customers. Consider how would a customer who bought his ticket in advance feel, if he nds out the same ticket is being sold for less on the day of the event? There is actual empirical evidence provided by Leslie (2004) showing that oering steep discounts on the event day lowers long run revenues for Broadway shows. We assume the low valuation, V L to be suciently low relative to V H , such that it is never optimal for the seller to sell out the event by charging a suciently low price to attract the low valuation customers. In general this is true, and one can see many events that are not sold out. Football games are sometimes blacked out on television due to the game not being sold out, or teams that are constantly struggling to ll out seats and are looking to relocate to better markets are common these days. There is no doubt that any event promoter could, in fact, sell out any event for a suciently low price. I also assume W < K, S > W and (1)W +S < K. In other words, there are not enough high value customers in period 1 to guarantee a sellout, there are more speculators active on the market than there are strategic high valuation customers, and also the speculators and myopic high type customers cannot guarantee a sellout in the rst period. These last assumptions are not critical for the model, but they ensure that all possible demand 17 situations can occur at the second stage of the game. The timing of the game is the following: rst, the seller announces the ticket price P , then the speculators and the customers (both the strategic and the fanatic ones) make their purchasing decisions, then the random demand X is realized, then speculators set the secondary market price P S , then the remaining high valuation customers buy, and nally, if there are any tickets available at a low enough price, some low valuation customers can also buy. On the day of the event, every attendee buys merchandise according to their surplus, as explained earlier. I implicitly assume the high valuation customers always have priority in buying tickets. That is, if one ticket is available at a low enough price so that both a high valuation and a low valuation customer would like to buy it, the high valuation customer will end up purchasing the ticket. This can be justied in a number of ways. Fans usually look to buy tickets well before the general public does. Also a customer with high valuation can always slightly overbid a low valuation guy. Many promoters also give priority to members or to previous buyers, in the case where some competition for tickets exists. 2.3.2 Equilibrium Analysis We will solve the model using backward induction, starting with the last stages and moving backwards to the rst stages. First, note that the merchandise purchasing decision in the last stage does not aect the consumers' optimization problem in the intermediary stages, since essentially consumers care only about maximizing their surplus. It goes without saying that the "fanatic" consumers act myopically, and their decision is even more straightforward. From the seller's perspective, it does not matter whether the surplus is extracted through ticket sales or merchandise sales, so there is no direct strategic behavior on the seller's part to in uence higher or lower merchandise sales. The amount 18 of merchandise being sold only matters for the seller's decision to allow speculators on the market or not, which will be discussed in more detail later. Basically, there will be a tradeo between prots lost during periods of high demand and prots gained during periods of low demand, which the seller has to take into account. For now, we will focus on the sub-game where speculators are allowed on the market and we will show later that this is indeed optimal from the seller's perspective. The situation presented here ts very well the reality of sports franchises and, more generally, repeat sellers who face large demand uctuations during a full season and prefer smoothing and maximizing their attendance, rather than simply maximizing ticket revenue. In the second stage of the game, after the random component of demand is realized, there will be some form of competition between the seller and the speculators. Also, if demand is suciently high, there will be some rationing, which I assume to be random. If there are two customers ghting for the same ticket, each has an equal chance to get it. Thus, for the strategic high value customers, their decision to wait or buy in the rst period depends not only on the expected price, as argued in Su (2010) model, but also on the probability they will be rationed in stage 2. We will deal with the strategic consumers' decision a bit later. First, let's analyze the speculators' pricing decision. 2.3.2.1 Speculators Pricing In stage two, after speculators observe the realized high type demand, they set the sec- ondary market price P S . Let W 2 denote the number of rst period strategic consumers who decided to wait. The entire high type demand in period 2 will thus be equal to X +W 2 . Also letK 2 represent the number of available tickets the seller has, after selling 19 to speculators and high type customers in period 1. We characterize the pricing strategy of speculators in the following lemma: LEMMA 1. Depending on the realized demand and the seller's price P , competition among speculators, and competition with the seller, results in the following pricing strategy for speculators: P S = 8 > > > > > > > < > > > > > > > : V L ; if X +W 2 <S P; if S <X +W 2 <S +K 2 V H ; if X +W 2 >S +K 2 To prove the previous lemma, we analyze the three possible demand scenarios: low demand, high demand, and intermediate demand. First consider the case where demand is very small, that isX +W 2 <S. In this case, there are less high type customers willing to purchase a ticket than there are speculators with tickets to sell. Speculators will engage in price competition among themselves until the point where P S = V L . At this point, all high type customers will buy, and also there will be enough low type customers to clear the speculative market. The seller cannot adjust its price and hence, will not be able to sell additional tickets. There will be no rationing for high type customers, some low valuation customers will get to buy tickets, and there will be empty seats. No other prices can constitute an equilibrium in this sub-game. Any price lower than V L cannot be an equilibrium outcome, since any speculator can increase his price to V L and still sell his ticket for sure. At the same time, any price higher than V L cannot be an equilibrium, since at this price, there will be at least one speculator who will not be able to sell his ticket and thus could prot from deviating. 20 The other extreme case is when demand is high, that is X +W 2 >S +K 2 . There are more high type customers willing to buy a ticket than there are actual tickets available (both from the seller and speculators). It is pretty straightforward that in this case the speculators can actually extract all the surplus from consumers by charging V H . Customers will rst buy from the seller, who only charges P and, after the seller sells out his leftover capacity, they will buy from speculators, who are guaranteed to nd a buyer. Since demand exceeds supply, there will be some rationing. Some high type customers will not be able to get a ticket, and it might be the case that a strategic type who decided to wait in period 1 will not be able to get a ticket anymore. We need to take that into account when analyzing the strategic type decision later on. Under this scenario, there will be no low type consumers getting tickets, and there will be a sellout. Finally, consider the intermediate demand situation. IfS <X+W 2 <S+K 2 , demand is enough to cover the speculative supply, but not enough to generate a sellout. In this situation, it is optimal for speculators to set their priceP S =P . I assume speculators can sell their tickets before the seller, since they are able to slightly undercut the seller's price, even if by a negligible amount. After they sell all their tickets, there will be some leftover high type customers who will buy from the seller, but there will still be empty seats in the stands. There will be no rationing, and no low type customers can get access to the event. Any other pricing strategy cannot be an equilibrium. It would not make sense for any speculator to go below P , since they are guaranteed to sell at this price. Also, any price above P cannot be an equilibrium, since there will be at least one speculator who will not be able to sell his ticket, and thus would prot from deviating. Note that K 2 = KS (WW 2 ). After selling to speculators and to some high type customers in period 1, the seller has only a limited number of tickets left. He 21 cannot oversell the given capacity K. Hence the inequality X +W 2 < (or >)S +K 2 can be rewritten as X < (or >)KW . Given the three possible demand outcomes and the optimal pricing strategy described above, the expected resale price for speculators is given by the following: E(P S ) =Pr(X <SW 2 )V L +Pr(SW 2 <X <KW )P +Pr(X >KW )V H Speculators will only enter the market if the expected resale price exceeds the price set by the seller. 2.3.2.2 Primary Market Pricing In the rst period, the seller has the option of setting any price he considers optimal. Naturally, it wouldn't make sense for the seller to oer a price lower thanV L , since at this price, a sellout is guaranteed no matter what the random demand will be. Also, the seller cannot price above V H , since that wouldn't generate any sales. Moreover, we assumed it is always optimal for the seller to sell to the high type customers only, at the high price (V H ), rather than selling out by charging the low price (V L ). Therefore, the seller is confronted with solely one decision: should he price low enough for speculators to nd it optimal to buy tickets, or should he eliminate speculators from the market by charging a higher price? Speculators will enter the market if the price charged by the seller is not higher than the expected resale price, so the seller can either charge P = E(P S ) and attract speculators, or simply charge V H and eliminate speculators from the market. For the time being, we will assume that attracting speculators is preferred by the seller. Later on, we will prove that this is indeed protable. 22 2.3.2.3 Strategic Consumers' Decision After the seller sets the face value price, if this price allows for speculators to enter the market, strategic consumers are faced with the choice of buying a ticket immediately from the seller, or waiting until period 2 and buying a ticket from either the seller or the speculators. Naturally, if they choose to wait, they are exposing themselves to the risk of being charged more, or even rationed in the second period. On the other hand, if demand turns out to be low, they will benet from waiting and will be able to secure a ticket at a much lower price. We characterize the equilibrium strategy of strategic consumers in the following lemma: LEMMA 2. If speculators are present on the market, all strategic consumers choose to postpone their purchasing decision until the second period. To prove this, consider the alternatives a strategic type faces. Alternative one is buying straight from the seller in period one at the price of P . Hence, any strategic type who does not wait, and buys in period one, will get the following surplus: nw =V H P Now consider the alternative of waiting to buy in period two. Depending on the realized demand, a strategic type who waits will pay dierent prices, and hence realize dierent surpluses. Additionally, there is a chance he will be rationed if demand is very high. In the case of low demand, every strategic consumer is guaranteed to be able to buy a ticket from speculators at the price ofV L . They will all get a surplus ofV H V L . If demand is moderate, again each strategic consumer is guaranteed a ticket and it does not 23 matter if they buy from speculators or from the seller, since in this case the prices are the same. The surplus in this case will thus be V H P . Finally, in the case of high demand, strategic consumers might be rationed (which will yield zero surplus), they might get to buy a ticket from speculators at a price of V H (which again will yield zero surplus), or they might be able to buy a ticket straight from the seller, at the price P , which will yield V H P surplus. If we denote the probability of low demand by p 1 , the probability of moderate demand by p 2 , the probability of high demand by p 3 , and the probability of getting a ticket from the seller in case of high demand by, then the expected surplus for a strategic type who waits will be: w =p 1 (V H V L ) +p 2 (V H P ) +p 3 (V H P ) We show that the surplus from waiting is greater than the surplus from buying now. Remember that, in order to attract speculators, the seller has to set his price P at a level that does not exceed the speculators' expected resale price. Hence, given the above simplied notations for the three probabilities regarding the dierent demand scenarios, we have: P =E(P S ) =p 1 V L +p 2 P +p 3 V H and since p 2 = 1 (p 1 +p 3 ) we get: P = p 1 V L +p 3 V H p 1 +p 3 24 Hence, we can rewrite V H P =V H p 1 V L +p 3 V H p 1 +p 3 = p 1 (V H V L ) p 1 +p 3 and w =p 1 (V H V L ) +p 2 p 1 (V H V L ) p 1 +p 3 +p 3 p 1 (V H V L ) p 1 +p 3 = = p 1 (V H V L ) p 1 +p 3 (p 1 +p 3 +p 2 +p 3 ) = = (V H P )(p 1 +p 2 +p 3 +p 3 ) = = nw (p 1 +p 2 +p 3 +p 3 ) = = nw (1 +p 3 ) which proves that the surplus from waiting is higher, since both p 3 and are positive numbers. We can now prove the protability of allowing speculators to enter the market. 2.3.2.4 Protability of Allowing Speculators Consider rst the high demand case. Under this scenario, not allowing speculators would mean the seller prices at V H and guarantees himself a sellout, since high demand means there will be enough high type customers to completely cover the capacity. That would translate in KV H prots for the seller. Allowing speculators under this demand scenario would mean the seller rst sellsS tickets to speculators at a price ofP and the remaining KS tickets directly to consumers at the same price of P . Note that some of these KS consumers, who buy directly from the seller, are myopic consumers who buy in period one, while some are new customers who arrive at period two. Regardless of that, 25 all of them are high type consumers who achieve a surplus of V H P and, as assumed, spend their entire surplus in buying merchandise. That means that the seller still captures the entire surplus of these KS consumers, as he would if there were no speculators. However, the rest of the attendance is composed of S high type customers who get their tickets from speculators at a price ofV H and hence, there will have no surplus left to buy merchandise. For these S consumers, the seller can only get the price that speculators initially pay. Therefore, summing all up, under the high demand case, the seller is worse o with speculators on the market. Compared with the case where the seller would price the speculators out of the market, its net loss is: Seller =S(V H P ) Now consider the intermediate demand case. The expected high type demand in period two is denoted by E(X). Hence, the total expected high type demand, which is the same with expected attendance (since low type consumers don't come into play under this scenario) can be denoted byA =W +E(X). When speculators are present, customers buy at the same price ofP regardless whether they buy from speculators, or directly from the seller. That leaves them withV H P surplus that they spend on merchandise, which means that the seller extracts the same prots that he would if he priced the speculators out of the market. Essentially speculators make no prots under moderate demand, and the seller gets V H from each attendee (partially from the ticket price, and partially from merchandise sales). This is equivalent from the seller's perspective with charging V H in the rst place, and eliminating speculators from the game. 26 Finally, we turn our attention to the low demand case. If the sellers allows speculators, he sellsS tickets to them for a price ofP , which generates a prot ofSP . The seller also sells directly to the myopic type in period one, at the price ofP . These myopic customers buy merchandise once they attend the event, which will eventually generate a prot of (1)WV H . The seller will also earn additional prots from merchandise sales to high type customers who buy from speculators. These customers buy tickets at a price of V L , then they each spend V H V L on merchandise. The low type consumers who manage to buy tickets don't buy any merchandise, since they have zero surplus. Remember that all strategic customers wait until period two, so there are W strategic customers, plus the expected amount of new customers arriving at period two, E(XjX <SW ). Since we assumed uniform distribution forX we can write the seller's prot if he allows speculators: S Seller =SP + (1)WV H + (W + SW 2 )(V H V L ) Alternatively, if the seller decides to price speculator out of the market, he will sell to the entire period one demand and to the expected period two demand, at a price of V H , which yields the following expected prot: S Seller = (W + SW 2 )V H Therefore, under the low demand case, the seller's net gain from allowing speculators on the market is: + Seller = S Seller S Seller =SP S +W 2 V L 27 The seller will allow speculators on the market if the expected gains are greater than the losses: p 1 + Seller >p 3 Seller which can be rewritten as: p 1 SPp 1 S +W 2 V L >p 3 S(V H P ) () (p 1 +p 3 )SP >p 3 SV H +p 1 S +W 2 V L () (p 1 +p 3 )S p 1 V L +p 3 V H p 1 +p 3 >p 3 SV H +p 1 S +W 2 V L ()p 1 SV L >p 1 V L S +W 2 ()S > S +W 2 ()S >W which is true by assumption. It is therefore proven that it is always in the seller's best interest to underprice its tickets in period 1, and allow speculators on the market, in spite of potential future competition during periods of low demand, or potential losses under periods of high demand. 2.3.2.5 Describing the Equilibrium We have shown that, under demand uncertainty, the seller will nd it optimal to share risk with speculators, and set a face value price equal to the speculators' expected resale price. More specically, given the distributional assumptions, the face value price will be: P = (SW )V L +WV H S + (1)W 28 Given this price, speculators enter the market, the fanatic portion of the demand buys directly from the seller in period one, while all the strategic customers wait until period two, with the hope of buying a cheaper ticket from speculators. In period two, the random demand component is realized (more high type consumers arrive on the market), the seller maintains his price and tries to sell his leftover inventory, and speculators set their resale price: P S = 8 > > > > > > > < > > > > > > > : V L , if X <SW P , if SW <X <KW V H , if X >KW Both speculators, and the seller (under moderate and high demand) sell tickets to the residual demand. Depending on the realized demand, some low valuation customers might get tickets (in the case of low demand), and some high valuation customers might get rationed (in the case of high demand). The main qualitative characteristics of the equilibrium match fairly close the reality of these industries. There is underpricing, excess demand, and signicant prots left on the table for brokers, when demand is high. There are also situations, when demand is very low, when resale prices are set below the face value. Also, when demand is low, there is competition between seller and speculators, which is a serious problem for seller from both a prot, and image perspective. Michael Young, Chief Revenue Ocer for the LA Dodgers was complaining about this problem in a recent lecture he gave to business students at USC. He was arguing that customers were coming to attend games that were undersold, and were turned away from the gates by the high prices at the box oce. They were complaining that similar seats were sold online for 5 dollars, while the box oce price was 30 dollars or more, and they could not understand 29 why the Dodgers would not lower their prices with so many empty seats.The seller has his hands tied, since lowering the price might set up a bad precedent, and get season ticket holders angry. But refusing to lower the price while having a lot of empty seats might alienate casual customers. We focus mainly on the popular event situation, but the model is capable of capturing all aspects of the real world. Note that, from an ex ante perspective, the seller likes to lower his risk by underpricing and attracting speculators, but from an ex-post perspective, the seller dislikes the presence of these speculators on the market. This is aggravated by the fact that, in reality, many resellers are actually ticket season holders. They essentially act like speculators by buying discounted packages but then resell tickets to certain undesirable events. Sellers are constantly looking for ways to stop these patrons from reselling their tickets for low demand events by providing additional \members only" benets which can be oset by extra revenues generated from the resulting lower competition. 2.3.3 Comparative Statics In order to t the model to the actual data collected from these markets we need to consider the model implications and see if they correspond to the empirical evidence. The focus will mainly be on the high demand situation, since the analysis focuses on popular products. The analysis regarding pricing on the primary market is the same for all cases. The only part of the analysis that requires focusing on a specic demand situation is the analysis of the secondary market markups. These markups are V H P in 30 the model. We analyze the eects of dierent parameter values on the two variables, at the theoretical level. The model predicts the following functional forms: P = (SW )V L +WV H S + (1)W and P = SW S + (1)W (V H V L ) Taking partial derivatives with respect to each parameter yields the following com- parative statics results for the two variables of interest: Table 2.1: Comparative Statics Variable of Interest Parameter Eect P V H + S - V L + + W + P V H + S + V L - - W - A higherV H results in both higher prices on the primary market and higher markups for the speculator. A higher number of speculators means that the price needs to be smaller on the primary market, which in turn will yield higher markups for each individual reseller. The valuation of casual fans is benecial for the seller, since it increases the expected resale price, but it hurts speculators, which have a smaller prot margin when demand is high. Both a larger proportion of strategic fans, , and a larger number of certain high valuation customers, W , result in higher prices on the primary market, and 31 lower markups on secondary markets, as they both increase the expected resale price, which allows the seller to price higher and still attract speculators. We will later test to see whether these theoretical predictions t the empirical facts. 2.4 Complementarities and Social In uence In this section, I develop two simple models that t the two separate ticket markets. I start with a model of social in uence in the spirit of Becker(1991) and follow with a model with complementarities. I show that, when demand is positively correlated to the popularity of a product and the level of excess demand, producers might have incentives to under-supply the market. The optimal level of excess demand depends on market size, sensitivity to social in uence, and consumers' valuation. On the other hand, when complementarities are present, and consumers' utility from buying an album is positively related to the popularity of a live event, promoters lower ticket prices in order to generate hype around the band, and increase album related revenue. The models focus on two distinct factors that aect these markets dierently. The social in uence model assumes uniform preferences and hence, cannot t the primary market pricing, but ts fairly well the secondary market picture. On the other hand, the model with complementarities does not include excess demand, but ts the primary market pricing. There are two separate eects that can cause under-pricing and excess demand on these markets. Prot maximization under social in uence depends on excess demand regardless of the price, while under complementarity externalities, excess demand is not necessary, and all that matters is lowering the price of the good that creates exter- nalities to increasing its consumption. When capacity constraints are present, reducing 32 prices can cause excess demand, but in itself, this is not necessary. As a matter of fact, for some industries we do not observe excess demand while arguably these complementarities are present. For this reasons, I choose to focus separately on these two eects in two separate models, and clearly distinguish between them. 2.4.1 A Model with Social In uence We consider a situation where a monopolists sells a product on a market withN consumers in two separate periods. We assume consumers have uniform preferences and they demand one unit of the good in each period. More specically, let consumers' valuation be V t , witht = 1; 2. In period one, letV 1 =V . Social in uence manifests in that, in period two, consumers update their valuation depending on the level of excess demand observed in period one. Specically,V 2 =V +F (x), wherex is the level of excess demand andF (x) is some function of it. The monopolist decides how much to produce and sell in each period. Since consumers have uniform preferences, the pricing decision is simply setting P t =V t . The monopolist's main problem is to choose the optimal level of excess demand in period one. In period two, the monopolist will serve the entire market. The prot maximizing problem can therefore be written as: max x =V (Nx) +N[(V +F (x)]; subject to Nx 0 We assume a specic form for the functionF (x) in order to capture a number of desir- able properties. We assume that some excess demand increases consumers' valuations, but at the same time, too much excess demand is not good, since it might anger consumers. 