Bandwagon Effects and Local Monopoly Pricing In Professional Team Sports Market. J M Kang, Y. J. Ryu, Peng Liu

Transcription

1 CAES Working Paper Series Bandwagon Effects and Local Monopoly Pricing In Professional Team Sports Market. J M Kang, Y. J. Ryu, Peng Liu Faculty of Economics Fukuoka University WP Center for Advanced Economic Study Fukuoka University (CAES) Nanakuma, Jonan-ku, Fukuoka, JAPAN

2 Bandwagon Effects and Local Monopoly Pricing in Professional Team Sports Market. J. Moonwon Kang Professor, Faculty of Economics, Fukuoka University, Japan. Young Jin Ryu Assistant Professor, Kitakyusyu City University, Japan Peng Liu Assistant Professor, Guangdong Ocean University, China. Abstract: This study establishes a case that bandwagon effects impart upward sloping segments to market demand curves. As an example of such cases, we analyze a professional team sports market characterized by local monopoly supply and demand induced by bandwagon effects. Assuming consumers choice of attending the game is indivisible and there exist systematic differences in loyalty to the local team among potential attendants, we build a positive relation between ticket price and the number of entrants to stadiums. We derive theoretical results that size of stadium does not affect the optimum ticket pricing of monopoly team, and the strong of bandwagon effects is associated with lower ticket prices. Further, we show that enlargements of stadium size do not increase teams investments to team quality. A look at the evidence suggests our theoretical results are largely consistent with real world observation in Japan and Europe. * This study is supported by the program for scientific research start-up funds of Guangdong Ocean University. 1

3 Introduction In his 1991 paper, Gary Becker suggested that, when individual demand is positively related to the market demand, i.e., when there exist bandwagon effects in market demand, the demand curve for the good is positively sloped for a wide range, and this upward sloping demand curve could explain the well-observed and perpetuating phenomenon of excess demand(queues to attend the successful sporting events) or excess supply(vacancies in the stadium) in sports product markets. Becker suggested that, if the pleasure from attending the game is greater when many people want to attend the same event, the demand curve first rises and then falls, and combined with the fixed supply(given number of seats in the stadium), the upward sloping demand curve would be a source of excess demand or supply. This view, however, has been criticized by Gisser et. al.(2009) who assert that Becker`s hypothesis of upward rising demand curve is valid only when bandwagon effect is preposterously large, and is inconsistent with standard empirical observations. Both Becker s hypothesis and criticism by Gisser et. al. and others (1) remain unsatisfactory because these studies do not make clear the corresponding utility-maximization and profit-maximization problems while discussing the possible relations among bandwagon effect, demand curve and market outcome. The purpose of the present study is to establish a sensible case wherein Becker s hypothesis is valid, and to examine its implications in sports product market. The model we present here is based on the following basic assumptions: one, we describe individual s choice of attending a professional sport game and assume this choice is indivisible(attend or not), two, loyalties to local sport team differ among potential attendants to the game, and strong loyalty to the team yields higher utility from the game, three, there exists bandwagon effect, which produces positive relation between the number of attendants and pleasures obtained from attending the game, four, the sport team under our investigation is a local monopoly and, in the short-run, the cost of providing the game is constant regardless of the number of attendants. This study is organized as follows: Section 2 describes the basic model and establishes a case in which the demand for the sports game is positively related to ticket prices for a wide range. In Section 3, we explain how local monopoly pricing of match day ticket is affected by bandwagon effects in demand sides. We will derive a theoretical view that 2