33 We also need to have zero external eect if there is no shortage, or if the monopolists doesn't sell to anyone in period one. We therefore choose the following quadratic form: F (x) =a(Nxx 2 ) which ensures that F (0) = F (N) = 0 and, for any level of excess demand between 0 and N, consumers' valuation is rst increasing in x, then decreasing, for large values of x. Parameter a represents the sensitivity to social in uence. Solving, yields the optimal level of excess demand: 8 > > > < > > > : x = aN 2 V 2aN ; if aN 2 V x = 0; if aN 2 <V The monopolists is faced with a tradeo between losing sales in period one, and generating larger revenues in period two. If the sensitivity to social in uence and the market size are small relative to valuation, then there is no need to generate excess demand, and the monopolist will simply sell to the entire market at the price of V . If the opposite is true, then the second period benet of marginally increasing the valuation by under-producing, exceeds the loss of sales from period one. In this case, the monopolist should restrict its production and ensure the optimal level of excess demand is achieved. When sellers allow a larger level of excess demand, resellers can extract higher prof- its. We can therefore link the theoretical variables from the model to the actual mar- ket variables, and see whether the theoretical implications hold. The model predicts that, under certain conditions regarding market size and consumers' valuation, sellers 34 might have incentives to maintain excess demand, and the optimal level of excess de- mand depends highly on these factors. The comparative statics show how the optimal level of excess demand varies with the model's parameters. The excess demand increases with a ( @x @a = 2NV (2aN) 2 > 0), decreases with V ( @x @V = 1 2aN < 0), and increases with N ( @x @N = 2a 2 N 2 +2aV (2aN) 2 > 0). These eects intuitively show the tradeo that the seller is faced with, and they will be empirically tested later to see whether such models of social in uence can oer good explanations for underpricing and persistent excess demand. 2.4.2 A Model with Complementarities We develop a simple model with complementary goods, inspired by the literature on goods with network externalities 3 . The main dierence is that I do not require the goods to be consumed together for utility to be positive. Music consumers derive utility from albums and live events separately, but arguably there exist consumption externalities where the utility from buying an album is positively related to the popularity of a live event. The model is consistent with the primary market pricing observed in the data. It does not include excess demand, but we can argue that when capacity constraints exist and bind, as is the case with live events, lowering the price automatically results in excess demand. We however abstract from this, and only focus on the pricing decision on the primary market. We assume consumers have dierent individual valuations for albums and shows, and the utility from buying an album is positively correlated with the popularity of the show. This is based on the idea that consumers buy tickets for live events because they are fans 3 Katz and Shapiro (1985), Farrell and Saloner (1986), Economides (1989), Economides and Viard (2009) 35 of the band, but when the band records a new album, its quality might not always be clear. Consumers might derive higher utility from buying an album if the band had a very popular show, which might act as a quality signal. We assume the following functional forms for the utility functions: U s =sP s ; and U a =aP a +X s where U s and U a denote the utilities derived from attending shows, and respectively buying albums. Consumers have identically and independently distributed preferences for albums and shows, given by the parameterss anda. I assume a massN of consumers with individual preferencesa;sU[0;N]. P s andP a are the prices for shows and albums, X s represents the total number of tickets sold or how many people attend the concert, and is a parameter which signals the strength of the externality. We require 0 1 in order to get an interior solution, but theoretically the strength of the externality can be higher. When this happens, bands nd it optimal to oer free shows and make money solely from album sales. This phenomenon can be observed frequently, especially with new artists that are unknown to the public. For instance, there are street musicians who often perform for free, with the hope that people will like their music and buy their albums. Given the prices set by the band, consumers decide to buy tickets and/or albums if their individual utility is positive. That is, for shows, all consumers with s>P s will buy a ticket. This means that the quantity of tickets sold will be X s =NP s . On the other hand, for albums, consumers' utility is aected by X s . The marginal consumer, who gets zero utility from buying an album, has the individual preference parametera 0 =P a X s . 36 All consumers witha>a 0 will buy the album, therefore the total quantity of albums sold will be X a =NP a +X s . Given consumers' strategy, bands maximize their prots from selling albums and tick- ets: max Ps;Pa =P s (NP s ) +P a (NP a +(NP s ) which results in the following optimal prices: P s = N(1) 2 ; and P a = N 2 and the corresponding quantities sold and prot: X s =X a = N 2 ; and = N 2 2 : The second order conditions are satised for 2 [0; 1]. Note that a high = 1, implies a zero ticket price. In fact, if the externality is allowed to be even higher than 1, this will imply negative prices or subsidies for shows. While it is not the objective of this chapter to analyze this type of phenomena, it is worth noting that while not very common, there are situations where attendees are given free t-shirts or other merchandise to attend certain ticket-free events. Also note that in the absence of externalities, when = 0, the optimal prices, quantities, and prots are: P s =P a = N 2 ;X s =X a = N 2 ; = N 2 2 : 37 We can see that, when complementary externalities are present, bands have an incen- tive to lower the prices for tickets in order to increase the demand for albums. Prots from ticket sales will be lower, but the prots from albums sales will more than compensate for these partial losses. The model presents implications for both album and ticket sales, but in the absence of any album related data, we can only focus on ticket pricing. The model implies that ticket prices increase with market size ( @Ps @N = 1 2 > 0) and decrease with the strength of the externality ( @Ps @ = N (2) 2 < 0). We will later link these parameters to certain empirical variables, and test the model's predictions against the evidence provided by data in order to see if such explanations based on complementarities are indeed valid. 2.5 Ticket Pricing Data and Empirical Analysis In order to test the validity of the theoretical models, one needs to assemble data on face value prices and secondary market markups. A problem in assembling a data set that contains secondary to primary market price dierentials for tickets, is to match secondary market prices with the corresponding face value prices, when more than one pricing zones are used. I collect secondary market prices from Ebay, by looking at completed transac- tions for any given event. I observe the transaction price, including all possible transaction costs (i.e. delivery fees), the date of the transaction, the location of the seat, and the number of tickets being purchased. Most resellers do not post the face value price of the ticket, which makes the matching process slightly complicated. A common exception are resellers who sell below face value, but these are usually outliers. For the vast majority of observed transactions, the secondary market prices are higher than face value prices, 38 and face value prices are not directly observable. The other diculty is that tickets are usually sold on the primary market months before the actual event date. Transactions on secondary markets are usually sluggish at early dates and they pick up as the concert date nears. Ebay does not keep transaction data on their servers for too long, and one needs to continually monitor and collect data until the actual date of the concert. This is a long and tedious process. The matching is made by collecting additional data from Ticketmaster, the main online ticket seller in the United States. Ticketmaster is a ticketing agency, and it does not have any control over the actual pricing decision. They just provide a computerized box-oce system to event promoters in exchange for a simple per-ticket-sold fee. The pricing decision, and how nely to scale the house, belongs to the promoter. The venue is usually rst split into sections. Then, multiple price levels are used to price tickets in each section. Often times, multiple prices are used for the same section. The main problem in matching arises when scaling is too ne. When multiple price levels are used for the same section, it is practically impossible to nd a true correspondence. Resellers usually post the exact location of the seat, but a true match cannot be determined if the particular section is price segmented. In order to get good matches, we need to focus on sections that are priced uniformly. In addition to the face value price, we collect information regarding the event date, the city and venue, the ticket limit per household (if any), and the three dierent measures about how well the house is being scaled. These are the number of physical sections the venue is divided into, the number of price levels used, and a dummy that shows whether multiple prices are being used for a given section. On top of that, a variable that shows the relative rank of the price is used to proxy for seat quality. 39 Finally, some local market and band specic variables are being constructed. The population and income per capita of the city where the concert takes place point to certain demand side dierences that can aect both pricing on the primary market, and the markups resellers can extract. We also collect data on the total number of live events taking place in each specic city, to control for supply side dierences. The band specic variables point to the historical longevity, experience and success of the band, to the more recent recording activity and success, and also to the overall productivity in terms of studio albums recorded. A list of all relevant variables, along with a short description for each one, is provided in Appendix A.1. The data collected and used in the estimation consists of a sample of 45 music concerts, of 9 very popular bands, in 24 dierent US cities. In terms of the price dierences, prices on the secondary market are on average 84.93 dollars more expensive than face value prices. In percentage terms, this translates to 114.3% more expensive. This is a surprisingly high dierence, which means promoters leave huge prots on the table. This dierence is even greater if we only consider the truncated sample, where we drop the below the face value price transactions. A simple picture of the price dierences between primary and secondary markets can be observed in the table below: Table 2.2: Summary Statistics - Price Dierences Variable Observations Mean St.Dev. Min Max Full Sample Absolute Dierence 355 84.93 97.62 -77.75 858 Percentage Dierence 355 114.30 95.40 -58.57 549.03 Truncated Sample Absolute Dierence 322 96.28 95.29 1.43 858 Percentage Dierence 322 127.99 89.39 0.97 549.03 40 2.5.1 Empirical Analysis We now proceed in estimating the eects of the band and event specic variables on the decision to price, to price discriminate, and even more importantly, the eect of the price discrimination strategy on the dierence between face value and secondary market prices. It is also extremely important to see what determines the secondary market pricing. The results of the following estimations will be later used to test the previously presented theoretical models that explain underpricing and excess demand maintenance. At the same time, analyzing the eect of the level of price discrimination on the markups generated on secondary markets will directly prove or disprove the scaling the house hypothesis. 2.5.1.1 Primary Market Pricing The rst thing that we need to look at is what determines the promoters' pricing decision on primary markets. Face value prices dier signicantly from artist to artist, from city to city, and from weekdays to weekends. When trying to compare these prices, one thing we need to remember is the way they were collected in the rst place. To be more precise, because of the matching with the secondary market prices problem I described previously, dierent price levels were collected for dierent events. For some events we have collected the most expensive price level, for some others the cheapest, and everywhere in between. Therefore, if we were to compare these prices pooled together, we could get biased results. We might compare ,for instance, the cheapest price level of a very successful band with the highest price level of a less successful one, and might nd that the less successful band priced higher. To avoid this problem, I restrict to only the highest price level. These 41 are the most expensive tickets for any particular event, and represent approximately two thirds of the total sample. This truncated sample is only used for this particular regression. For all the following analyses we take the full sample into account. The estimated eects are presented in the following table: Table 2.3: Price Regression { Dependent Variable: Price Variable Coecient (St. Error) DebutAlbum -7.93** (0.91) GoldRec 9.88** (0.96) GoldSin 1.61* (0.70) Albums -20.05** (1.92) LastAlbum -19.34** (6.31) Population 1.69e-06* (7.79e-07) Income -0.0012* (0.00047) Weekend 20.28** (4.91) const 54865.42** (11336.54) *-signicant at 5% level; **-signicant at 1% level; R 2 = 0:8187 All coecients are statistically signicant, and most of them have the expected signs. It seems that more experienced artists price higher. Also more successful bands, in terms of sales, demand higher ticket prices. We measure sales success by the number of gold albums and gold singles an artist earned. As expected, the eect of gold albums is much higher than the eect of singles. The number of studio albums recorded seems to aect ticket prices negatively. In a way, one can look at the number of albums as being another measure of success and longevity, and hence expect higher prices. However, we already accounted for longevity and sales success. The remaining variance picked up by this variable speaks of the complementarity issues we discussed earlier, and the negative estimated coecient agrees with this hypothesis. That is to say, everything equal in terms of longevity and success, some bands produce more studio albums than others, and price their live shows lower in order to attract larger masses and promote their albums. The 42 more productive an artist is in terms of recorded albums, the more likely it is that he cares more about revenues from album sales, rather than revenues from live concerts. A similar argument can explain the negative coecient for the most recent album variable. The more recent an album is, the more likely it is for the band to go on tour to promote the album and therefore under-price concert tickets to generate hype about it. Regarding the show location specic eects, larger markets yield higher prices, just as expected. However, surprisingly enough, income has a negative eect, with lower ticket prices in cities with higher income per capita. It might be the case that income is strongly correlated with some other unobserved demand side characteristics which aect prices. For instance, it might be the case that the limited sample of artists we have, or even the whole pop/rock music scene, do not necessarily target the richer segment of the population. Richer cities might have older populations, or high income inequality which might translate in actually lower income levels for the young audience. Supply side eects 4 or higher protability of complements on richer markets might also be the cause of this negative eect. Lastly, as expected, the weekend shows are generally priced higher. This shows the higher demand for live events during weekends, when people have more time to spend on leisure activities. Moving on to the promoter's decision to scale the house, it is very likely that this decision is largely aected by the same variables that aect prices. We therefore need to estimate the eects of the band and location specic variables on the level of segmentation employed for any given concert. I chose the number of the price levels being used as the 4 Supply side eects could also explain the negative income eects, but when included in the regression, the coecient for the total number of live events turned out to be insignicant and was therefore dropped from the estimation, in order to minimize the multi-collinearity with the other location specic variables. 43 most representative measure for scaling the house. The measure regarding the number of physical sections the venue is divided into, can be misleading. Many events. for which there are numerous sections available, use the same price level for all sections, which is obviously uniform pricing. On the other hand, there are concerts that use multiple prices for the same section. The dummy variable that accounts for this strategy is also limited in nature. Assigning weights and constructing a variable to include all three measures would be extremely subjective. The number of price levels speaks in a straightforward way of how well the promoters are trying to segment the audience into dierent groups, and is therefore the best available measure. Additionally, instead of using all the success related variables, I use a composite variable, Success, which is just the simple sum of the gold, platinum and multi-platinum records. The reason is to avoid multicollinearity issues associated with using all these variables, and at the same time to be able to capture a deeper level of variance among artists, in the absence of precise sales gures which are practically impossible to obtain. There are signicant dierences between claimed sales, certied sales, and actual sales. The estimation results are presented below: Table 2.4: Price Segmentation Regression { Dependent Variable: Price Levels Variable Coecient (St. Error) DebutAlbum -0.12** (0.02) Success 0.06** (0.01) Albums -0.27** (0.04) LastAlbum -0.30* (0.17) Population -6.43e-08* (2.99e-08) Income -0.000054** (0.000015) Weekend 0.21 (0.16) const 849.26** (318.01) *-signicant at 5% level; **-signicant at 1% level; R 2 = 0:8187 44 It appears that, as expected, more experienced and successful artists price discrimi- nate better. Also, bands with more albums, and bands with more recent studio albums, primarily use live events as a way to promote their albums and, therefore, use a less than optimal segmentation. Although it is not exactly clear why, it seems that promoters scale the house more nely in cities with smaller and poorer populations. This might happen due to supply side competition and protability of complements sales in larger and richer markets, or due to income distribution of the target audience. Supply side eects are proven insignicant in a separate regression that includes the number of all live events in each city as a proxy for supply side competition. All coecients, except for that of the weekend dummy, are highly signicant. 2.5.1.2 Secondary Market Pricing A large number of resellers sell their tickets on Ebay. Some of them are professional brokers, while some others are regular people who either want to make a quick prot, or just want to get rid of a ticket for a show they can no longer attend. Approximately 46 percent of the tickets transacted are tickets sold by non-brokers 5 . This variety of resellers, and the variety of seat qualities being oered, lead to a signicant variance in prices on secondary markets. More experienced brokers always pursue buying better seats and resell them for higher markups using more elaborated mechanisms such as auctions, while less experienced traders just trade the tickets they already have, sometimes not even using an auction, but posting an ask price. Sometimes, we observe transactions being made at below the face-value price, which might be explained by risk taking behavior on the part of resellers, or by consumers who intended to attend the concert, but due to unforeseen 5 Leslie and Sorensen (2009) 45 circumstances are no longer able to do so and are trying to recover part of their costs. There are only 33 such observations, and they will be dropped from the sample as they are not particularly relevant for the purpose of this chapter. It is very likely that the same variables that aect pricing on the primary market might also aect pricing on the secondary market and hence, the observed markups. Also extremely important is the fact that these markups are arguably the direct result of sub- optimal scaling. According to theory, price dierences should be higher for those events that use a lower number of price levels. Therefore, the band and event specic variables aect the secondary market markups both directly, and indirectly, through the level of scaling. In order to estimate the correct eects, we need to use a simultaneous equations model. Ignoring this, and simply estimating a regression that includes the number of price levels as an explanatory variable yields biased results 6 . I also include other elements such as how many tickets a person can buy, how many tickets are packaged together for any given transaction, how many days before the concert the transactions take place, and the relative seat quality. I use a three-stage least-squares (3SLS) estimation, and use the number of physical sections and the gold records variables in the second equation to instrument for the endogenous variable representing the number of prices used by the promoter. I argue that both these variables are correlated with the degree of price discrimination, but not with the actual markups. The number of physical sections a venue is divided into presents the promoter with a natural way to price dierently, but the degree to which a venue is segmented does not aect consumer preferences and secondary market 6 We estimated a simple OLS regression which yields a positive and signicant coecient for the number of price levels being used. This is an extremely counterintuitive result which would suggest that markups are actually higher for events where promoters better price-discriminate. 46 markups. Also the ne detail of success that the number of gold records represents, should aect the pricing decision of the promoter, since they have detailed information regarding the band, but should not aect preferences that much, since consumers generally have less detailed information regarding the band success, which is captured by the composite variable success. To check for any sensitivity to the estimation method used, I also include the results of a simple Instrumental Variable (IV) 2SLS estimation. The results are presented below: Table 2.5: 3SLS Regression Results Variable 3SLS Coecient IV(2SLS) Coecient Dependent Variable - Price Dierence DebutAlbum -7.54** -7.36** Success 2.90** 2.94** Albums -18.82** -18.65** LastAlbum 71.88** 70.90** Population 6.63e-06** 6.72e-06** Income -0.014 -0.001 Weekend -13.27 -13.12 Limit 0.28 0.29 NrTickets -5.07 -4.97 Days 0.06 0.09 PriceRank -30.86** -31.90** Prices 7.66 8.01 const -129172.5** -127574** Dependent Variable - Price Levels DebutAlbum -0.08** Success -0.04* Albums -0.30** LastAlbum -0.55** Population -9.00e-08** Income -0.000075** Weekend 0.22 GoldRec 0.25** Sections 0.32** const 1281.83** ** { signicant at 1% level * { signicant at 5% level 47 The band and event specic variables aect the price dierence in a signicant way. First of all, in spite of the fact that more experienced and successful bands price discrim- inate better and charge higher face-value prices, they still leave the highest amount of money on the table. The number of albums aects the level of segmentation negatively, which would suggests that artists with more albums recorded, primarily care about album sales and they use live events as a way to promote their albums. Surprisingly however, is that one would expect the price dierence to be higher for these artists, but in fact, the eect is also negative. This might be due to unpopular bands that have a lot of albums on their resume, but struggle to sell out their shows. The variable for the most recent album picks up the complementarity kind of eect correctly. Bands with more recent albums use live events primarily to promote their albums. They do not price discriminate eciently, under-price, and generate higher markups on secondary markets. Both the local population and average income aect the price discrimination strategy negatively, but the eect on the price dierence is positive for population, and not signicant for income. Finally, the price rank aects the price dierence negatively, which means that better seats generate higher markups on secondary markets. We are primarily interested in the eect of the level of house scaling on resellers' markups. The main theoretical prediction of the theory related to price discrimination, is that secondary markets emerge because promoters are not able to price discriminate eciently. If this was true, the coecient should be statistically signicant and negative, meaning a ner segmentation by the promoters should result in lower markups. How- ever, this hypothesis nds little support in the data, as the estimated coecient is not statistically signicant. This means that, although bands and promoters use dierent 48 segmentation and pricing strategies, the level of segmentation does not aect the left-over prots that resellers can generate on secondary markets. The results are robust to the estimation method, and also the identication tests for the instruments used are all valid. An Anderson canonical correlation LM statistic rejects the null hypothesis that the endogenous variables are under-identied. A rule of thumb for testing for weak IV's proposed by Staiger and Stock (1997) is to conclude that the instruments are weak if the F-statistic from the rst stage regression is smaller than 10. A more rened test proposed by Stock and Yogo (2005), based on the Cragg-Donald (1993) Wald F-statistic, is to compare this statistic to critical values determined by multiple factors among which is how much bias and size distortion is tolerable. The Cragg-Donald statistic has a value of 71.25, much larger than either 10, or the critical value for a 10% maximal IV size that is 19.93. I also test for over-identication, using a Sargan(1958) IV validity test. The null hypothesis that the instrumental variables are uncorrelated with the residuals, and hence valid, cannot be rejected. Also note the similarity of our 3SLS and 2SLS results. We therefore conclude that our instruments are valid, and the results robust. 2.5.2 Model Testing This chapter presented a number of theoretical models that explained situations where sellers may nd it optimal to underprice and maintain excess demand. We also collected data and analyzed the main factors that aect pricing on primary and secondary markets. We now need to t the models to data and see whether the theoretical predictions t the empirical evidence. Since the theoretical variables are not the same with the empirically observed variables, we cannot have a direct link between theory and data. However, we 49 can make a number of reasonable assumption regarding indirect links that can be tested. We will specify the assumed links and interaction channels for each theoretical model, and then test if these assumed links lead to a consistent overall eect on prices and markups. 2.5.2.1 Sharing Risk with Speculators The model with speculators and uncertain demand presented in Section 2.3 has nice theoretical implications for both prices on the primary market and secondary market markups. Prices and markups depend on the low and high type valuation (V L and V H ), the number of speculators (S), the number of certain high type consumers (W ), and the proportion of strategic consumers (). Since we are interested in situations where we observe excess demand, it is natural to focus on the model's predictions corresponding to the high demand situation. The model can also t data for below face value price transactions, but this is not our purpose here. In order to test the model's predictions, we now proceed to linking the theoretical variables from the model to the empirical variables from our previous regressions. We link the parameter V H to band specic variables related to success and longevity. We argue that more successful and experienced bands have a higher fan valuation. This ts the data quite nicely, since all the success and experience related variables aect positively both the price on the primary market and the speculative markup. Low type customers represent the general public and we assume thatV L is not a band specic parameter, but rather a market specic one. V L might be closely related to the local income. Casual fans in richer markets have a higher willingness to pay than fans in poorer markets. Another possibility is to link V L to the local population. More populous markets have more options in terms of live events and hence, casual fans are willing to 50 pay less for any given event. Both these links t the secondary market picture, but they are not consistent with the face value pricing. We assume the number of speculators to be market specic and dependent on the local population. More populous cities have a larger number of active speculators. The data shows that event promoters price higher on markets with higher populations and speculators can extract higher prots. These eects are partially consistent with the model predictions. For, the proportion of strategic consumers, we use the year of the most recent studio album. Bands with recent albums are more likely to be \in the news" and have many fans who are more likely to behave myopically and buy tickets as soon as they are oered, without strategically anticipating a lower price in the future. Hence, a more recent last album leads to a lower . The model predicts that a lower results in lower prices on the primary market and higher markups for speculators which is consistent with the data. Another possible argument is that, on poorer markets, people have a higher price sensitivity and therefore, are more likely to act strategically. Such a link with the income variable is only partially supported by data. The eect on face value price is consistent, but the eect on speculative markups is not. Lastly, the number of certain fans W can be linked in at least two possible ways with the data. The success and longevity variables aect W in a natural way. More experienced and successful bands have larger fan bases, while less successful ones have a higher uncertain component. This assumption ts the data well for the primary market pricing, but goes against it for the secondary market pricing. At the same time, if the show is on a weekend, more consumers arrive and buy tickets early, which again translates 51 to a higher W . This link ts the data well, although the estimated eect on speculative markups is not highly signicant. We summarize all these results in the following table: Table 2.6: Theoretical Predictions vs. Empirical Evidence { Speculators Model Empirical Assumed Theoretical Th. Implied Emp. Observed Variable Eect Variable Eect on P (and P ) Eect on P (and P ) DebutAlbum V H +(+) () Success + V H +(+) +(+) Population V L +() +(+) Income + V L +() () Population + S (+) +(+) LastAlbum +() (+) Income +() () Weekend + W +() +(*) DebutAlbum W +() () Success + W +/ +(+) * { not signicant The assumed eects (column 2) link the empirical variables to the theoretical ones. The theoretical implied eects (column 4) represent the model's prediction implied by the comparative statics exercise. The combination of these two eects should match the empirically observed eects (column 5) for the model to be valid. As we have mentioned, there are some inconsistencies between theory and data. First of all, if we accept that the success related variables aect W , the resulting eects on speculative markups are not consistent. However, note that the success related variables are also aecting V H , and the eects on markups through that channel are consistent with the data. Therefore, it is possible that the combined eects are overall consistent, if the positive eects through V H are dominating the negative eects through W . This argument is supported by the fact that the estimated eects of success and longevity on face value price are higher than those on secondary market markups. At the theoretical level, success and longevity have the same eect on face value price through 52 both channels. These eects reinforce each other and lead to a higher overall eect on price than on markups. It is also possible that complementarities are present. We will show that success and longevity aect markups in a consistent way under complementarities assumptions. Another inconsistency in the eects of population on price. Empirically, larger pop- ulations result in higher prices. Our model suggests however, that larger populations result in lower prices. This occurs through both the V L , and S channels. However, these inconsistencies will be mitigated by the fact that the population eect on price under complementarities is consistent. If we allow complementarity eects, and if these eects are dominant, then we can still have consistent overall eects. This is supported by the fact that the estimated population eect on price is smaller than that on markups. The- oretically, the population eects on markups are consistent under both models, so the overall eects should be higher than that on price, which is exactly what we observe. Lastly, the income aects face value price positively through the V L channel and negatively through the channel. If the eect through the channel is dominant, then we still have overall consistent results. The eects on markups are reversed, but it is possible that their relative magnitudes are also changed, and it is also possible that we have social in uence present. We will show that in the social in uence model these eects are consistent. The estimated eect of income on markups is higher than the eect on face value price, which supports the argument that social interactions are indeed present. 2.5.2.2 Social In uence The simple social in uence model predicted persistent excess demand that depends on the market size (N), customer valuation (V ), and the sensitivity to social in uence (a). 53 First of all, we assume that the secondary market markups are positively correlated with the magnitude of excess demand. In other words, the higher the excess demand level implied by the model, the higher the secondary market markups we should observe in the data. We further assume that the market size N is positively aected by the success and longevity of the band, and by the local population. Consumers' valuation V could also be linked to some of the success related variables, but I argue against it. A die hard fan of a very new or even underground artist might actually be willing to spend more for a ticket than a fan of a more established band. I therefore assume the valuation V not to be band specic, but rather income specic. The band specic variables will aect the market sizeN as described earlier, while the local income per capita will aectV . Lastly, I assume the date of the most recent album to aect the sensitivity to social in uence a. The argument is that live shows are experience goods, and there is always an uncertainty regarding the quality of the event. Bands with older albums have less of a sensitivity to social in uence, since they already had a chance to play their songs on radio and TV and hence, the quality uncertainty is smaller. On the other hand, for very recent albums, with less public exposure, people might be more inclined to be receptive to social in uence in the absence of other quality signals. All these eects are summarized in the next table: Table 2.7: Theoretical Predictions vs. Empirical Evidence { Social In uence Model Empirical Assumed Theoretical Th. Implied Emp. Observed Variable Eect Variable Eect (on x) Eect (on P ) DebutAlbum - N + - Success + N + + Population + N + + Income + V - - LastAlbum + a + + 54 The assumed eects link each empirical variable to the corresponding theoretical vari- able in the direction expressed by the sign. Each theoretical variable induces an eect on the optimal level of excess demand x, and these two eects combined should match the empirically observed eect, since we assumed excess demandx to be positively correlated with the observed price dierence P . The last column of the table presents the empiri- cally observed eects { the way in which the empirical variables from column 1 aect the price dierence. When considering the assumed eects from column 2, we can see that the comparative statics eects implied by the theoretical model (column 4) match perfectly the eects observed in the data. The model proves that when certain social in uences are present, sellers might nd it optimal to maintain excess demand on the market. The theoretical implications t the secondary market data quite well. In addition, the eect of income on excess demand through this model can mitigate some of the inconsistencies present in the risk sharing model. We will also show that, in a principal-agent setting, social in uence lowers the prof- itability and incidence of price discrimination. That in itself provides a plausible explana- tion for the relatively low incidence of price discrimination on ticket markets. The model also predicts less price discrimination when social in uence is high, which is consistent with the empirical evidence that newer, up-and-coming bands, or bands with more recent albums price discriminate less. For such bands the social in uence is higher since their exposure is lower that that of very successful bands and hence, the public is less informed and more likely to be in uenced by these externalities. Also, for certain cult products, we generally observe less product dierentiation and price discrimination that for generic products. Fashion products and other types of product for which trend setters have a 55 big in uence are also following similar patterns of targeting mainly the high end of the market. 2.5.2.3 Complementarities The model with complementarities provided predictions regarding face value prices be- ing aected by market size and the strength of the complementarity. We assume that market size is aected by success, longevity, and local population. We assume stronger complementarities for bands with more recent albums, for bands with more albums, and for newer or less successful bands. Taking into consideration the assumed links, we can summarize the results as follows: Table 2.8: Theoretical Predictions vs. Empirical Evidence { Complementarities Model Empirical Assumed Theoretical Th. Implied Emp. Observed Variable Eect Variable Eect (on P s ) Eect (on P s ) DebutAlbum - N + - Success + N + + Population + N + + DebutAlbum + - - Success - - + LastAlbum + - - Albums + - - The empirically observed eects t precisely the direction implied by the theory. Note also that the longevity and success of a band act through both N and to aect price. Moreover, these two actions work to reinforce each other and provide a consistent com- bined eect, which ts the one empirically observed. Besides the good t of the stand- alone model, these results can also mitigate some of the previous inconsistencies found in the risk sharing model. In fact, it is extremely likely that all these three scenarios are true in the entertainment industry, and the observed band and local market characteristics act 56 through multiple channels. While building a model that incorporates all these forces at the same time might be better suited for these industries, it might be overly complicated and un-intuitive. At the same time, any particular issue might not be relevant for certain other markets that present excess demand. I present these three models separately, in order to be able to study these forces and their eects separately and clearly, and with the potential of larger scale applicability to other markets. 2.6 Conclusions This chapter presented several theoretical models that can explain how underpricing and persistent excess demand have come to be so pervasive on certain markets. We depart from the assumption that excess demand is simply a result of inecient pricing or bad planning, and oer instead models that show how underpricing and maintaining excess demand can be perfectly optimal marketing strategies that generate certain externalities and stimulate demand. Sharing risk with speculators when demand is uncertain and certain complementarities directly lead to underpricing, which can result in excess demand if capacity constraints are binding. Even with no binding capacity constraints, excess demand can still occur if social in uence is present. We also assembled a robust data-set of face value prices and corresponding secondary market markups for a sample of 45 popular music concerts. We used this data to analyze the main determinants of pricing and price discrimination on the primary markets, and also what determines the protability of secondary markets. We then t the theoretical models to the data and study their validity. We nd that the hypothesis that secondary markets emerge because promoters do not scale the house eciently nds no support 57 in the data. After controlling for endogeneity issues, secondary market markups do not seem to be dependent on the level of price discrimination used. What matters for both markups and for primary market pricing are the band- and location-specic characteris- tics. More experienced and successful artists price higher, price discriminate more, but also leave more money on the table. Bands with more studio-recorded albums, or with more recent albums, price lower and price discriminate less. This seems to suggest the tradeo between revenues from ticket sales and revenues from album sales, and some advertising-like externalities associated with the consumption of live events and albums. Some artists seem to focus on producing more albums, and using live events as a way to advertise and promote these albums. They do so by underpricing their shows, selling out, and generating hype around the band, which in turn increases album sales. The empirical evidence is largely consistent with the theoretical predictions. These results provide insights not only into ticket pricing, but more generally into secondary markets and the reasons why some monopolists adopt underpricing and excess demand maintenance strategies. It is hard to dierentiate between the uncertainty of demand, social externalities, and complementarities. It is likely that, on any given market where excess demand is present, all or any of these eects may be at work. Demand might be easier to estimate for certain products, and complementarities and social externalities might not be important factors for others. Arguably, all these are important factors for the live entertainment industry. The markets for concert tickets provide not only data, but also simple economic intuition that is consistent with all three theories. Underpricing and excess demand maintenance can thus be shown to be protable in many cases, and the emergence of secondary markets should not be seen as the result of sub-optimal management, but rather as a perfectly normal result of prot maximization. 58 Chapter 3 When Price Discrimination Fails: A Principal Agent Problem with Social In uence 3.1 Introduction In a seminal paper, Becker (1991) noted that many rms allow excess demand to persist on the market without adjusting prices or quantities, and justied this behavior using social in uence as the main driving factor. If someone's demand is positively correlated with the demand of others, then this kind of social interaction can fully explain the apparent under-pricing observed in many industries. Under-pricing and persistent excess demand are commonly observed in the entertain- ment industries such as popular sporting events, Broadway theater, and music concerts. They are also observed in the case of popular electronic products such as the video gaming console Nintendo Wii, or the Apple products { Ipod, Iphone, and Ipad. When markets are under supplied, secondary markets emerge where speculators can obtain hefty prots from reselling goods in high demand. Speculative markets are extremely common in the en- tertainment industries where, many times, attending a popular event cannot be achieved through traditional box oce ticket purchases, but only through secondary market trans- actions that come at a steep price. Such speculative markets are slowly encompassing 59 other industries and dramatically expanding, with the emergence and development of online marketplaces such as Ebay and Craigslist. Many tried explaining why this phenomenon is happening, why sellers do not increase prices or simply produce more when confronted with persistent excess demand. Capacity constraints, mistakes in demand estimation, or sub-optimal pricing strategies are among the most quoted explanations. However, such explanations cannot fully explain the ob- served patters. Even if the seller is capacity constrained, market clearing could be achieved by slowly increasing prices. Or if, on the other hand, demand is estimated incorrectly, or a sub-optimal pricing strategy is devised, then the seller can adjust his strategy in time in a way that will again lead to market clearing. In the entertainment industry, improper or sub-optimal price discrimination is proba- bly the most popular explanation for the existence of speculative markets. Since, arguably, no two seats oer the same experience, they should be priced dierently. If the promoter does not optimally price discriminate, speculators take advantage and resell the better seats for higher prices on secondary markets. Price discrimination and scaling the house for live events is a quite common practice for many promoters, but still surprisingly un- derused in general. A 2003 survey found that 43% of all live events use uniform pricing rather than oering multiple pricing zones, in spite of business common sense. There are also many studies which documented the protability of price discriminating for enter- tainment events at both the theoretical 1 and the empirical 2 level. Given all this evidence, the results of the previous chapter that found no correlation between the level of price discrimination employed by promoters and the leftover prots that resellers are able to 1 Huntington (1993), Rosen and Roseneld (1997) 2 Leslie (2004), Courty and Pagliero (2012) 60 extract from consumers are puzzling. This is especially true given the large number of events that use uniform pricing. These results suggest that the observed price discrimi- nation is actually optimal, and the protability of secondary markets does not stem from the underuse of price discrimination. This chapter tries to shed some light on this apparent puzzle and studies price dis- crimination in a setting where social externalities are present. I develop a principal agent problem that includes social in uence in the spirit of Becker (1991), with the main dif- ference that the external eect is not generated by aggregate demand, but rather by the level of excess demand itself. I nd that, when compared to a benchmark case where no externalities are present, social in uence increases seller's prots and induces the seller to articially create and maintain a certain level of excess demand by rationing some customers. I also nd that rationing is more protable, and it can be as high as full rationing, at the low end of the market. Social in uence also reduces the protability and incidence of price discrimination, and in some cases, where social in uence is very strong, sellers will completely eliminate price discrimination and only serve the high end of the market. This is consistent with the empirical observations that product dierentiation and price discrimination is low for cult products, and is also consistent with our previous results that found less experienced and less successful artists (that were more likely to be aected by social in uence) using less price discrimination for their live shows. 3.2 Benchmark Model In this section, I present a standard price discrimination model without social externalities. I will use this model as a benchmark later, to analyze the qualitative implications that 61 social in uence has on price discriminatory strategies. The model is a simple principal agent problem with the principal producing two slightly dierentiated versions of the same base product and selling them to two separate groups of customers without being able to distinguish between members of the two groups. The seller has to devise incentive compatible mechanisms in order to successfully price discriminate among the two groups. To formalize, there is one seller who can produce and sell two slightly dierent qualities of the same base product to a market of N consumers. One can think of front and back seats at a concert, or dierent memory capacity for cellphones, etc. For simplicity, we assume no production costs for either one of the two possible qualities. The seller knows that there are two types of customers on the demand side, but cannot distinguish between them. Customers don't know ex ante the overall quality and usefulness of the base product, but have dierent beliefs regarding it. Some customers truly believe the seller is oering a good product overall, regardless of which version they buy. We will refer to these customers as being high type customers. The high type customers have valuations V H , and V L for the high quality, and respectively low quality version of the product. On the other hand, there are low type customers who don't believe the product is that good or useful. Low type customers don't dierentiate between the two versions of the product, their valuation isV 0 no matter what version they buy. We assumeV 0 <V L <V H . Let the proportion of high type consumers on the market be denoted by. Without being able to tell who is a high type customers and who is a low type customer, the seller must choose a pricing scheme to maximize his prots. In essence, the seller will have to choose between serving the entire market using an incentive compatible price discrimination mechanism, or oering a single price and just serving the high types. 