4 the stadium size would have no influence to the optimum ticket pricing, which seems largely consistent with real world observations in England Premier League and Japan J-1 League. Section 4 extends the basic analysis to examine how changes in the strength of bandwagon effect affect the ticket pricing and derives a result that strong bandwagon effects will lower the monopoly price. We suggest a view that regional differences in bandwagon effects could explain the wide discrepancies in match day ticket prices observed among top leagues in European football. In Section 4, we further analyze the possible relations among bandwagon effects, stadium sizes and investments in team s quality. We found that investments in team quality are not strongly related with stadium sizes. Concluding remarks is given in Section 5. Basic Framework We assume the net surplus of the ith attendant to the game is(see L. Pepall and J. Reiff(2016) among others for similar specification of utility function) (1) { U i = θ i υ(n d ) λp = 0 if attend the game if not where p is the ticket price, n d is the number of fans who want to attend the game with the given ticket price p, and λ is the marginal utility of income which is assumed to be identical to every individual. The parameter θ i [0 1] ranks orders of population by the intensity of their preference of the game(which would be related to their loyalty to the team). We assume population is uniformly distributed on the line θ [0 1]. Thus, normalizing total population n 0 = 1, the number of population whose preference parameter θ i is larger than θ will be simply (1 θ ) (see Figure 1). It is important to note that the utility associated with the game is defines as a function of n d, which is not necessarily equal to actual number of attendants in our model as we will show below(see footnote). We assume υ is a twice differentiable function and υ = υ(nd ) n d > 0, υ = 2 υ(n d ) (n d ) 2 < 0 3

5 FIGURE 1 Bandwagon effect, originally defined by Leibenstein(1950) as the desire to join the crowd, be one of the boys`, etc. phenomena of mob motivations and mass psychology either in their grosser or more delicate aspects, is captured in this model by the assumption of υ > 0. Define θ i as in (2), (2) θ i υ(n d ) λp = 0 then, it would be apparent that, for given ticket price p, those fans whose preference for the game θ i is larger than θ i will want to attend the game, and the following relation holds, (3) n d = 1 θ i. From (2) and (3), we obtain (4) n d = 1 λp υ(n d ) or P = 1 λ (1 nd )υ(n d ) The equation (4) represents the demand schedule in the proposed model showing the relation between P and n d(2). The demand curve implied in (4) can be upward sloping for a wide range. This possibility can be shown as follows: Total differentiating (4) yields the equation, dn d = λ υ(n d ) dp + P υ [υ(n d )] 2 dnd Substituting (4) into the above equation and rearranging, we have 4

6 (5) P n d = β[(1 nd )υ υ], β = 1 λ Which is positive when n d is sufficiently small and the bandwagon effect υ is υ sufficiently large (υ > 1 n d). Put differently, differentiating (2) with respect to nd, it follows that, P n d = β { θ i n d υ(nd ) + θ i υ (n d )} The first term θ i n d υ(nd ) is negative, which implies that the marginal attendant s enthusiasm to the game is falling as the number of attendants increases(which we want to call loyalty weakening effect), and the second term is positive when there exist bandwagon effects. When the number of attendants, n d, is small, it is probable that the bandwagon effect dominates loyalty weakening effect, and P > 0. In general case of d consumer demands, an individual adjusts quantity consumed to equate the marginal utility of consumption and the utility evaluation of the given price. In the model we investigate here, however, an individual can t adjust her level of consumption because the relevant choice is either 1(to attend the game) or 0(or not). In the specific model this study presents here, we have positive bandwagon effects and the negative loyalty weakening effect instead of the usual income and substitution effects. Both Bandwagon effect and loyalty weakening effect changes systematically according to the changes in the number of possible attendants as our analysis below will show. To make our argument simple and clear, we will denote n d by n, and we will specify the utility function υ as n (6) υ(n) = An α, A > 0, 0 < α < 1 We could call α as the strength of bandwagon effect. We will think in a way that A means team quality which is assumed to be fixed here. We will discuss the problems related with monopoly investments in team quality in Section 4. The demand relation (4), then, will be rewrote as, 5

7 (7) n = 1 λp An α Or P = βan α (1 n). From (7), we can calculate, (8) n P = 1 βan α 1 [α (1 + α)n] Which is positive when n < α 1+α. The demand curve is upward sloping when n < α 1+α reaches the maximum at n = α 1+α, then decreasing thereafter as Figure 2 shows. The maximum reservation price denoted by P max in Figure 2 can be calculated from (7) as, α α (9) P max = βa (1 + α) (1+α) FIGURE 2 If we assume the marginal utility of income λ decreases as the income level rises, then, other things being equal, an increase in income level of potential attendants shifts the 6