62 Serving only the high types, implies that the seller will oer only the high quality version, set the price P = V H , and sell to the entire high end of the market. There are N high end customers, therefore the seller's prots, if he chooses to use this strategy, will be: NX1 =NV H Alternatively, the seller might design a price discrimination strategy and serve the entire market. The seller will oer both quality versions, with the high quality designed for the high type customers, and the low quality designed for the low type customers. The seller will have to optimally choose a pair of prices, P H and P L , that are both incentive compatible and individually rational for the two groups of consumers. The seller has to solve the following mechanism design problem: max P H ;P L NX2 =NP H + (1)NP L subject to: (IR H ) :V H P H 0 (IR L ) :V 0 P L 0 (IC H ) :V H P H V L P L (IC L ) :V 0 P L V 0 P H The individual rationality constraints, IR H and IR L , simply require that each cus- tomer gets positive utility if he buys the product version designed for his type. The incentive compatibility constraints,IC H andIC L , require that each customer gets higher utility from buying the version designed for his type than from buying the version designed for the opposite type. 63 To solve the problem, rst note that the incentive compatibility constraint for the low type (IC L ) never binds since P L will always be lower than P H . With this constraint removed, the seller can now increase P L up to the point where the IR L constraint binds. This is consistent with prot maximization as it increases prots from the low types, and, at the same time, makes the low quality version more unattractive for the high types, thus reducing the informational rents the seller has to pay to high type customers. Therefore, the optimal price the seller has to choose for the low quality version is P L = V 0 . The next step for the seller is to increase P H as much as he can, without violating the IC H constraint. A violation of this constraint would prompt the high type customers to buy the low quality version instead, thus destroying the price discriminatory mechanism. Making theIC H constraint to bind results in the seller setting P H =V H V L +V 0 . At this price, the IR H constraint is satised without binding. In essence, the seller is extracting all consumer surplus from the low end of the market, while leaving some surplus to the high end in order to incentivize them to buy the version designed for them. Summarizing, the optimal incentive compatible pair of prices is: 8 > > > < > > > : P L =V 0 P H =V H V L V 0 The informational rents that the seller has to pay to each high type customer will equal to V L V 0 , while the seller's total prot will be: NX2 =N(V H V L +V 0 ) + (1)NV 0 =NV 0 +N(V H V L ) 64 The next logical question to ask is when will the seller nd it protable to oer both qualities and serve the entire market, and when will he nd it protable to only serve the high end of the market. Comparing the two prots, the seller will only serve the high type customers if: NX1 > NX2 ,NV H >NV 0 +N(V H V L ),V L >V 0 ,> V 0 V L Concluding, the optimal strategy for the seller in the benchmark model is: 8 > > > < > > > : if > V 0 V L , oer only the high quality version and charge P =V H if V 0 V L , oer both qualities and charge P L =V 0 , and P H =V H V L +V 0 It is interesting to compare the results of this base model with the results that emerge when we include social in uence as a driving force. One especially interesting question to ask is how does social in uence aect the protability and incidence of price discrimina- tion? As discussed earlier, one of the most puzzling questions that emerges from studying ticket pricing strategies for popular music concerts is why don't promoters make more use of price discrimination? Another question that we will address is which sellers should we expect to use price discrimination more often? Studying social in uence in a price discrimination framework might provide some answers. 3.3 A Model with Social Externalities In this section, we enhance our benchmark framework by including social externalities to the mix. The intuitive explanation for social interactions can take many forms, but the 65 most natural one is the informational role of social in uence. If some customers are not ex ante convinced of the usefulness or overall quality of the product, they might alter their beliefs if they notice the product is extremely popular. In that sense, shortages on the market act as a form of advertising by providing quality signals to uninformed customers. The original Becker (1991) paper explains social externalities as something specic to those markets dealing with social goods, that are consumed in groups and therefore, people prefer attending more popular events because they might derive utility not only from the concert itself, but also from the screaming fans. While this explanation is perfectly possible for music concerts, sporting events, or popular restaurants, explanations based on quality signaling can be applied to virtually any product, whether people consume it groups or alone. Another departure from the original model is that I use the excess demand itself, and not aggregate demand, as a driving force for social externalities. This can be motivated by people deriving utility from competing for goods and snob eects, but even more naturally, excess demand is a measure of popularity which is easiest to observe by individual customers. A customer might nd it impossible to quantify the total aggregate demand for a particular product, but a line in front of a store is an easy to see quality signal that can in uence his perception immediately. We can see this strategy employed frequently by stores during special sales events, or by trendy nightclub managers who constantly maintain a line outside, whether the club is crowded or not. We model social externalities by allowing a portion of the low type customers to change their beliefs and become high types. Under these forces, the seller might nd it protable to create excess demand on the market and allow these externalities to work. In industries such as professional basketball or baseball, where a club has a a game every 2 or 3 days, these externalities work naturally from game to game. In durable goods industries, 66 such as electronic products, sellers have to be more creative. A popular strategy that is being used nowadays before virtually any product launch, is to oer so called pre-sale periods during which only a limited number of units is made available to the public. We will allow this kind of strategy in our model and assume that, after the pre-sale period, the remaining low type customers are in uenced by the level of excess demand observed during this period and will become high types with a probability that depends on the level of excess demand. To formalize, the seller rst commits to a pricing scheme. Just as in the benchmark model, the seller can choose to serve only the high end of the market and set a single price for only the high quality product, or he can choose to serve the entire market and price discriminate accordingly. Note that the social in uence does not change the incentive compatibility constraints, nor does it provide new incentives to customers. Therefore, the optimal prices the seller will set will be exactly the same as before: the seller will set P = V H if only serving the high types, and will set P L = V 0 and P H = V H V L +V 0 if serving both types. After committing to the pricing scheme, the seller will oer a pre-sale period by making available some quantities of the product. We denote by Q L the quantity made available of the low quality product, and by Q H the quantity made available of the high quality product. The producer will ration some customers by settingQ L (1)N, and Q H N. We denote the resulting excess demand by x =NQ H Q L . Naturally, if a one price commitment has been made, the only rationing will be possible in the high end segment, and the resulting excess demand will simply be x =NQ H . Based on the realized excess demand, with some probability p(x), each remaining low type customer will update his belief about the product and become high type. We 67 assume the probability function to be of the form p(x) =f(x), where is a parameter measuring the sensitivity to social in uence, andf(x) is a concave function which reaches its maximum value of one at some x and is increasing for x < x and decreasing for x>x . We also require f(x) = 0 if no excess demand is created or if the entire market is being rationed. The parameter speaks of how likely it is for a particular seller to be impacted by social in uence. Consider for instance, that some sellers have established a history of quality and reliability, and therefore are less likely to be aected by social in uence. On the other hand, relatively new sellers, or sellers who introduce revolutionary products with no previous public exposure, are more likely to face uninformed customers who are more likely to be in uenced by any sort of advertising strategy. The probability function f(x) simply states that the probability that a low type customer is in uenced by the observed excess demand is increasing in x for relatively small values of x, and decreasing if the excess demand becomes too big. In other words, for limited values, the larger the excess demand, the more people believe that the product is good. However, if excess demand becomes too big, people start getting angry or start feeling deceit. As mentioned earlier, we denote byx the level of excess demand that maximizes the function f(x). Naturally, f(x ) = 1 and p(x ) = . After the excess demand is realized during the pre-sale period and the social externalities aect the market shares of customers, the seller produces as much as needed to clear the market. 3.3.1 One Price Commitment We now analyze the optimal choice of the seller in the sub-game corresponding to a one price commitment strategy. If the seller commits to only serving the high end of the 68 marker, he will set the price P =V H , oer a quantity of Q H during the pre-sale period, realize an excess demand of x =NQ H , and generate the following prot: X1 =Q H V H +xV H +p(x)(1)NV H The seller will have to optimally choose the level of excess demand by choosing how much to supply during the pre-sale period. The seller's problem can be written as: max Q H X1 =V H [N +p(x)(1)N] Taking the appropriate derivative, we obtain the marginal eect of changing Q H : @ X1 @Q H = (1)NV H @p(x) @x @x @Q H = @p(x) @x (1)NV H which is negative for x < x and positive for x > x . This means that, as long as the level of excess demand is smaller than x , the seller can increase his prots by lowering Q H . The maximum level of prots is reached when Q H is chosen in such as way as to generate an excess demand exactly equal to x . Of course at this level of excess demand, p(x) = and the seller's prot will be: X1 =NV H [ +(1)] 3.3.2 Two Prices Commitment We now turn to the more interesting case of price discriminating under social in uence. If the seller chooses to serve the entire market, he will oer both qualities and set the 69 incentive compatible prices P L =V 0 and P H =V H V L +V 0 . The seller will also choose quantities Q L and Q H to oer during the pre-sale period, which will induce an excess demand ofx =NQ H Q L . After the pre-sale period, the residual demands in the two dierent market segments will be x L = (1)NQ L and x H =NQ H . The seller's prot when using two prices will be: X2 =Q H P H +Q L P L +x H P H +x L p(x)P H +x L [1p(x)]P L which can be rewritten as: X2 =P H [N +p(x)x L ] +P L [Q L + (1p(x))x L ] The seller can collect P H from all the initial high types plus the transfers due to the externality, and P L from the initial low types served during the pre-sale period plus the leftover low types after the externality takes eect. As before, it is in the seller's interest to generate excess demand and increase the number of transfers from the low type group to the high type group. The seller can achieve the same excess demand by rationing either the low types or the high types. In order to see in which group rationing is more protable, we analyze the marginal eects of changing Q H , and Q L respectively: @ X2 @Q H = (P H P L )[(1)NQ L ] @p(x) @x @x @Q H @ X2 @Q L = (P H P L )[(1)NQ L ] @p(x) @x @x @Q L p(x)(P H P L ) 70 Since @x @Q H = @x @Q L =1, we can draw a number of conclusions from analyzing these marginal eects. The rst, and most important conclusion is that rationing the low end by lowering Q L is always more protable than rationing the high end and lowering Q H . Secondly, lowering Q H is only protable if the resulting excess demand is x x , while lowering Q L can also be protable for some levels of excess demand x > x . For later purposes, we denote by ~ x the level of excess demand where further lowering Q L becomes unprotable. Intuitively, loweringQ H simply aects prots by increasingx and the value of the externality function p(x). This benets stop once we reach x and the maximum value of the externality function. On the other hand, lowering Q L has a double eect: it increases the excess demand and the value of the externality function in a similar fashion, and also it increases the size of the low end market available for this externality to aect. This is why it is always better for the seller to rst ration the low end, and this is also why the seller will sometimes ration the low end even past the optimal threshold where the externality function in maximized, an extent to which he will never ration the high end. Of course, the seller can never ration more than the original market share, and therefore, depending on these initial market shares, a few distinct cases emerge. First, let's assume that there are not enough low type customers on the market to reach the top of the externality function by only rationing the low types. That is to say, assume 1 < x N . In this case, the seller will fully ration the low types by setting Q L = 0, then continue to ration the high types until he reaches the desired level of excess demand x = x . In this case, the externality function will be p(x ) = . The seller's prot in this case will be: X2 =NV 0 +N(V H V L )[ +(1)] 71 Now, let's consider the case where there are enough low type customers to reach the top of the function p(x) without needing to ration the high types at all. In this case, the entire excess demand will be created by rationing the low types, since it is never optimal to ration the high types past the point where x = x . There are however, two separate scenarios here. Remember that, given enough low type customers, one should lower Q L until he reaches the point ~ x, where it is no longer protable to do so. We know that 1 > x N , so there are enough low types to ration and reach x , but we don't know whether there are enough low type customers to reach ~ x, since ~ x>x . If there are enough low type customers, 1 ~ x N , then the seller will set x = ~ x and obtain the following prots: ~ X2 =NV 0 + (V H V L )[N +p(~ x)[(1)NQ L ]] If however, there are not enough low types and x N < 1 < ~ x N , then the seller will do his best and fully ration the low types by setting Q L = 0. In this case the excess demand realized will be some ^ x, with x < ^ x< ~ x, and the seller's prot will be: ^ X2 =NV 0 +N(V H V L )[ +p(^ x)(1)] Note that x < ^ x < ~ x < N and, since the function p(x) is decreasing in this region, we will have > p(^ x) > p(~ x) > 0. It is easy to see that the presence of social externalities increases prots and creates excess demand on the market no matter what scenario we consider. For further insights, especially to see the eects of social externalities on the decision to price discriminate, we now have to analyze, case by case, the seller's optimal strategy regarding which market segments to serve, and compare the results with those found in the benchmark model. 72 3.3.3 Prot Comparisons In order to see whether the seller will decide to use price discrimination, or just serve the high end of the market, we need to compare the prots obtained under a one price commitment with the prots obtained from oering two versions of the product and price discriminating accordingly. Summarizing the previous results, the seller will obtain the following prots: 8 > > > > > > > > > > > > < > > > > > > > > > > > > : X1 =NV H [ +(1)], if no price discrimination X2 =NV 0 +N(V H V L )[ +(1)], if price discrimination and 1 x N ~ X2 =NV 0 + (V H V L )[N +p(~ x)[(1)NQ L ]], if price discrimination and 1 ~ x N ^ X2 =NV 0 +N(V H V L )[ +p(^ x)(1)], if price discrimination and x N < 1< ~ x N First, assume the rst case, where 1 x N . Under this case, the seller will decide to only serve the high type customers if: X1 > X2 ,NV H [ +(1)]>NV 0 +N(V H V L )[ +(1)] ,NV L [ +(1)]>NV 0 , +(1)> V 0 V L Note that, in the benchmark case, the condition for serving the high types only was > V 0 V L . Since 0 1, we have +(1) 1. Comparing the benchmark case with the externality case we conclude that for certain values of the parameters, social in uence reduces the incidence of price discrimination. More specically, if < 73 V 0 V L < +(1), the seller would nd it optimal to price discriminate if there were no externalities present, but only serves the high type customers under social in uence. Considering the second case, when 1 ~ x N , the seller will only oer the product to the high type customers if: X1 > ~ X2 ,NV H [ +(1)]>NV 0 + (V H V L )[N +p(~ x)[(1)NQ L ]] which, after adding and subtracting the term (1)NV L from the right hand side, and rearranging becomes: (V H V L )[(1)p(~ x)(1) + p(~ x)Q L N ] +V L [ +(1)]>V 0 Let ~ " = V H V L V L [(1)(p(~ x)) + p(~ x)Q L N ]. Note that ~ "> 0, since >p(~ x). We can rewrite the above condition as: +(1) + ~ "> V 0 V L Again, compared with the benchmark case, there is wedge between and +(1 ) + ~ " where the seller does not nd it optimal to price discriminate anymore when social externalities are present. This wedge is even more pronounced that the one from the previous scenario due to the addition of ~ ", and also due to the fact that 1, the proportion of low type customers, is higher in this scenario. Even more so, under certain values of the parameters, the addition of the ~ " term might raise the whole lefthand side of the inequality above 1, and in that case, the seller will always nd uniform pricing preferable to price discriminating. 74 Finally, considering the third possible case, when x N < 1 < ~ x N , the seller will choose to only serve the high end of the market if: X1 > ^ X2 ,NV H [ +(1)]>NV 0 +N(V H V L )[ +p(^ x)(1)] Adding and subtracting (1)V L on the righthand side, yields after rearranging: (V H V L )[(1)p(^ x)(1)]>V 0 V L (1)V L Let ^ " = V H V L V L [(1)(p(^ x)]. The above condition becomes: +(1) + ^ "> V 0 V L which just as before, compared with the benchmark model, creates the same situa- tion where the seller does not nd it protable anymore to oer both qualities and price discriminate under social in uence. Moreover, for a large enough ^ ", the seller will always use uniform pricing and price discrimination will be completely eliminated. Figure 2.1 presents a graphical representation of the analysis regarding the incidence of price dis- crimination in the benchmark case versus the social in uence case for the rst scenario. Figure 3.1: The Incidence of Price Discrimination 75 One can observe the wedge created by the social externality, between and+(1). In this region, the seller would serve both market segments and price discriminate in the absence of social in uence, but will only serve the high end of the market when social externalities exist. Note also that if the social in uence becomes maximal, that is if = 1, price discrimination is completely eliminated since V 0 V L 1. The analysis for the other two cases, where the level of excess demand is ~ x or ^ x is analogous, with the only dierence that the point +(1) gets moved further to the right by the additional terms ~ ", or respectively ^ ". This additions increase the wedge further, and even more so, price discrimination can be completely eliminated even for smaller values of , as long as ~ " or ^ " are high enough. It is also easy to observe from the graph that, for given and given customer valuations, sellers with larger sensitivity to social in uence price discriminate less. This is consistent with the empirical observations that cult products do not usually oer a lot of product dierentiation or variety and at the same time they usually target the high end of the market. Also the same kind of empirical ndings can be found in the entertainment industry, where less experienced and less successful bands price discriminate less. Less experienced and successful bands have more uninformed customers and their customers are more likely to be in uenced by social interactions in forming their beliefs regarding the quality of the shows. 3.4 Conclusions We have studied the eects of social in uence on the seller's incentives to maintain excess demand and to price discriminate. Social in uence increases total prots by inducing some low type customers to revise their beliefs regarding the overall quality of a product. Under 76 social in uence, sellers have incentives to create and maintain excess demand during pre- sale periods or from sale to sale in the case of frequent, repeat sales. This excess demand can be achieved by rationing some of the customers. It is always in the seller's best interest to ration the low end of the market rst. Also I show that, when compared with the benchmark case of no externalities, having social in uence reduces the protability and incidence of price discrimination. The incidence of price discrimination diminishes with increases in the sensitivity to social in uence. For suciently high externalities, the price discrimination is completely eliminated. This ndings are consistent with the empirical observations that we observe for cult products, or live entertainment events. These results fully explain the empirical puzzle from the music industry and also what we observe on certain cult product markets. Extremely trendy products such as the Apple products or certain fashion products are generally targeted towards the high end of the market with very little product variety and price discrimination being employed. Moreover, the model explains why some sellers use the so-called pre-sale periods when they only make limited quantities available to customers. During these periods, it is usually the lower quality version of the product that quickly runs out of inventory which is exactly what the model predicts. Taking all the evidence into account, I argue that economists should focus more on theories where preferences are not rigid but exible, where social in uence and peer pressure are seriously considered since it is obvious they do exist in reality and they can seriously aect the outcomes of standard economic models such as the one considered here. 77 Chapter 4 Price Discrimination and Collusion in the Automotive Industries of the European Union 4.1 Introduction When analyzing prices of dierent products across international borders, one can often observe large and persistent dierences. This contradicts the idea that in a world with no trade frictions, arbitrage forces should lead to a convergence in prices. These deviations from the law of one price have been traditionally associated with exchange rate uctua- tions, costly arbitrage, non-homogeneous products, dierent local distribution and retail services, trade and geographical barriers, and other institutional factors that eectively translate into cost dierences. Dierent costs automatically lead to dierent prices, and this is true even under perfect arbitrage conditions 1 . All these supply side based argu- ments sparked large waves of trade liberalization talks and agreements, but in spite of all this, price dispersion can still be observed on many international markets. A demand side based hypothesis needed to be formulated and tested. The idea that manufacturers could, in fact, price strategically across destination markets according to local demand conditions generated a whole new strand of literature that pointed to some very important issues. Among these, probably the most important one is that, when 1 See Krugman (1991), Eaton and Kortum (2002) 78 considering strategic pricing issues, we need to focus on specic industries rather than considering macro-level baskets of goods and price indexes. For strategic pricing to be possible, manufacturers need to be able to segment the markets successfully. Signicantly dierent demand side characteristics need to be present, and free arbitrage needs to be prevented. All these factors are very dierent across industries, and therefore the analysis should focus more on the micro level and consider specic markets rather than the whole economy. As Knetter (1993) shows, pricing to market explains price dispersion across a large number of products and countries, but the main source of variation comes from industry specic eects. This proves that in some industries, strategic pricing is more prevalent than in others. Arbitrage forces, for instance, are very dierent across indus- tries. A specic example, provided by Knetter (1997), is the observed price dispersion for The Economist. This example shows that the lack of arbitrage opportunities is often obvious even if it cannot be quantied. For this specic case, the time sensitive nature of the product makes it extremely dicult for potential resellers to make any prots from arbitrage. Additionally, more factors than simply exchange rates uctuations need to be considered as driving forces in pricing to market arguments. This chapter takes into account these points and focuses on a specic industry - the auto manufacturing industry. At the same time, the role of any exchange rates uctuations is eliminated by studying the European markets. Since many member states are now part of the Euro zone, there are no exchange rates to worry about. However, signicant demand side dierences still exist, and a very prohibitive exclusive dealership system is in place, which both lead to successful market segmentation and price discrimination across countries. Many have also suspected that possible collusive agreements between major manufacturing groups might also further aect price dierences. Using a panel data set 79 of prices for identical models across European Union member states, I estimate the major country specic eects and show that dierences in consumers' preferences, purchasing power and income heterogeneities across countries, alongside high market concentrations and collusive behavior in certain markets, lead to signicantly dierent prices for identical models that are not likely to converge in spite of the trade liberalization eorts and the adoption of the common currency. 