8 demand curve upwards and P max becomes higher as the above Figure shows. As we will show in the next section, P max is the profit-maximizing ticket prices in most cases, and Figure 2 can explain historical trends of rising ticket prices associated with rising household income. Local Monopoly Pricing in Sports Product Market We assume the team under our investigation is local monopoly and there is only one team in the region. Further, we assume the local monopoly team maximizes the short-run profit. Ignoring revenues from the media, sponsors, and other sources, for simplicity of exposition, we define the profit obtained by the local monopoly team from the game as in (10) for the case that the given size of stadium(denoted by n ) is smaller than n. (10) π = Pn C Where C represents the total cost which is assumed to be fixed and not varied by the changes in the number of attendants. Here, firstly we explain the local monopoly team s profit maximization problem using the specific utility function (6), and then generalize the results obtained. Note that, by the chain rule, π P = ( π n ) ( n P ) If utility function is as given in (6), it follows from (7) and (8), (11) π P = βanα [(1 + α) (2 + α)n] ( n P ) When n < n (i.e., when π 1+α > 0), if (1 + α) (2 + α)n > 0(i.e., if > n), then P 2+α π > 0. Both α P 1+α 1+α and 2+α 1, 1 < 1+α < 2, and thus, α α 3 are monotonic increasing in α (0 < α < 1), and 0 < α < 1+α 1+α 2+α. Therefore, in the case of n < n (< 1+α π ), 2+α 1+α < P > 0 7

9 without further conditions. Accordingly, if n < 1+α, then the profit maximizing pricing 2+α will be P max as π > 0 is positive within the relevant region. P This result can be generalized easily as follows. From (4), (10), π n = β[n(1 n)υ + (1 2n) υ] And π P = [n(1 1 n)υ + (1 2n) υ] { (1 n)υ υ } In the case of n P = 1 (1 n)υ υ > 0, if n(1 n)υ + (1 2n)υ > 0 then π P > 0. Note that, when n < 1 2, n(1 n)υ + (1 2n) υ is positive. Thus, if we assume n < n < 1 2 which is reasonably the case, P max is a unique profit maximizing price. Figure 3 explains the above arguments. When the given stadium size is n, the local monopoly pricing will be P max and there exists an excess demands for the game of n n (3). 8

10 FIGURE 3 When the given stadium size n is larger than n, we redefine the expected profit from the game as in (12). Suppose that profit from the game is maximized at the point a in Figure 3 where the number of attendants is n 0 and the corresponding ticket price is P 0 if there is a way to implement the point a, excluding the other possible outcome of b. In the present model, however, there is no way to implement a and there arises a problem of indeterminacy if n > n. So, if the team is risk neutral, expected profit from the game will be defined as follows, (12) π = 1 2 (Pn + Pn) C where n > n and n is defined as in Figure 3. From (12), (13) π P = 1 2 [(n + n) + P ( n P + n P )] Thus, we know that π n > 0 when n > n if P P is sufficiently small, i.e., if the price 9

11 elasticity of demand is sufficiently small. From (7), the price elasticity of demand(ε p ) can be calculated as, (14) ε p = 1 n α (1 α)n which is decreasing in α. Accordingly, if bandwagon effect is sufficiently strong(which we assume as the case under our investigation), π P is positive when n > n. FIGURE 4(a) FIGURE 4(b) Even if the stadium size becomes larger to n, the local monopoly pricing remains unchanged and we can observe the vacancies as many as n n. An important and interesting observation can be made here that the level of monopoly pricing is not affected by the stadium size. It seems that this theoretical result is largely consistent 10