4.2 The European Automobiles Market Even before there was a European Union, but especially after its creation, people have been concerned with the obvious price dierences for similar or identical car models across countries. Studies conducted by the European Bureau of Consumers Unions between 1980 and 1995 showed that large price dierences for automobiles across European countries was a long persistent problem. Pre-tax prices for nearly identical models were found to vary by up to 90 percent. Europe is geographically-wise very concentrated, hence any dierences in transportation costs from the manufacturing country to the destination country should not matter that much. The European population is also fairly uniform with respect to their preference for car specications and features. At the same time the European Union is designed to function as a single, central market with no trade restrictions of any kind. In a competitive environment, prices should re ect production costs and therefore they should depend on the characteristics of the cars. Judging by all these facts, one would expect prices to be fairly uniform across European borders. However, this is not even close to the market reality. 80 Mertens and Ginsburgh (1985) were among the rst to ask what are the factors that can explain these dierences in prices. They found both product dierentiation, and mar- ket imperfections to be signicant. However, product dierentiation could only explain a smaller part of the variation. The larger part was not explained by any physical or technical characteristic, and could only be attributed to price discriminatory practices. Furthermore, I argue that the importance of product dierentiation has gone down dra- matically since their study in 1985. With the EU integration, there has been a signicant convergence in terms of the hedonic indexes across countries, as all member states had to implemented uniform standards of safety and pollution. Models became more and more similar in terms of physical characteristics. Nowadays, models are virtually iden- tical across countries, with only some minor dierences present, such as right hand side driven cars in the UK. There is no doubt that this technical convergence, together with the market integration and trade liberalization, have brought price dispersion down since the early years of the EU, but a signicant level still persists nowadays. A dierent approach in trying to explain price dispersion was based on a price- leadership model in Kirman and Schueller (1990). However, their model assumes a price leader with high costs and fails to explain how a certain producer might become dominant on any given market. Ignoring the demand side and solely focusing on cost aspects will not paint a complete picture. It is actually extremely likely that exactly these demand side aspects are what strengthen the position of any given producer on any given market. Verboven (1996) showed that price dispersion was getting smaller as the EU was mov- ing towards more integration, but was still at a signicant level. He pointed to dierent price elasticities across countries resulting from a preference for domestic brands, to im- port quota constraints present is some countries, and nally to the possibility of collusion. 81 Continuing on the topic, Goldberg and Verboven (2001, 2004 and 2005) bring other fac- tors into discussion, such as the eects of local currency stability, and the importance of exchange rates on local cost dierences. Their results relate well with my analysis and I will refer to them throughout this chapter. However, my approach diers from theirs in some very important aspects. First of all, the data is from very recent years and the focus is mainly on those aspects that are likely to persist in the European Union in spite of the integration eorts. The eorts of previous papers were directed at explaining the evolution and convergence of price dispersion. Many factors considered to be relevant in the past are no longer an issue today. We can no longer think of import quotas for instance - they have been completely eliminated by all EU member states. Starting with the year 2000, the European Union banned all import quota restrictions for this particular industry. Also, in the Euro zone there are no longer exchange rate uctuations of any kind to worry about. As the EU became more and more integrated, some of the factors that could explain price dispersion in the past were eliminated. The fact that price dispersion went down as a result of these institutional changes is well documented in Goldberg and Verboven (2005) and also in Pareja and Rivero (2008). The question now is what exactly keeps the markets from fully converging? The eects of exchange rates, which were initially thought to be the main problem, were actually found to have been signicantly over estimated. The introduction of the Euro as the common currency should have reduced price dispersion dramatically if previous uctuations in exchange rate were indeed the main culprit. However, Goldberg and Verboven (2004) estimate only a 1 percent decrease in price dispersion after the introduction of the Euro as common currency. Today, there are still signicant dierences 82 in prices across member states in the Euro zone { more than 30 percent for some models as we can see in the following table: Table 4.1: Price Dierences in the Euro Zone Small Segment 2008 2007 2006 Peugeot 206/207 32.6% 24.9% 18.7% Renault Clio 23.4% 19.1% 15.3% Ford Fiesta 21.4% 20.2% 16.3% Fiat Punto 21.4% 17.5% 18.6% VW Polo 25% 25.4% 13.4% Medium Segment VW Golf 24.3% 25.2% 23.4% Ford Focus 27.4% 23.8% 28.5% Renault Megane 17.3% 19.2% 22.3% Opel Astra 18.4% 24.8% 24.8% Peugeot 307 34.8% 31% 21.2% Large Segment VW Passat 17.1% 20.3% 22% BMW 320D 12% 9% 5.5% Audi A4 7.4% 13.9% 12.7% Peugeot 407 15.2% 15.9% 14.3% Mercedes C 11.9% 12.1% 5.6% The gures in the table represent price dierences for a selection of best selling cars, expressed as percentages of prices in Euro (excluding taxes), comparing the most expen- sive market with the cheapest one. They were published by the European Commission in 2008 and they only include countries in the Euro zone. It is very easy to see that, for many of the best selling models, price dispersion actually went up between 2006 and 2008. This is fundamentally opposing the theory that market integration reduces price dispersion. I argue that, whatever portion of the past observed price dispersion was due to trade barriers and restrictions, it has already been eliminated with the integration eorts. There is no doubt that price dispersion went down signicantly over the past twenty-some years. However, as presented, we are still dealing with dierences of around 30 percent 83 and these dierences can only be explained by strategic pricing based on dierent local demand conditions. An important issue to discuss is the presence and importance of local costs. It has been argued that up to 35-40% of the nal cost of a car is represented by local costs arising from marketing, distribution, and servicing. These estimates are based solely on opinions of "inside experts", and no rigorous study to estimate these local costs exists. More than this, one can argue that even if this magnitude is accurate, its importance in picking up some of the variance in prices is quite small. The argument for this is that the EU is a highly integrated market nowadays with a very high level of factor mobility and hence, these local costs cannot be dramatically dierent across member states, especially across the Euro zone. It is practically impossible to measure and estimate exactly these eects without private dealership data. In Goldberg and Verboven (2001), an attempt has been made to proxy these costs using the log of the wage rate, and the corresponding coecient has been found to be statistically signicant. However, given the close correlation between wage rates and per capita income, this might not be a cost related eect at all, but a direct proof of price discrimination where manufacturers take advantage of wealthier consumers by charging higher prices. Since we cannot precisely distinguish local cost dierences from higher purchasing power and willingness to pay, I will neglect this supply argument and just use the income per capita levels to test for possible price discrimination. For all the estimations, I will use the pre-tax prices in euros as published by the European Commission. Before going further into explaining the data and the demand side factors that allow for market segmentation, there are two major things we need to discuss without which 84 price discrimination could not be employed{ market power and the ability to prevent resales. We brie y discuss these two issues in the following paragraphs. The automobiles manufacturing industry is highly concentrated and entry barriers are high. Six corporate groups control over 70 percent of the worldwide markets for passenger cars. In Europe, the rst three groups control over 45 percent of the entire market. It goes without saying that this degree of market concentration gives manufacturers the ability to easily control prices and it also signals potential collusion problems. At the other end, resale prevention is easily achieved through the use of the exclusive dealership system. With the introduction of the open borders policy, practically anyone could go in the neighboring country and buy a car if found cheaper. In fact, some individual consumers do that. But these are the exceptions that conrm the rule, as for the average customer the transaction costs to buy abroad are still higher than the potential prots coming from price dierences. However, large rms could buy and sell automobiles on a large scale and prot from that. So why is this not happening? The answer lies in the fact that manufacturers sell their cars and oer maintenance and warranty services exclusively through authorized dealers. The anti-competitive practices associated with this exclusive dealership system go to the point where manufacturers explicitly forbid dealers to sell to foreign customers or to oer service for cars bought abroad. There were numerous anti-trust actions taken by the European Commission with the intention of discouraging the use of such practices. The Volkswagen group was ned 102 million ECU in 1998, Daimler-Chrysler got a similar ne of 72 million Euros in 2001, and Peugeot had to pay 49.5 million Euros in 2005 for using such anti-competitive practices. In spite of all this, the exclusive dealership system is still in place today all over the world and still 85 achieves the same major role - preventing arbitrage and allowing for market segmentation and international price discrimination. 4.3 Basic Model and Data Description We are trying to pin down the factors responsible for the observed price dispersion for automobiles in the European Union. More specically, we want to determine what are the market conditions and demand side characteristics that allow manufacturers to price discriminate across borders. As pointed by several previous studies, consumers' preference for a domestic brand is a major factor to take into account. In addition to it, we include factors that point to income dierences across European countries, which allow for price discrimination based on purchasing power. Another factor that can aect competition and prices, is the presence of a local manufacturer. Under a strong domestic brand bias it is likely that the local producer might be able to monopolize the domestic market in a way that cannot be replicated on foreign markets. Note that this kind of eect can work through two separate channels. On one hand local producers might get more market power and price higher on local markets, and at the same time this translates into increased competition for foreign producers who might be forced to lower their prices on markets with a domestic producer in order to stay competitive. We use a fully balanced panel dataset comprising of 51 automobile models across 21 European countries, which gives a total of 1071 observations. The particular shape of this data set diers from previous studies in its very essence { all previous studies focus either on cross sectional data, or more traditional panels with models across time in a given country. My specication improves on the previous literature by accounting for all cross 86 country heterogeneities. By studying country by country eects, we cannot observe the importance of country specic variables, such as income or income inequalities. Instead of estimating country specic eects, I estimate average eects across countries. This approach is based on the fundamental idea that the European Union is supposed to be a fully integrated market and we need to analyze things from a wider perspective instead of just focusing on individual countries. The dependent variable is the pre-tax manufacturer's suggested price in Euros for each model in each country of the sample on the 1st of January 2009. The price data was assembled from the European Commission report on car prices for the year 2009 2 . The European Commission publishes such a report every year as a measure of monitoring competition and following the numerous complaints from customers unions about the industry standards, dierences in prices and anti-competitive practices. The independent variables consist of a series of model specic variables which repre- sent both the eect of the manufacturing costs on prices, and the eect of consumers' preferences regarding the physical characteristics of the cars they buy. These variables refer generally to the physical size of the cars and the engine attributes, both in terms of power and fuel eciency. All the data referring to these physical characteristics was collected from multiple online sources such as manufacturers' websites and various auto review websites 3 . Besides these hedonic variables, I also use a list of country specic vari- ables, which account for the cross country heterogeneities. To account for the domestic brand bias, I use a dummy for the country of origin for each individual model. Lastly, 2 http :==ec:europa:eu=competition=sectors=motor vehicles=prices=report:html 3 Websites used to compile technical specs: www:carmagazine:co:uk;www:ultimatespecs:com 87 I also include a dummy variable to address the competitive implications associated with the presence of a local producer. When analyzing the eects of the physical characteristics on prices, it is often hard to distinguish between cost eects and preference eects. These eects might work in the same direction, or might clash against each other. People might prefer larger and more powerful cars which cost more to make, or they might prefer smaller and more economical cars. Thus, the sign and signicance of these hedonic variables might be hard to interpret and often surprising. At the same time, there is a strong correlation between many of these variables. I applied the variance decomposition method of Belsley, Kuh and Welsch (1980) which shows clear evidence of strong multicollinearity. This is an understandable issue since many of the physical characteristics variables refer to the same larger aspect of the car - some deal with the size, some with the engine power, and some with the fuel economy. Also, more times than others, the physical size is also correlated with the engine size and power, and of course a larger and more powerful engine is less fuel ecient than a small one. The strong multicollinearity will blow up the standard errors and could potentially lead to rejecting good values as being insignicant. This particular issue has been reported in previous studies on the US auto market 4 . Having all these issues in mind, this chapter does not try to explain any of the eects associated with these physical characteristics. The main reason to include them in the regression is just to control for possible cost dierences and not to actually explain any sort of price discriminatory practices based on physical of technical aspects. The more important factors, for the purpose of this study, are the eects of the country specic variables on prices. These variables are the national per capita income, the GINI 4 Arguea and Hsiao (1993), Arguea, Hsiao and Taylor (1994) 88 coecient, the RP10 ratio (the ratio of the average income of the richest 10 percent to the average income of the poorest 10 percent), and the local producer dummy. The income related data is collected from UN sources. Per capita income points to the average purchasing power of consumers in a given country, and purchasing power is the most basic thing one can think of and take advantage of when trying to price discriminate. Including dierent measures of income inequality might not appear important, but a simple look at the data provides some striking evidence. For instance, Romania has approximately one fourth of the national income per capita of Ireland, yet higher average prices for cars. Slovakia has approximately one half the national income of Denmark, yet 8 percent higher prices on average. While the national per capita income might have an important eect, it obviously does not tell the whole story. There are more examples to prove this point, and the majority of them are found in the poorer, central and eastern European members where imported cars are not marketed towards the entire population, but rather towards the upper tier formed of the rich and the very narrow, emerging middle-class. This phenomenon was the main motivation for including income inequality measures. An additional note on the variables regarding income inequality is in order at this point. The GINI coecient is the most common measure of income inequality, while the RP10 ratio is a measure of extreme income inequality. At this point, it might not be very intuitive why we should include both measures in the regression. However, after a more thorough analysis, one can see that the two measures actually can aect price discrimination in two dierent ways. In countries with some income inequality producers can target their products toward the high end of the market and charge higher prices, but if income inequality is too high this strategy might leave them with too narrow of a market. In 89 such cases producers might want to lower their prices to serve a larger population so we expect the RP10 ratio to have an opposite eect to the GINI coecient. Other variables are the country of origin and the local producer dummies. The country of origin has been shown to have a positive eect in some countries 5 . I test whether this eect is still signicant at the average level, when we sample the countries together. At the same time, if a domestic brand bias is present then we should expect that the presence of a local producer will aect overall market competitiveness. Note that out of the 21 countries in my sample, only 8 have a domestic producer. A list with all relevant variables and their description is included in Appendix B.3. The basic model specication can be summarized by the following equation: P ij =X i +Y j + Domestic ij +Industry j where P ij represents the price of model i sold in country j, X i is the vector of model specic characteristics,Y j represents the country specic income measures,Domestic ij is a dummy variable that is coded with 1 if model i is made in country j, and Industry j is a dummy which takes value 1 in country j has a local producer. 4.4 Estimation Results of the Basic Model I estimate the basic model using random eects, xed eects, and MLE specications with robust standard errors. The coecients are fairly similar for all three specications, with the main dierence that, under xed eect specications, the model specic coecients cannot be estimated. The random eects specication yields more ecient estimates, but 5 Goldberg and Verboven (2001) 90 they might be inconsistent. A Hausman test was employed to test for the consistency of the coecients estimated using the random eects specication, and they were accepted as consistent. Therefore all the following discussions will focus on the random eects estimates. The regression results are presented in the following table: Table 4.2: Regression Results Dependent Variable - Price in Euros (excluding taxes) Variable RE Coecient FE Coecient MLE Coecient Length -3835.12 - -3835.17 Width 33466.99* - 33467.09* Height 2488.36 - 2488.23 CC 12.57** - 12.57** HP 79.99 - 79.99 NM 36.07 - 36.07 Sec100 1698.09* - 1698.11** Top Speed -20.58 - -20.58 MPG -3.12 - -3.12 Gear Box 2250.46 - 2250.48 AWD -6521.67* - -6521.70* Diesel -3311.26 - -3311.23 MadeIn 1017.29* 1022.36* 1015.53* Income 0.023** 0.023** 0.023** Gini 229.32** 229.31** 229.32** RP10 -421.09** -421.05** -421.09** Own Industry -406.11* -406.59* -405.94* const -96230.82* 165.73.14** -96231.09** *-signicant at 5% level **-signicant at 1% level Focusing the discussion on the hedonic variables is of little interest, as they are clearly aected by collinearity. However, it seems that the few signicant eects are consistent with the basic intuition that people prefer larger, more powerful cars which are also generally speaking more costly to produce. What is more important is that all country specic variables have highly signicant coecients, and also make a lot of economic sense. The domestic brand bias is still 91 present, even at the average level, in the aggregate sample. This conrms previous studies made at the individual country level. This eect, combined with the presence of a local manufacturer, leads to more competition for the rest of the industry in each country having a domestic producer. This, in turn, leads to lower overall prices in those countries. This eect is somehow surprising, since a local producer who is preferred by local customers might manage to monopolize the market which would result in higher prices. Domestic market monopolization and increasing competitive pressure on the foreign market segment are channels with opposing eects through which the presence of a local producer might in uence prices. We will analyze these channels in more detail in the extended model. Finally, all the income related variables have signicant signs. The national per capita income is positively related to price. Manufacturers successfully price-discriminate based on purchasing power. However, the per capita income does not tell the whole story. There are countries with relative lover incomes, that rank high on the price list. Most of these countries are part of the central and eastern European block that joined the European Union more recently. They have a large segment of their population that is poor, but also a narrow rich and middle class emerging. These income inequalities allow manufacturers to market their products exclusively to the richer segments of the population. Hence, in these member states, income per capita is low, but that does not show the true picture of the market for imported automobiles. Prices in these countries are still higher because of income inequalities. In fact, the same car that is marketed to the general public in a richer western European country is marketed only to the rich segment in the eastern European countries, and the per capita income of the rich here could actually be much higher than the corresponding income of the general public in the west. The GINI variable picks up exactly this type of eect. On the other hand, too much inequality is not good for 92 manufacturers since it shrinks the market too much. The RP10 variable picks up this eect. In countries where the income distribution is too skewed, if manufacturers target only the rich segment they will lose too many sales and their prots would go down. In such countries, too much income inequality makes it protable for manufacturers to lower their prices and capture a larger market. All three income related variables are highly signicant which clearly shows the important role income plays for price discrimination strategies to be eective. For illustrative purposes, I ran an additional random eects specication with the collinear hedonic variables dropped after applying the variance decomposition method. The results are summarized in Table 4.3. Table 4.3: Regression with no Collinear Variables Dependent Variable - Price in Euros (excluding taxes) Variable Coecient St. Error MadeIn 1026.39* 432.55 Income 0.023** 0.005 Gini 229.29** 38.64 RP10 -421.02** 61.36 Own Industry -406.98* 164.90 MPG -1185.27** 213.71 AWD 1336.289 4774.55 Diesel 14249.18** 3341.36 const 54632.65** 7783.33 *-signicant at 5% level **-signicant at 1% level As expected, the country specic variables do not change much, which shows the ro- bustness of the results. The remaining hedonic variables however, show quite dierent eects. The constant term remains signicant and it proxies for all size and power charac- teristics. Larger and more powerful cars cost more to produce and they are also preferred by consumers, which translates into higher prices. The all wheel driven cars seem to be 93 priced higher, but this coecient is not signicant. Also diesel cars are priced higher, which seems to either suggest that diesel cars are more expensive to produce, or that they are preferred by consumers due to their fuel eciency. This explanation might actually be the cause for the negative MPG coecient. It is possible that customers who put a high value on fuel eciency, simply steer towards diesel engines, while those who buy gas do not care that much about fuel eciency, but rather about power performance which is negatively related to fuel eciency. It is important to note here that in Europe, unlike the US, diesel fuel is, and has been, priced considerably lower than gas which in turn created a large market share for diesel engines which, on top of the lower fuel price, are also more ecient than gas engines. 4.5 Extended Model: Competition, Collusion, and other Fixed Eects In this subsection, we expand our analysis to include and estimate additional xed eects associated with the producing rm and country, and also associated with the destination country. These eects can further explain price dierences resulting from cost hetero- geneities, brand and overall market preferences, market concentration, and also possible collusive behavior. To further capture dierences in both cost, and preferences between dierent car brands, I will include producer xed eects in all the following estimations. Producer xed eects are included to control for any other unobservable characteristic that is brand specic. These unobservables might be cost related, if for instance some producers are more ecient than others or use cheaper materials, or preference related, if people prefer 94 certain car brands over others. We do not expect these brand specic coecients to be very signicant for a number of reasons. First of all, while dierent brand preferences might exist among consumers, they are likely to average out, and they are also likely to be outweighed by the domestic brand preference. Secondly, given the high level of market concentration, it is likely that certain technological advantages were shared among rms belonging to the same group. It is also possible that certain mergers were the direct result of dierent comparative advantages, and as a result, the technology is likely to be quite uniform among the present competitors. Therefore, cost and preference parameters are not very likely to be dierent among brands once we control for the technical character- istics and domestic brand preference. However, controlling for these brand xed eects is still important in the same way that controlling for all hedonic variables was. I also tried including destination country dummies for all countries in the sample, which would possibly account for things such as local cost dierences. However, there is a serious collinearity problem, and the inclusion of these dummies strongly aects the signicance of all the country specic variables. Therefore, I chose to exclude these destination coun- try variables from my estimation, and only keep producer dummies. Besides controlling for individual producer xed eects, I also tried including dummies for the country of origin, with no signicant results. The producing country does not seem to aect pricing at all. As a rst exercise, I study the dierent eects on prices that result from dierent competitive forces associated with the presence of a local producer. Instead of having a single dummy variable, I construct dierent dummies for countries with only one producer, with 2 or 3 producers, or with more than 6 producers. The omitted group is obviously the group of countries with no domestic industry. Under a strong domestic brand bias, 95 a local producer might monopolize the market and charge higher prices. At the same time, more domestic producers might engage in erce competition which might drive prices down. Another aspect to consider is the competitive pressures engaged on the foreign segment. As a response to the domestic brand bias, foreign producers might try to attract customers by lowering their prices. In order to distinguish between these eects, I construct interactive dummies between the presence of local producers and the cars being domestic or foreign. The estimation of these coecients points to the fact that the eect on prices is mainly due to foreign cars pricing, and not to domestic cars. All the separate regressions are random eects estimations with robust standard errors. Although not reported here, we control for all physical characteristics, cross country income heterogeneities, and other brand xed eects. All the eects are summarized in the table below: Table 4.4: The Eects of a Domestic Producer Dependent Variable - Price in Euros (excluding taxes) Variable Coecient St. Error One Producer 459.70** 132.80 Two Producers -1135.027** 257.74 Six Producers -871.76** 283.64 Own Industry Domestic 523.65 346.59 Own Industry Foreign -394.30** 133.99 One Producer Domestic -194.27 159.69 Two Producers Domestic -542.06 1195.81 Six Producers Domestic 1097.27** 275.84 One Producer Foreign 531.99** 139.95 Two Producers Foreign -1066.34** 259.01 Six Producers Foreign -1027.08** 308.19 *-signicant at 5% level **-signicant at 1% level In the rst specication, we simply disaggregated the group of countries with a local producer into three dierent sub-groups: countries with only one producer, countries with 96 two or three producers, and countries with more than six producers. The coecients are all highly signicant. They seem to suggest that countries with only one producer have higher prices, while countries with two, three, or more than six producers have lower overall prices. An intuitive explanation would suggest that a local producer might monopolize the market easier, and this would lead to higher prices, while having more producers competing against each other would lead to lower prices. However, note that cars on markets with more than six producers are priced higher than cars on markets with only two or three producers. Competition among domestic producers has to be higher on markets with six producers and hence prices should be lower on these markets if this was the sole result of domestic competition. In fact, what matters is not only domestic competition, but also the competitive pressure that domestic rms exert on foreign rms. Also note that many individual producers are part of larger groups of rms, and sometimes these groups control domestic and foreign brands. For instance, the Volkswagen Group controls not only the Volkswagen brand, but also the Audi, Seat, and Skoda brands. Therefore, collusive behavior has to be taken seriously, and having six or more domestic producers does not necessarily mean more competition. A second estimation, containing two interaction terms between the presence of a local industry and whether the car is domestically produced or foreign clearly shows that the domestic cars are not priced any dierent, at least at this level of aggregation. What actually matters is how foreign rms price their cars. It seems that the domestic brand bias pressures foreign rms to price lower than the domestic rms. For a much clearer picture, we go one step forward and again disaggregate the number of domestic producers and then interact it with the car being domestic or foreign. Some surprising results emerge. 97 Firstly, although not statistically signicant, it seems that domestic cars are priced lower in countries with only one or two domestic producers. At the same time foreign cars are priced higher in countries with only one domestic rm. This coecient is highly signicant. The overall price level in countries with only one producer was found to be signicantly higher than in countries with no domestic industry, but this was thought to be the direct result of a domestic brand bias and monopolization of the market by the domestic rm. But in fact, our last estimation clearly shows that it is the foreign cars, and not the domestic ones, that are priced higher on these markets. This shows that one needs to be very careful when generalizing about domestic brand preferences. A likely explanation for my results is that the domestic brand preference cannot be generalized to all countries with a local industry. In fact, for countries that only have one domestic manufacturer (such as Romania or The Czech Republic), it is likely that the preference is instead for foreign cars. This is not surprising at all since countries with a comparative advantage in car manufacturing are countries with a long history of producing good quality products and countries that were able to develop multiple manufacturing rms. On the other hand, countries with only one domestic rm are more likely the result of direct government planning, rather than comparative advantages. It is therefore not surprising that citizens of these countries prefer better quality cars coming from abroad. In countries with two or three domestic producers, the domestic brand bias seems to be present. Domestic cars are still not priced dierently than cars on markets with no domestic producer, but foreign cars have now signicantly lower prices. The highest degree of domestic brand preference seems to be on markets with more than six domestic producers. On these markets, prices for domestic cars are signicantly higher, and at the same time, prices for foreign cars are signicantly lower. As discussed earlier, these are 98 the countries with a long history of quality when it comes to automobiles manufacturing. There is denitely a high consumer preference for quality, which raises the price of these cars. At the same time, possible collusive behavior between manufacturing rms cannot be rejected. A secondary eort in this subsection is made by including two dierent types of inter- actions: interactions between the producing country and the destination country for all manufacturing countries in our sample, and interactions between each individual producer and the destination countries. Once again, these are all random eects specications with robust standard errors where we control for all hedonic variables, income heterogeneities, the presence of local producers, and brand xed eects. The main motivation for including this type of interactions is to account for any possible transaction or transportation costs between any two countries, but most importantly to see if we can observe any patterns of collusion, competition, or overall preference for cars in these countries. There are seven manufacturing countries for which we have models in our sample: Italy, Germany, France, Sweden, The Czech Republic, Spain, and UK. We interact each of these countries with the remaining six and with itself, and obtain a table of 49 interaction terms that present the price dierences compared with the average car price in the rest of the European Union. The self interaction terms (country Y country Y) will pick up the individual domestic brand bias (in country Y), while the other interactions (country Y country Z) will simply pick up the way cars produced in country Y are priced in country Z, relative to the rest of the EU. For the second specication, we have 15 brands of cars, representing 15 producers, that we interact with the destination countries to go one step deeper from just interacting the producing country with the destination country. We do so because, as mentioned earlier, some producers are actually owned 99 by certain groups and collusions would be more likely within the same group. One can think of two dierent types of eects associated with collusive behavior. One one hand, within any given country, local producers might collude among themselves, or even with foreign producers to increase prices in a cartel type fashion. This type of collusion would increase all prices within that country. The other type of possible collusive behavior is when producers, or groups of producers from dierent countries, collude to preserve their domestic market monopoly and stay out, or not competing hard with their accomplices on foreign markets. For instance, collusion between say Volkswagen and Fiat could mean that Volkswagen would price their cars so high in Italy that it won't threaten Fiat's position, and in response, Fiat would do the same in Germany. Both rms would maintain their dominant position on their domestic market and make higher prots overall. Table 4.5 presents the eects of the country by country interaction terms, with the producing country on the rows, and the destination country on the columns. Table 4.5: Country by Country Interactions Italy Germany France Sweden Czech Rep. Spain UK Italy n.s. + + n.s. n.s. Germany + + + n.s. n.s. France + + + n.s. n.s. Sweden + + + n.s. n.s. Czech Rep. + + + n.s. Spain + + + n.s. n.s. n.s. UK n.s. + n.s. n.s. { statistically not signicant As already mentioned, the boxed eects from the main diagonal can be interpreted in terms of the domestic brand bias. There is an obvious domestic brand bias in Germany and France, where German, and respectively French made cars are priced higher than the average in the rest of the EU. At the same time however, most other European cars 100 are priced higher in these two countries. With the exception of the UK made cars, all coecients are positive and highly signicant. This is also true for Italy, where the only insignicant coecients are those for Italian and British made cars. Although Italian cars do not seem to be priced any higher in Italy, and they are denitely cheaper than other European made cars, this is not to say that a domestic brand preference is not present in Italy. Remember that foreign cars are on average cheaper than domestic cars in countries with more than 6 producers. These countries are Italy, Germany and the UK. Even if Italian cars are priced at their European average in Italy, as long as foreign cars are priced under their average, this is proof that the domestic producer has a market advantage in terms of consumers' preferences. Actually, even German cars in Germany are price lower than some other European cars, but overall foreign cars are cheaper than domestic cars, and this proves the domestic brand preference. Note that we already accounted for model specic characteristics, for income eects and other types of xed eects. The remaining dierences can only be interpreted as an overall higher preference for cars in these three countries, or as a direct result of collusive behavior. We can relatively easily dismiss an argument based on an overall higher preference for cars in these three countries. As mentioned, foreign cars are priced lower in all these three countries on average. However, since almost all European cars are priced higher, this can only mean that the remaining models in our sample (mainly Japanese and Korean cars) are way cheaper than European cars. Hence, we cannot argue that German, Italian, or French consumers value cars higher than other European consumers. There might be a stronger preference for European cars, but this is unlikely. A more plausible explanation is that a strong collusive behavior is at work in these three countries. Firstly, note that with the exception of Sweden, all other brands, regardless of their country of origin, are owned by German, Italian, or French 101 groups. Fiat owns Fiat and Alfa Romeo, PSA owns Peugeot and CItroen, and Volkswagen owns Volkswagen, Audi, Seat, and Skoda. Also, within each one of these countries, a very small number of groups controls virtually the entire market for automobiles. Fiat in Italy, PSA and Renault in France, and Volkswagen, BMW, and Daimler in Germany control virtually the entire domestic market, or at least the volume producers segment. We are talking about 6 groups who control approximately 70 percent of the Western European market. It would be a valid argument to assume that these 6 groups, or a smaller subset of them, can easily collude and set prices to maximize joint prots. This is done in both ways mentioned earlier. First, within a given country, all colluding rms increase prices from the competitive level where other rms (mainly Japanese) operate. Then, across countries, foreign colluding producers increase their prices even more, above the price of the domestic colluding partner, reducing competition in return for a similar treatment in their own home countries. These types of behavior can be easily observed in Appendix B.1, where the actual magnitudes of the eects are presented. Moving on to the other destination countries, note that in The Czech Republic and Spain, most prices are not signicantly dierent than in the rest of the European Union. In terms of the domestic brand bias, these countries actually have a domestic preference for foreign cars, and this is especially true with the Czech Republic, where Skoda is signicantly cheaper that other cars. Besides the lack of a preference for domestic cars, these countries do not have a strong domestic industry, and even more so, their brands are owned by the Volkswagen group. Hence, these two countries are practically identical, from a market structure perspective, to countries with no domestic producers and the pricing picture perfectly re ects this. 102 On the other hand, Sweden and the UK seem to be highly competitive countries, with much lower prices across the board. In the UK, this might be the direct result of the market structure. The UK has a large number of domestic automobiles manufacturers, but most of them belong to the premium class. The UK is still home to seven volume manufacturers, but their combined market share is nowhere near the gures present in France or Germany. For instance, while PSA and Renault have more than 50 percent market share in France, in the UK more than 75 percent of the market is shared by many foreign rms, with the largest group only controlling slightly more than 10 percent. As a result, the market is extremely competitive with American, European, Japanese, Korean, and British rms aggressively cutting down prices to stay in business. In Sweden, on the other hand, the lower prices are most likely the direct result of the nancial struggles of the two main producers { Volvo, and especially Saab. During 2009-2011 Saab had tremendous diculties in operations. It switched owners a couple of times, and actually led for bankruptcy after more than three years of ghting for survival. Similar to what the American companies experienced in the recent years, Saab had to drastically cut prices in order to sell inventory and stay a oat. In order to further clarify the collusive patterns among the top three auto manufactur- ing groups, I disaggregate the country of origin dummies into brand dummies and interact them with the destination country dummies in the same way as before. The relevant re- sults are presented in Table 4.6 where the boxed eects represent the pricing eects in the origin country. Since dierent local producers who do not belong to the same group might actually behave dierently, we are primarily interested in nding cells that are not robust with the previous estimation that pooled together all the brands produced in a 103 given country. While most results are consistent with previous ndings, a few interesting dierences emerge. Table 4.6: Brand by Country Interactions Italy Germany France Sweden Czech Rep. Spain UK Alfa Romeo n.s. + + + n.s. Fiat n.s. + + n.s. n.s. BMW n.s. n.s. n.s. Mercedes + + + n.s. n.s. Opel n.s. + + n.s. Audi + + n.s. n.s. n.s. VW + + + n.s. Seat + + + n.s. n.s. n.s. Skoda + + + n.s. Volvo + n.s. n.s. n.s. n.s. Saab + + + n.s. + Citroen + + + n.s. Peugeot n.s. + + n.s. n.s. Renault n.s. + + n.s. Mini n.s. + n.s. n.s. { statistically not signicant First of all, it seems that in spite of the fact that the main patterns between the three top manufacturing countries are conrmed, only some of the manufacturers use collusive strategies. To be more exact, BMW does not seem to act in a collusive way on any market. BMW models are not statistically dierently priced in either Italy, Germany, or France and are actually priced lower in the remaining four countries analyzed which is a clear sign that BMW is acting competitively across the board. Also Opel does not reciprocate the Fiat group in pricing higher on the Italian market. It seems that the VW group and Mercedes are the only two German rms that actively engage in collusion with the Italian group Fiat. Also, the only French group that apparently acts collusively with Fiat is PSA. Renault on the other hand, only seems to reciprocate high prices with the 104 German rms. It is very possible that both Renault, on the French market, and Opel and BMW, on the German market, free ride on the other domestic producers. If say PSA enters a collusive agreement with Fiat, and Fiat does not compete aggressively on the French market, then Renault can benet from it without need of reciprocating. Same goes for Opel and BMW in Germany, they could take advantage of a VW-Fiat agreement without needing to compete less on the Italian market. Of course this hurts Fiat on its domestic market, which is supported by the nding that in spite of a domestic brand bias, Fiat does not enjoy the same kind of price control that German or French rms enjoy on their respective domestic markets. It therefore comes with no surprise that Volkswagen, Daimler, PSA, and Fiat seem to be the major groups engaging in price xing strategies and collusive behavior. These groups have been previously ned serious amounts by the European Commission for uncompetitive practices related to their dealership systems. Collusion is extremely hard to prove, but it is easy to understand that rms who engage in collusion benet more from articial market segmentation. A second interesting result points to at least two possible collusion patterns that were previously not observed. We already mentioned that the British and Swedish markets were found to be extremely competitive, and the main pattern persists when we disaggregate the local producers. However, two dierences can be observed: Alfa Romeo and Fiat models are priced signicantly higher on the highly competitive Swedish market and Saab cars are also priced higher on the reasonably competitive Spanish market. If we look at the reciprocal links we also observe Volvo (which otherwise acts extremely competitive) charging higher prices on the Italian markets and Seat pricing above all other European producers (except Alfa Romeo) in Sweden. These patterns seem to suggest collusive 105 agreements between Volvo and the Fiat group on one hand, and between Saab and Seat on the other. Without claiming to be a clear cut proof, the pricing patterns we observed support theories of collusion between the major manufacturing groups in the European Union. The major players pointed by the pricing data seem to be the same rms which were previously penalized for their uncompetitive practices. 4.6 Conclusions This chapter clearly shows evidence that signicant demand side dierences and market concentrations across member states of the European Union allow manufacturers to prot from engaging in international price discrimination and collusive behavior. What makes these sort of practices protable is the successful market segmentation and prevention of resales through the use of the exclusive dealership system. This system continues to function under basically unchanged rules in spite of numerous consumer complaints and in spite of numerous penalties imposed on manufacturers by the European Commission for anti-competitive practices. The fact that this continues year after year, is further proof that the practice is extremely protable for manufacturers. In spite of all the integration eorts, automobile prices in the European Union are not likely to converge any further in the near future as long as this mechanism is still in place. The very slow convergence observed in the recent years is most likely due to convergence in incomes, as the poorer states slowly get closer to the richer ones. Signicant demand side dierences still exist, especially the domestic brand bias, and they will not disappear even if full income convergence is to occur in the future. At the same time, strong local producers monopolize the markets and seem to be engaging in 106 collusive practices which further distort prices. Strong patterns of collusive behavior are observed for the major manufacturing groups in Italy, France, and Germany. The United Kingdom, which was previously pointed at as being one of the most expensive markets, turns out to be one of the most competitive markets after controlling for income dier- ences. This clearly shows the importance of accounting for cross country heterogeneities. This chapter also shows evidence that local producers clearly aect the competitive bal- ance on domestic markets, but the predominant eect on price is the eect through foreign cars and not through domestic cars as it is commonly thought. Therefore, in spite of trade liberalization and market integration, as long as manu- facturers are able to segment the markets successfully, we will still observe price xing, collusive behavior, and signicant price dierences for identical products across interna- tional borders. 107 Chapter 5 Rules of Evidence and Liability in Contract Litigation 5.1 Introduction In 1988 the U.S. Navy awarded a $4.8 billion xed-price contract to General Dynamics Corporation and McDonnell Douglas Corporation for the design and production of an advanced, carrier-based stealth aircraft called the A-12 Avenger. The government agreed to share certain classied information with the contractors since the project relied on state-of-the-art stealth technology already being used in other government programs, and such technology would have been prohibitively costly and time-consuming to reproduce (Schwinn, 2011). The project soon encountered a series of delays, and after failing to meet various benchmarks, the contractors formally requested a restructuring of the contract from a xed-price to a cost-reimbursement agreement, arguing that the cost was much higher than originally anticipated. Failing to reach an agreement and dissatised with the lack of progress, the Navy terminated the contract for default in 1991 and sought repayment of $1.3 billion plus $2.5 billion in accumulated interest. The contractors sued the U.S. claiming that their inability to complete the project was excusable due to the government's failure to share its superior knowledge regarding stealth technology. In response, the government invoked the state-secrets privilege to prevent the 108 classied information from being used as evidence. Thus, the contractors were caught in a Catch-22: they claimed that they failed to perform because the government did not provide critical information on stealth technology, but the contractors could not use that information as evidence in prosecuting their case because the government deemed the technology a state secret. (See Appendix C.1 for a detailed history of the litigation.) After twenty years of litigation, the case was resolved in 2011 by the U.S. Supreme Court in General Dynamics v. United States. The Supreme Court concluded that both parties must have been aware that the state-secrets privilege would prevent a resolution of such a contractual dispute, and both parties accepted this risk when they signed the contract. The court's decision was to let both parties remain where they were before the case was litigated. Thus, the contractors did not have to pay back any of the $2.7 billion they had received from the Navy, and the government did not have to make any additional payments to the contractors, which had spent $3.9 billion on the project. As Justice Scalia summarized: \It's the `go away' principle of our jurisprudence, right?" (General Dynamics v. U.S., 2011, Oral Argument.) While the Supreme Court's decision was primarily the result of the matter being non-justiciable due to the inability of the contractors to build a proper defense given the state-secrets privilege invoked by the government, the case raises broader economic issues. Virtually all contracts have some form of private information and such information can distort outcomes and lead to ineciencies. Legal rules of evidence and liability strongly in uence economic outcomes, since sophisticated contracting parties are aware of informa- tion asymmetries, anticipate future con icts, base their con ict-resolution expectations on these rules, and contract accordingly. 109 Thus, General Dynamics v. U.S. raises several interesting questions. First, which liability rule is more ecient: (1) forcing the contractors to be strictly liable for their failure to perform or (2) the General Dynamics rule? Second, what are the optimal bidding functions under strict liability and the General Dynamics rule? Third, how does the game change if the evidentiary rules require a buyer's private information to be admitted in court and used by the contractor in its defense? A vast literature exists on the law and economics of contracts (see Hermalin, Katz, and Craswell (2007) for a literature review), which includes theories of contract eciency and ecient default rules (Schwartz and Scott, 2003). A substantial literature also exists that examines the tradeo in rst-price auctions between price and contractual performance, see, e.g., Spulber (1990), Waehrer (1995), and Zheng (2001). Directly relevant to this research are theories of contract breach and enforcement, limits of the bargaining principle, exceptions from full contract enforcement, and contract interpretation, see, e.g., Eisenberg (1982) and (1995), Posner (2005), and Shavell (2005). Several papers within this literature study optimal mechanism design when bidders can default, see, e.g., Bruguet et al. (2009) and Chillermi and Mezzetti (2009). However, we are not aware of any research that studies either the risk of bidder default in a litigation context or the eciency eects of diering rules of evidence and liability in such litigation. We study a contracting auction environment where the buyer possesses private in- formation regarding the true cost of the project. This holds in defense contracting with secret technologies, but also holds more generally whenever the buyer has private cost information. We study the bidding process, the arrival and resolution of con icts, and the economic eciency implications of dierent rules of evidence and liability. In addition to the General Dynamics rule, we consider a strict liability rule where the contractor is 110 held liable and forced to complete the project regardless of cost. We also consider the eciency eects of an evidentiary rule requiring the buyer's private information to be admitted in court for use by the contractor in its defense. In our model, contractors are aware at the time of bidding that the buyer might have private information and that the true cost of the project might include an additional random cost component. Contractors anticipate future con icts and default situations and, depending on the evidentiary and liability rules, bid accordingly. We nd that the rules of evidence and liability strongly aect the incentives of both the contractors and the buyer. Our basic nding is that the evidentiary and liability rules in General Dynamics lead to a more ecient outcome than a strict liability rule or an evidentiary rule requiring disclosure of the buyer's private information. 5.2 The Model There are N 2 contractors who bid to undertake a government project. The govern- ment's valuation of a completed share q t 2 [0; 1] of the project is q t V (implying that the government's valuation of the completed project isV ). Bidderi's total cost of completing the project,C i , equalsc i +X, wherec i denotes bidderi's private cost (i.e.,c i is known only by bidderi) andX denotes an ex ante unknown, common cost associated with a techno- logical secret possessed by the government. Bidders' private costs are independently and identically distributed according to a cumulative distribution function (cdf) known to all bidders and the government: we assumec i is distributed according to the cdfF () on the support [0;V ]. Each bidder's total cost of completing the project includes the common cost X because construction of the project involves classied technology possessed only 111 by the government and to which no bidder has access. Bidders only know their individual costs and the presence of a random cost x, assumed to be uniformly distributed on the interval [0;V ]. We assume a rst-price, sealed-bid auction as the rule for awarding the contract. During execution of the project, the winning bidder nds out the true value of the random cost X and completes a part of the project q t . In order to avoid compli- cations associated with moral hazard, we assume close monitoring or \fair play" on the contractor's part such that the fraction of the project completed is a quantity propor- tional to her individual cost. The fair-play assumption is not as strong as it might seem at the rst sight, taken into account that usually contractors are repeat players who do not want to establish a bad reputation. This is especially true with government defense contracts which are often multi million dollar contracts and only a handful of rms are usually competing for these contracts. We specically assume q t = c i c i +X . The cost for the winning bidder to complete q t is c i . The timing of the game is the following: Step 1: Contractors bid for contracts in a rst-price, sealed-bid auction format. Step 2:. The contract is awarded to the lowest bidder. Step 3: The government pays the contractor the value of the bid and the contractor begins work on the project. Step 4: The contractor nds out X (the true value of the random cost), produces and delivers a part of the nal project q t = c i c i +X , from which the government infers the true value of the winning bidder's cost c i . Step 5: The government decides whether to sue the contractor for damages or support the cost over-runs and nish the project without legal intervention. Step 6:. If litigation occurs, the court passes judgement according to the existing set of legal rules of evidence and liability. 112 We study and compare the outcomes for dierent rules of evidence and liability. We assume these rules to be common knowledge at the time of the bidding process. We consider three dierent rules of evidence and liability: General Dynamics: the court (1) does not allow the contractor to use the buyer's private information regarding the cost of the secret technology in litigation; (2) voids the contract so that the project is not completed; and (3) allows the contractor to keep any compensation received, but does not require the buyer to make any additional payments. Strict Liability (SL): the court (1) does not allow the contractor to use the buyer's private information regarding the cost of the secret technology in litigation; (2) enforces the contract so the project is completed; and (3) requires the buyer to make all payments specied in the contract. Disclosure of Private Information (DPI): the court (1) allows the contractor to use the buyer's private information regarding the cost of the secret technology in litigation; and (2) the court rules for or against the contractor depending on the cost of the secret technology. Specically, if the cost associated with the technological secret is higher than some threshold, then the General Dynamics rules apply. If, however, the cost of the secret technology falls bellow the threshold, the SL rules apply. 5.3 Characterization of outcomes underGeneralDynamics If the court's rule is to void the contract and let both parties keep what they already received, the government's decision to sue or support the cost overruns and complete the 113 project is equivalent to an eciency condition. To see this consider the government's prots in the two possible scenarios: 8 > > > < > > > : Sue G =q t Vb i ; if the government sues Pay G =Vb i X; if the government pays the cost overruns and nishes the project whereb i is the winning bid,V is government valuation for the completed project,X is the secret cost, andq t = c i c i +X is the completed part of the project delivered by the contractor. The government knows precisely the value of both X and c i at the time of deciding whether to sue or not and therefore compares the two possible prots Sue G and Pay G . The decision to sue or not is given by the following rule: 8 > > > < > > > : Pay if V >c i +X Sue if V <c i +X: This condition ensures that from an eciency standpoint, when the valuation of the project exceeds the total cost and hence the project should be nished, it actually will be nished and the government will support the cost overruns. On the other hand, when the valuation of the project is less than the total cost and hence the project should not be nished, the government will sue, the project will not be nished, and the government will be at a loss. This can be considered fair since the government is the source of the information asymmetry, and the government will not allow the technological secret to be used by the contractor in litigation. In the inecient case, when the cost exceeds the valuation, it is impossible to decide ex ante whether the project should be undertaken or not due to the information asymmetry. The government has to pay a price in order to give 114 proper incentives to the bidders to reveal their costs truthfully and bid accordingly and at the same time keep its secret technology classied. If the cost of the secret technology were public information, there would be self selection on bidders' side and no bidder with a total cost above V would bid, hence ensuring eciency. We now analyze the bidders' optimal bidding strategy. We assume each bidder follows a bidding strategy increasing in its individual cost. Each bidder submits a bid b i (c i ), and the bidder with the lowest bid is awarded the contract. Since bids are increasing in costs, this ensures that the winning bidder is actually the bidder with the lowest individual cost. Regardless of whether the government decides to sue or cover the cost overrun, the contractor will always earn b i c i . Hence, bidders maximize their expected prots max b i i = [P (winning)](b i c i ) which yields the optimal bidding strategy (see Appendix C.2): b i (c i ) =c i + R V c i [1F (x)] N1 dx [1F (c i )] N1 : This is identical to the optimal bidding for a contracting auction with no secret cost. If both c i and X are assumed to be uniformly distributed on the interval [0;V ], then the simplied bidding function becomes b i =c i + Vc i N : The bids are dierent from a standard auction bids. In a contracting auction bidders bid slightly above their individual costs and not slightly below their individual valuation. 115 Under uniformly distributed costs, the ex post prots for the contractor and the government are: 8 > > > > > > > > > > > > < > > > > > > > > > > > > : C = Vc N G = 8 > > > < > > > : VcX Vc N when V >c +X q t Vc Vc N when V <c +X where c is the lowest individual cost (i.e., the individual cost of the winning bidder). 5.4 Characterization of outcomes under SL If the court's rule is strict liability, then in equilibrium the government will always sue and demand that the contractor fulll her obligations. The government will always earn: G =Vb i while the winning bidder's prot will be: C =b i c i X: Bidders do not know the true value of X at the time of bidding, so they consider the expected value. Following the same bidding strategy, they maximize their prots: max b i i = [P (winning)](b i c i E(x)): 116 SinceX is uniformly distributed on [0;V ],E(x) = V 2 and the optimal bidding function is (see Appendix C.3): b i (c i ) =c i + R V 2 c i [1F (x)] N1 dx [1F (c i )] N1 + V 2 : The optimal bidding function in the SL case is similar to the bidding function in the General Dynamics case, but with the addition of the last term ( V 2 ) and the dierent limit of integration. Since bidders know they will be held liable for the entire contract, they insure themselves against future losses by bidding more. Also since they increase their bids by the expected value of the random cost X, some contractors will not bid. Specically, only bidders with individual costs lower than VE(X) = V 2 will bid. If all costs are uniformly distributed on [0;V ], then the optimal bidding function is: b i (c i ) =c i + Vc i N + V 2 V N N2 N (Vc i ) N1 , if c i < V 2 and the ex post prots for the winning contractor and the government are: 8 > > > < > > > : C = Vc N + V 2 V N N2 N (Vc) N1 X G = V 2 c Vc N + V N N2 N (Vc) N1 where c is the lowest individual cost (i.e., the individual cost of the winning bidder). Note that when there is no bidder with individual cost below V 2 , no contractor bids and therefore both prots equal zero. It is now possible to study the eciency implications of the two dierent rules by comparing the outcomes of the General Dynamics rule with the ones of the strict liability rule. 117 5.5 Strict liability or not? Discussion From an ex post perspective, which court rule, General Dynamics or SL, would be prefer- able from a social perspective? For simplicity we continue to assume both individual costs and the secret government cost to be ex ante uniformly distributed on [0;V ]. Ex post, let X be the true value of the secret government cost andc the smallest individual (winning) cost. We dene total welfare as the sum of the government's and contractor's prots: W = G + C : If at least one bidder has individual costs below the V 2 threshold, there will be a winning bid, a contract, and total welfare under SL will equal: W SL =VcX: Under General Dynamics however, we will always have a winning bid and a contract. Total welfare under General Dynamics equals: 8 > > > < > > > : W GD E =VcX if V >c +X W GD NE =q t Vc if V <c +X where \GD" indicates General Dynamics, \E" indicates it is ecient to complete the project, and \NE" indicates it is not ecient to complete the project. Thus, in the ecient case, when the valuation exceeds the true cost of production, total welfare is the same under both rules. However in the inecient case, when the 118 valuation is smaller than the cost of production, there are higher losses under SL. From a social perspective, General Dynamics yields strictly better outcomes than SL if either there are bids under both rules or the project is ecient to complete. The only case when SL yields higher welfare than General Dynamics is when no individual cost is below V 2 and VcX < 0. In such a case General Dynamics yields small losses while SL eliminates these losses. However, the probability of this case is very small if the number of bidders is large. 5.6 Disclosure of Buyer's Private Cost Information Suppose the court allows the winning bidder to use in its defense the government's delay in providing the secret technology and the cost of that technology. This is the disclosure of private information (DPI) rule. The court uses a threshold cost criterion to decide for or against the contractor. Specically, if the cost associated with the technological secret is higher than some threshold, X >X, then the General Dynamics rules apply. If, however, the secret cost falls below the threshold, X <X, then the SL rules apply. The game under the DPI rule follows exactly as before: bidders bid, the contract is awarded to the lowest bidder, the government pays the amount of the bid, the project gets underway, the contractor delivers q t = c i c i +X , and then the government decides whether to sue or cover the cost overruns. The government will always sue when X <X, in which case the prots will equal: G =Vb i and C =b i c i X: On the other hand, if X > X the government will sue and terminate the contract in the inecient case (when V b i X < 0). The government will support the cost 119 overruns in the ecient case (when Vb i X > 0). In both these cases the prot for the contractor equals: C =b i c i while the government's prot equals: 8 > > > < > > > : G Sue =q t Vb i G Pay =Vb i X: Therefore, each bidder chooses her optimal bidding function to maximize expected prots: max b i i = [P (winning)][P (x>X)(b i c i ) +P (x<X)(b i c i E(xjx<X)]: Since x is uniformly distributed on [0;V ], E(xjx < X) = X 2 and the optimal bidding function is (see Appendix C.4): b i (c i ) =c i + R V X 2 2V c i [1F (x)] N1 dx [1F (c i )] N1 + X 2 2V : The bidding function with the DPI rule is similar to the previous cases: bidders bid their individual cost plus an adjustment factor to insure against potential future losses if the government terminates the contract for default and sues to recover its costs. The adjustment factor equals X 2 2V , which is the expected value of the secret cost conditional on the secret cost being below the court threshold times the probability of the secret cost being below that threshold. Again, as in the SL case, because of this additional term, contractors with individual costsc i >V X 2 2V will not bid and hence the integration limit 120 diers. If all costs are assumed to be uniformly distributed on [0;V ], then the bidding function becomes: b i (c i ) =c i + Vc i N + X 2 2V X 2N N2 N V N (Vc i ) N1 , if c i <V X 2 2V : In terms of aggregate welfare, if at least one bidder has a cost below V X 2 2V , then the sum of the prots will be: G + C = 8 > > > > > > > < > > > > > > > : VcX, if X <X (no matter if ecient or not) VcX, if X >X and VcX > 0 q t Vc, if X >X and VcX < 0: Thus, if there is at least one bid, the DPI rule is inferior to General Dynamics from a social perspective. This result is similar to the result obtained under the strict liability rule. Admitting the secret as a defense yields the same welfare as General Dynamics under most circumstances, but it is strictly worse whenever the secret cost falls below the court's threshold and it is inecient to build. As with SL, the only case when admitting the secret as a defense yields higher total welfare than General Dynamics is when we are in the inecient case and no bidder has low enough costs to bid. If that is the case, having the DPI rule actually prevents both parties from entering an agreement that they should not enter in the rst place. In this case, admitting the secret as a defense yields zero aggregate prots, while General Dynamics yields losses. Again, the probability of this happening is very small with a large enough number of bidders. 121 5.7 An Alternative Continuous Production Model In this section, we present an alternative way to model the production decision after the bids have been submitted. In the previous sections, we assumed the winning contractor produced a portion of the project, proportional to the individual cost/total cost ratio. We now consider a model in which the winning contractor, unaware of the true cost of the project, starts executing and keeps producing until she either nishes the project or reaches a point where the true cost would outweigh the winning bid. If this stopping point is reached, litigation occurs as before. To formalize, let there be N contractors bidding for a government project with val- uation V . Contractors have individual marginal costs c i identically and independently distributed on a commonly known cdf F (). The project diculty is ex ante unknown to the bidders. Let the true diculty of the project be D = D 1 +X, where D 1 is the known component and X is the random component that only the government knows ex ante. From a bidder's perspective, X is a random variable uniformly distributed on the interval [0;V ]. Bidders bid for the project, and the bidder with the lowest bid is selected as the winning contractor. The government pays the entire amount of the bid and the contractor begins working on the project. Initially, the expected diculty of the project is E(D) = D 1 + V 2 and the cost of nalizing the project is E(C) = c i E(D). The con- tractor builds more and more dicult parts of the project with each diculty increment coming at the marginal cost of c i . As the lower diculty threshold D 1 is reached and passed, the contractor starts updating her expectations regarding the random diculty component and hence the expected total cost of the project. There is no updating before reaching D 1 since this is the known diculty component, and we assume strict liability 122 for this portion of the project in order to avoid \weird bidding." Not imposing strict liability for at least a small portion of the project would lead to \weird bidding" behavior where bidders with high costs would bid zero and produce nothing in equilibrium. After passing theD 1 diculty level, the contractor keeps producing and updating her expected cost until either the project is completed or the contractor reaches a stopping point D stop where the expected costs exceed the winning bid. If this stopping point is reached, the government has the option to pay for the cost overruns and complete the project or sue for damages. Under General Dynamics, suing means nothing more than accepting the completed portion of the project and severing all contractual ties between the parties. We assume the government derives a value from an incomplete project proportional to the amount of the project that is nalized. More formally, for any stopping point D stop , the government's valuation is V Dstop D . If the stopping point is the completion point, then the government extracts its full valuation V . For any winning bidb i , the winning bidder can calculate her stopping pointD stop where the expected cost for completing the project would exceed the bid b i . If this stopping point is reached without completing the project, the random diculty component X is now distributed uniformly between D stop and D 1 +X. Hence, the expected cost of completing the project will beE(C) =c i Dstop+D 1 +V 2 . By setting the expected cost equal tob i , we can calculate the stopping point D stop = 2b i c i (D 1 +V ). Since we assume strict liability for the D 1 portion of the project, D stop has to be greater or equal to D 1 , so for any bid b i c i (2D 1 +V ) 2 the stopping point will be D 1 . 123 Summarizing: D stop = 8 > > > < > > > : D 1 , if b i c i (2D 1 +V ) 2 2b i c i (D 1 +V ),if b i > c i (2D 1 +V ) 2 : If a stopping point is reached, the government has the option under General Dynamics to pay for the extra costs and complete the project or litigate and dissolve all contractual ties with the contractor. The government knows the extra eort required to complete the project and hence the cost to do this. We denote this dierence by = DD stop . If this portion is completed, it would bring additional benets to the government equal to V D , with a cost equal toc i . The government will decide to pay for the cost over-runs if the extra benets are greater than the extra costs, and will sue otherwise. We write the pay and complete the project condition as V D c i ()V c i D which is equivalent to an eciency condition. In other words, the government will pay the cost over-runs and complete the project when the project is ecient to build. We can now express the prots for the government and for the contractor, and calcu- late total welfare depending on whether building the project is ecient or not. Since the government suing does not impose any additional costs on the contractor (if the govern- ment sues, the contract is simply terminated under General Dynamics without any further penalties), and the government paying for the cost over-runs does not bring additional benets to the contractor (the government pays exactly the additional completion costs and nothing more), the prot for the contractor will be the same regardless of whether 124 the government decides to sue or not: C = b i c i D stop . On the other hand, the gov- ernment's prot depends on whether the project is stopped or completed. If the project is ecient, G = Vb i c i , where is the extra diculty required to complete the project. In the inecient case, G = V Dstop D b i . By adding up the contractor's prot and the government's prot, we calculate total welfare under General Dynamics: W GD = C + G = 8 > > > < > > > : Vc i D stop c i =Vc i D, if V c i D V Dstop D c i D stop = (Vc i D) Dstop D , if V <c i D: Thus, as long as there exists at least one bid, SL is inferior to General Dynamics from a total welfare perspective. SL requires nishing the project at all costs, whether it is ecient or not. Therefore W SL =Vc i D, which is the same with W GD in the ecient case, but strictly lower in the inecient case. Again, SL would be preferred only in the improbable case when it is inecient to build and there is no winning bidder. We only focus on the case when the project is not completed by the contractor. The case where the contractor completes the project before reaching its stopping point does not involve litigation and, therefore, yields the same welfare under either SL or General Dynamics. However, we show below that the bids are such that there is no project completion in equilibrium. To study the optimal bidding strategy under General Dynamics we need to consider the stopping points and expected prots for dierent bids. We have already seen that any winning bidb i c i (D 1 + V 2 ) impliesD stop =D 1 and hence the contractor's expected prot if she wins the auction equals C = b i c i D 1 . On the other hand, if the winning bidb i >c i (D 1 + V 2 ), then the building continues past diculty pointD 1 , until the project 125 is either completed, or the stopping point D stop = 2b i c i (D 1 +V ) is reached. Therefore, project completion is only possible if the bids exceed the level c i (D 1 + V 2 ). But is this possible in equilibrium? To see that it is not, consider the expected contractor prots under this scenario. For any such bid that exceeds the threshold, there is a stopping point, D stop . With probability DstopD 1 V the completion point will be reached before reaching the stoppage point, in which case the contractor will earn b i c i E(DjD 1 <D <D stop ). On the other hand, if the true diculty is greater than D stop , which occurs with probability VDstop+D 1 V , the contractor will earn b i c i D stop . Therefore, each contractor will choose a bid to maximize her expected prot: max b i i =P (winning)[( D stop D 1 V )(b i c i E(DjD 1 <D<D stop )+( VD stop +D 1 V )(b i c i D stop )]: SinceD stop = 2b i c i (D 1 +V ), the expected prot from winning the auction can be rewritten as: E() = ( D stop D 1 V )( c i V 2 ) + ( VD stop +D 1 V )[c i (D 1 +V )b i ] = = ( 2b i c i V 2D 1 V 1)( c i V 2 ) + (2 + 2D 1 V 2b i c i V )[c i (D 1 +V )b i ]: This expression is a quadratic convex function of b i and, hence, by lowering her bid, each bidder can increase her expected prot and at the same time increase the probability of winning the auction. Very high bids, on the increasing portion of the quadratic function, that could in principle yield higher expected prots, cannot be equilibria since bidders with higher costs can deviate to a lower bid where they could win the auction. Therefore, there cannot be any equilibrium in bidding with bids b i >c i (D 1 + V 2 ). Thus, equilibrium 126 bidding implies no production past the D 1 diculty level and bids that maximize the following: max b i C =P (winning) (b i c i D 1 ): This is almost identical to the result in the base model, with the only dierence being that instead of having a total cost c i for the common knowledge part of the project, we now have a marginal cost c i and a total cost c i D 1 for the common knowledge diculty level. Following the same procedure, we obtain the optimal bidding function: B i (c i ) =D 1 [c i + R V D 1 c i [1F (x)] N1 dx [1F (c i )] N1 ]: In the base model, we assumed the contractor will produce a fraction proportional to the ratio of individual (ex ante known) cost to total (ex ante unknown) cost. In the alternative model with continuous production, we have shown that the winning contractor will bid such that she will produce a fraction of the total project equal to the ratio of the known diculty component and the unknown true diculty of the project. Thus, our results are robust to these two winning bidder production models. 5.8 Conclusions We have analyzed the welfare implications of three dierent sets of evidentiary and li- ability rules in contractual disputes with private information. Information asymmetries distort incentives and create ineciencies. When contracts are aected by asymmetric in- formation, con icts develop between parties and litigation is often the only way to resolve such contractual disputes. Therefore, when contracting parties are aware of the presence 127 of private information, they anticipate future con icts and litigation, and contracting terms are directly in uenced by the applicable legal rules. In a contracting auction set- ting, we studied the eects of a strict liability (SL) rule; an evidentiary rule that allows the contractor to build a case around the withholding of private cost information by the buyer (the DPI rule); and the General Dynamics rule. We showed that, as long as there is at least one bid, General Dynamics yields higher eciency than both the SL and DPI rules. We found this result to be robust to two dierent ways of modeling the winning bidder's production process. In addition, General Dynamics creates ecient incentives for both the buyer and the contractor. It gives the buyer the incentive to reveal his private information to contrac- tors before the bidding starts, and it gives contractors the incentive to lower their bids considerably. In contrast, SL gives the buyer the incentive to hide his private information and deceive the contractors. In return, contractors severely overbid in order to insure themselves against future losses, which results in large eciency losses. Our model's main qualitative implications could be extended to other types of auctions aected by asymmetric information. 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Journal of Economic Theory, 100:129{171. 132 Appendix A - Appendix to Chapter 2 A.1 List of Empirical Variables Price - the face-value price as collected from Ticketmaster PriceRank - the relative rank of the price (1 being the most expensive price level) SecPrice - the secondary market price collected from completed Ebay transactions Dif - the dierence between the face-value price and the secondary market price PercDif - the percentage dierence in prices NrTickets - the number of tickets sold during any given transaction on Ebay Days - the number of days between the secondary market transaction and the event day Limit - the limit imposed on the number of tickets that can be purchased by a single customer on Ticketmaster (usually 4, 6, 8, or no limit) Sections - the number of sections the venue is divided into for any given event Prices - the number of price levels used for any given event MultiplePrices - dummy for whether multiple prices are used for any given section Weekend - dummy for whether the concert takes place on a weekend 133 DebutAlbum - the year of the debut album of the performing artist GoldRec - the number of gold records an artist has earned PlatRec - the number of platinum records an artist has earned MPlatRec - the number of multi-platinum records an artist has earned GoldSin - the number of gold singles for any given artist PlatSin - the number of platinum singles for any given artist MPlatSin - the number of multi-platinum singles for any given artist Success - the simple sum of all previous variables related to sales success Albums - the number of studio recorded albums for each artist LastAlbum - the year of the most recent studio recorded album Population - urban population of the city where the event takes place Income - per-capita income of the city where the event takes place 134 Appendix B - Appendix to Chapter 4 B.1 Magnitudes of the Country by Country Interactions Table B1: Magnitudes of the Country by Country Interactions Italy Germany France Sweden Czech Rep. Spain UK Italy 455.9 1232.71** 1058.61** 558.09 -1548.07** -638.78 -1374.1** Germany 535.82* 1227.1** 533.2* -5514.64** -931.65 -510.73 -8887.77** France 527.4* 1944.55** 2082.32** -2651.16** -1497.43 -407.34 -4091.59** Sweden 1367.59** 1919.38** 1298.82** -5178.16** -327.6 639.16 -8879.76** Czech Rep. 706.35** 1239.16** 1220.77** -1232.04** -857.32* -294.73 -2069.64** Spain 518.83** 1250.64** 1061.75** -188.23 616.66 -668.25 -1339.83** UK -137.17 415.64* -316.25 -2742.56** -1650.33** -1345.24** -4233.16** * - signicant at 5% level ** - signicant at 1% level 135 B.2 Magnitudes of the Brand by Country Interactions Table B2: Magnitudes of the Brand by Country Interactions Italy Germany France Sweden Czech Rep. Spain UK Alfa Romeo 253.32 885.89** 1431.29** 898.63** -2082.24** -1327.72** 178.21 Fiat 506.68 1319.25** 965.65** 472.74 -1428.38** -466.36 -1762.18** BMW -378.31 392.46 67.27 -6662.6** -3109.27** -1041.15* -10957.82** Mercedes 1223.89** 1408.79** 814.87* -6205.47** -858.99 -122.48 -12423.89** Opel 600.59 1823.49** 895.89** -2660.44** 1693.36 -715.12* -3779.53** Audi 1072.39** 1714.46** 597.87 -8097.55** 176.33 -80.39 -10847.47** VW 619.65** 1170.72** 603.62** -725.54* -1752.41* -319.89 -2151.46** Seat 518.94** 1250.51** 1061.92** -188.42* 616.38* -668.09 -1339.84** Skoda 706.47** 1239.03** 1220.94** -1232.23** -857.59* -294.57 -2068.65** Volvo 1079.29* 1317.86 1108.26 -4470.41** -362.77 123.75 -9189.33** Saab 1944.47** 3122.03** 1680.44** -6594.23** -258.09 1670.43** -8260.65** Citroen 1112.61** 2444.18** 2075.58** -1808.09** -154.95 -1058.43** -3602.51** Peugeot 518.01 1871.92** 2059.99** -2966.02** -661.21 -138.69 -4425.77** Renault 249.22 1803.28** 2119.69** -2600.98** -3423.84** -484.32 -3834.89* Mini -130.33 422.24* -309.36 -2736.03** -1643.89** -1338.37** -4226.45** * - signicant at 5% level ** - signicant at 1% level 136 B.3 List of Empirical Variables Table B3: Relevant Empirical Variables Physical Characteristics Length exterior length (in meters) Width exterior width (in meters) Height exterior height (in meters) CC engine capacity (in cubic centimeters) HP engine power (in horse power) NM engine torque (in newton meter) Sec100 time needed to accelerate from 0 to 100 km/h (in seconds) Top Speed top speed (in kilometers per hour) MPG average fuel eciency (in miles per gallon) Gearbox number of transmission gears AWD all wheel drive dummy Diesel diesel engine dummy Country Specic Characteristics Income national per capita income (in dollars) Gini national income inequality measured by the gini coecient RP10 national income inequality measures by the rich to poor ratio Own Industry domestic producer dummy MadeIn domestic brand bias dummy Disaggregation Dummies One Producer dummy coded with 1 if there is only one domestic producer Two Producers dummy coded with 1 if there are 2 or 3 domestic producers Six Producers dummy coded with 1 if there are more than 6 domestic producers Domestic dummy coded with 1 if the car is produced domestically Foreign dummy coded with 1 if the car is produced in a foreign country Brand Dummies a series of brand dummies to capture brand xed eects Country Dummies a series of country dummies for the countries with at least one manufacturer Interaction Dummies a series of interaction dummies as explained in the main text 137 Appendix C - Appendix to Chapter 5 C.1 A Brief History of General Dynamics v. U.S. Within weeks of terminating the contract for default, the Navy concluded that it had provided progress payments for work that was never performed. The Navy then sent the contractors a letter demanding that the contractors repay the Government approximately $1.35 billion. Both parties then entered into a deferred payment agreement for this amount. However, the contractors later led suit in the Court of Federal Claims (CFC) in order to challenge the termination decision under the Contract Disputes Act of 1978. The contractors claimed that their failure to complete the project, resulting in contract default, was excusable due to the fact that the Government failed to present the contractors with its \superior knowledge" about how to design and manufacture stealth aircraft, which the Government had agreed to provide. Pursuant to GAF Corp. v. United States (1991), the Federal Circuit has recognized that the government has an obligation \not to mislead contractors about, or silently withhold, its `superior knowledge' of dicult-to-discover information `vital' to contractual performance." 1 Furthermore, the contractors requested that the termination for default be converted to a termination for convenience, a much less attractive outcome for the Government (Schwinn, 2011). Major problems began to arise when the diculty of determining the extent to which the Government had prior experience with stealth technology became apparent, as all 1 General Dynamics Corp. v. United States, 563 U.S. 2 (2011). 138 information pertaining to the design, materials, and manufacturing process of previously developed B-2 and F-117A stealth aircraft are closely guarded military secrets. Despite this, the Government allowed ten members of the contractor's litigation team \access to the Secret/Special Access level of the B-2 and F-117A programs," four of which were also given access to the most sensitive details of the programs. 2 But in March of 1993, the Acting Secretary of the Air Force asserted the state-secrets privilege in order to prevent discovery into certain details of stealth technology that were not considered part of the contractor's \need-to-know" authorizations. There were two depositions of military ocials in which military secrets were revealed during questioning that neither side's litigation team was authorized to know, and copies of one unclassied deposition were widely distributed in unsealed court lings. Such actions led the Acting Secretary of the Air Force to le a declaration with the CFC alleging that any further discovery into the breadth of the Government's superior knowledge would present a serious risk of the divulgence of military and state secrets, and that even presumably harmless questions would create unacceptable risks of disclosure of classied and special access information. 3 The state secrets doctrine provides that the United States Government can withhold certain information in a judicial proceeding given that disclosing such information would pose a \reasonable danger to national security" (Capra, 2011). Prominent cases regarding state secrets are United States v. Reynolds, Totten v. United States, and Tenet v. Doe. The CFC terminated discovery with regards to superior knowledge and later deter- mined that the extent of the Government's superior knowledge was a non-justiciable question. Although the CFC found that both sides had adequate evidence to argue their 2 General Dynamics Corp. v. United States, 563 U.S. 3 (2011). 3 General Dynamics Corp. v. United States, 563 U.S. 3 (2011). 139 case eectively, the CFC was concerned that \with numerous layers of potentially dispos- itive facts," convoluted by the superior-knowledge privilege, any ruling would be a sham, and a potential threat to national security. 4 In 1996, the CFC converted the termination for default to one of convenience, much to the despair of the Government, and awarded petitioners $1.2 billion. This decision was then reversed by the Federal Circuit, leaving the CFC to revisit, on remand, the decision of whether discovery into the superior-knowledge issue was precluded by the necessity of guarding military secrets. The CFC sustained the default termination, once again conrming that the issue of whether the Government's superior knowledge excused the petitioners' default could not be safely litigated. The Court of Appeals then reversed the default termination, but conrmed that the state-secrets privilege precluded the courts from deciding whether the Government's superior knowledge exonerated the petitioners from default. However the Court of Appeals, pursuant to United States v. Reynolds, rejected the petitioner's argument that the Government should not be allowed to issue a claim against a party if it is going to use the state-secrets privilege to trump any defenses to that claim. The CFC then, once again on remand, found that the petitioners had defaulted. The Court of Appeals armed and nally, the Supreme Court granted certiorari to evaluate the state-secrets holding. 5 The Supreme Court held that the terminology of the A-12 agreement restricted the Court from converting the termination to one for convenience and reinstating the CFC's $1.2 billion dollar damages award. Pursuant to the agreement, the Court could only convert a termination for default into one for convenience if it \determine[d] that the 4 General Dynamics Corp. v. United States, 563 U.S. 4 (2011). 5 General Dynamics Corp. v. United States, 563 U.S. 4 (2011). 140 Contractor was not in default, or that the default was excusable," and the Court found these issues to be non-justiciable. Further, a termination for convenience generally allows the contractor the right to recover its incurred costs of performance, reasonable termi- nation expenses, and a reasonable prot for the work performed. Such damages would be impossible to calculate without establishing how much of the petitioner's cost over- runs were contributable to the failure of the Government to share its superior knowledge. Without evidence of the existence and extent of the superior knowledge, the $1.2 billion award might be an unwarranted consequence. The Government had requested that the $1.35 billion that it had paid the petitioners in progress payments be returned, as it stated those payments were for work that had never been performed. The Supreme Court held that due to the assertion of the state- secrets privilege, it was impossible to rule on whether or not the petitioners had indeed been compensated for work that was not performed and subsequently defaulted on the contract. The issue was non-justiciable. The Supreme Court ultimately decided to leave both parties where they were, that is to let the petitioners keep the $1.35 billion they had received in progress payments and to forgo the $1.2 billion award requested by the petitioners. The Court held that both parties must have been aware of the fact that state secrets would prevent the resolution of many contractual disputes in court, and that this was a risk both parties understood when they entered into the contract. It was the opinion of the Court that the greatest impact of this ruling would be to clarify the law with regard to like matters, leaving future contractors better t to predict and accommodate outcomes and make more informed contractual decisions. 141 C.2 Derivation of the optimal bid underGeneralDynamics Under General Dynamics, bidder i maximizes his expected prot: max b i i = [P (winning)](b i c i ): Probability of winning for bidder i is the probability that his bid b i = B(c i ) is smaller than all other bids. Since there are N-1 other bidders and all bids are increasing in cost, then P (winning) = Y c j 6=c i P (c j >c i ) = [1F (c i )] N1 = [1F (B 1 (b i )] N1 where B 1 (b i ) is the inverse bid function and F is the cdf from which individual costs are drawn. Given that in equilibrium all bids are symmetric we obtain the necessary condition for bids to be optimal: [1F (c i )] N1 + (N 1)[1F (c i )] N2 (f(c i )) 1 B 0 (c i ) (b i c i ) = 0) )B 0 (c i )[1F (c i )] N1 +B(c i )(N1)[1F (c i )] N2 (f(c i )) =c i (N1)[1F (c i )] N2 (f(c i )): Let G(c i ) = [1F (c i )] N1 . Then we can rewrite the necessary condition as: B 0 (c i )G(c i ) +B(c i )G 0 (c i ) =c i G 0 (c i ): 142 We can now solve for the optimal bidding functionB(c i ) by integrating the above equation with the boundary condition B(V ) =V . That means that a bidder with individual cost equal to V makes zero prot. By integrating we obtain: B i (c i ) =c i + R V c i [1F (x)] N1 dx [1F (c i )] N1 + K [1F (c i )] N1 : The boundary condition B(V ) =V implies K = 0 and hence we get the optimal bidding function: B i (c i ) =c i + R V c i [1F (x)] N1 dx [1F (c i )] N1 : The boundary condition makes sense since for a bidder with individual cost c i = V , bidding b i =V and making zero prots weakly dominates any other bid. Bidding higher than V will result in the bid being rejected by the government since it is more expensive than the valuation for the project and bidding less than V will result in negative prots. 143 C.3 Derivation of the optimal bid under SL Under SL, bidder i maximizes his expected prot: max b i i = [P (winning)](b i c i E(x)) = [P (winning)](b i c i V 2 ) since x is uniformly distributed on the interval [0;V ]. Using the same expression for the probability of winning and the result that in equi- librium bids are symmetric we can again write the necessary condition for an optimal bid: B 0 (c i )[1F (c i )] N1 +B(c i )(N1)[1F (c i )] N2 (f(c i )) = (c i + V 2 )(N1)[1F (c i )] N2 (f(c i )) which by using the same notation G(c i ) = [1F (c i )] N1 we can rewrite as: B 0 (c i )G(c i ) +B(c i )G 0 (c i ) = (c i + V 2 )G 0 (c i ): We solve for B(c i ) by integrating which yields: B(c i ) =c i + V 2 + R V c i [1F (x)] N1 dx [1F (c i )] N1 + K [1F (c i )] N1 : To ndK we use a dierent boundary condition this time,B( V 2 ) =V . Since bidders have to insure themselves for potential losses they increase their bid by the expected value of the random cost. Bidders with individual costs higher than V 2 won't participate since 144 their bids will exceed the government valuation and hence the highest cost bidder able to participate is the bidder with cost V 2 . His prot will be zero by the same argument made before. Using this boundary condition gives: B( V 2 ) = V 2 + V 2 + R V V 2 [1F (x)] N1 dx [1F (c i )] N1 + K [1F (c i )] N1 =V ) )K = Z V V 2 [1F (x)] N1 dx: Plugging back into the bidding function we get: B(c i ) =c i + V 2 + R V 2 c i [1F (x)] N1 dx [1F (c i )] N1 : 145 C.4 Derivation of the optimal bid under DPI Bidder i chooses his bidding strategy to maximize his expected prot: max b i i = [P (winning)][P (x>X)(b i c i ) +P (x<X)(b i c i E(xjx<X)]: As before, we look for a symmetric equilibrium. The probability of winning is just like before and we use the properties of the uniform distribution to write expressions for the other probabilities in the prot function and for the conditional expectation. We obtain the following necessary condition for the bids to be optimal: [1F (c i )] N1 + (N 1)[1F (c i )] N2 (f(c i )) 1 B 0 (c i ) [B(c i )c i X 2 2V ] = 0: Again we use the notation G(c i ) = [1F (c i )] N1 and by rearranging we can rewrite the necessary condition as: G(c i )B 0 (c i ) +G 0 (c i )B(c i ) =G 0 (c i )(c i + X 2 2V ): We solve the dierential equation by integrating which results in: B(c i ) =c i + X 2 2V + R V c i [1F (x)] N1 dx [1F (c i )] N1 + K [1F (c i )] N1 : Observe that compared to the strict liability case, this is somehow similar only the size of the overbid \insurance" is dierent since bidders only need to insure themselves for a particular situation and not for every possible situation. Hence we use a similar argument 146 to determine the boundary condition B(V X 2 2V ) =V . A bidder with such an individual cost has no incentive to bid higher since that would make his bid higher than the gov- ernment valuation and hence not accepted and he would also not be able to bid less than V since that would result in negative expected payos. Using this boundary condition implies K = R V V X 2 2V [1F (x)] N1 dx which results in the optimal bidding function: B(c i ) =c i + + X 2 2V + R V X 2 2V c i [1F (x)] N1 dx [1F (c i )] N1 : 147

Abstract (if available)

Abstract This dissertation is concerned with studying certain pricing and contracting issues that are motivated by real problems. The second chapter is focused on determining why persistent excess demand is pervasive on certain markets. The focus is on the markets for popular concert tickets which present a number of viable theoretical issues to consider and also allow us to assemble a unique data set of prices from both primary and secondary markets that we can use to test the alternative theories. We find that secondary markets emerge not because promoters fail to price or price discriminate optimally, but because they have strong incentives to either underprice or artificially maintain shortages on the market. These incentives are provided by their desire to share risk with speculators when demand is uncertain, by the presence of complementary products, and by social influence. ❧ Continuing to study the effects of social influence, the third chapter builds a theoretical model of price discrimination under social influence. We show that when consumers are uninformed about a product they can be persuaded through social influence to update their preferences. Under these conditions social influence reduces the profitability and incidence of price discrimination. We show that sellers that are more sensitive to social influence price discriminate less and offer less product variety. We also show that rationing occurs mainly at the low end and it can be severe. All these results are consistent with the empirical evidence from the entertainment industry and also with other observations from certain fashion and cult product industries. ❧ The fourth chapter considers a long studied pricing problem in both the Industrial Organization and International Trade literature. We try to shed light on why the law of one price does not always hold. The focus is on the automotive industry inside the European Union. We show that prices for identical models failed to converged in spite of the elimination of virtually all trade barriers and the adoption of the common currency. We argue that the exclusive dealership system allows for successful market segmentation and price discrimination based on purchasing power. We also point to pricing patterns that are consistent with collusive agreements among the three major manufacturing groups in Italy, France, and Germany. ❧ The final chapter of this thesis analyzes the efficiency implications of different sets of legal rules in contract litigation. When contracts are affected by asymmetric information, litigation often occurs. The legal rules under which the contracts are being written affect the incentives of both contracting parties and therefore the prices and efficiency of these contracts. We show that a non interference rule that allows the parties to settle the dispute on their own is more preferable to a strict liability rule that forces the contractor to fulfill his obligations regardless of the cost, and also to a rule that allows the private information to be made public and awards damages based on this information.

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Asset Metadata

Creator Radoias, Vlad (author)

Core Title Essays on pricing and contracting

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 04/03/2013

Defense Date 03/11/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag excess demand,OAI-PMH Harvest,price discrimination,social influence

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Wilkie, Simon J. (committee chair), Dukes, Anthony (committee member), Magill, Michael (committee member), Tan, Guofu (committee member)

Creator Email radoias@usc.edu,vradoias@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-230557

Unique identifier UC11293366

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Legacy Identifier etd-RadoiasVla-1506.pdf

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Document Type Dissertation

Rights Radoias, Vlad

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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