12 with some empirical observations. Figure 4(a) shows the relations between the stadium sizes and match day highest and lowest ticket prices in England Premier League, , and Figure 4(b) is the relation between the average ticket price and stadium sizes in J1 League(1 st division of professional football league in Japan) in 2016 season. Figure 4 seem to support the above theoretical result (4). Bandwagon Effects, Match Day Ticket Price, and Investments in Team Quality. We will examine the relation between the strength of bandwagon effects and the market demands. In below, we will prove that, for the given ticket price p, an increase in α expands the demands for the game when n < n. Firstly note that P max α > 0 and for given n, (15) P max α = βa(1 n)nd ln n < 0 Further, from the demands curve (7), P = An α (1 n), if we write P(α) = βan α (1 n) and P(εα) = βan εα (1 n) where ε > 1 is an arbitrary number. Then, it is evident that P(α) P(εα) = βa(1 n)n α (1 n ε ) > 0. When n > 1, ε > 1, therefore P(α) > P(εα) for n (0 1). Therefore, an increase in α shifts the demands curve downward as described in Figure 5, and P max is decreasing as the bandwagon effect becomes stronger. Combined with the results obtained in Section 3, The above result implies that the team in a region of stronger bandwagon effect would charge cheaper ticket price. We want to suggest a possibility that, though it would be a difficult job to measure the strength of bandwagon effect α, regional differences in bandwagon effects can explain wide discrepancies in match day and season ticket prices among top leagues in European football(see, for example, G. Nufer and J. Fischer, 2013). 11

13 FIGURE 5 Next, we will investigate the relation between the bandwagon effect and monopoly s investment to team quality. When n < n, we redefine the profit from the game as (16) π = P max n (c + ωq) = ha(q)n (c + ωq) Where h = β ( α α (1+α) 1+α), and q means the total number of talents that the team possesses, ω is the unit cost of talents, c is the other fixed costs(see, for example, S. Kesenne, 2007). From above, it follows that, π q = ha (q)n ω 2 π q 2 = ha (q)n < 0. 12

14 If we define q by A (q ) = hn, ω it follows (17) q ω = 1 A hn < 0 (18) q n = A A n > 0 (15) shows that the optimum investments to team quality increases as the stadium size becomes larger when n < n. When n > n, the profit is defined as (19) π = P max n (c + ωq) = ha(q)n (c + ωq) And, following the same procedure as above, we can calculate that A (q ) = ω hn and (20) q = 1 q < 0, = 0. ω A hn n The relations (14) ~(17) reveals that, firstly, an increase in the price of talents decreases investments to team quality, secondly, when the stadium size is smaller than n so that when there is no vacancy in the stadium, enlargements of the stadium size increases investments to team quality, thirdly, when there are vacancies in the stadium, enlargements of the stadium size does not affect investments to team quality. Figure 6 shows the relation between stadium sizes and teams investments to players in England Premier League(Fig. 6(a)) and Italian Serie A(Fig. 6(b)) (5). These relation show that, tough we can of course find differences between big market clubs and small market clubs, it can be safely argued that teams investments to team quality are not strongly related with stadium sizes. 13

15 FIGURE 6(a) FIGURE 6(b) Concluding Remarks Recent years have witnessed a boom of researches exploring the possible relations between social relations and market demands, and this study can be viewed as one of these researches. We elaborate Becker s inferences(1991) that bandwagon effects could bring an upward sloping demand curves, and examine how bandwagon effects would affects local monopoly pricing in sports product market. We establish a case wherein Becker s inferences are valid and make explicit what has been implicit in Becker s arguments. We can derive further implications of the upward demanding curve combined with local monopoly by specifying the strength of bandwagon effects. We 14

16 explain the excess demand and supply, often observed in professional team sports worldwide, as equilibrium phenomena wherein both consumers utilities and producer s profit are maximized. We provide a view that this seemingly awkward equilibrium is ascribed to bandwagon effects associated with upward demand curves and market structure of local monopoly. Upward sloping demand curves would yield several new insights in studies about competitive balance, revenue sharing, players labor markets and other important research areas of professional team sports markets. We think the model we propose in this study could be extended and applied in these directions. However, an important question remains unanswered in this study, that is, the very basic question how we can measure the bandwagon effect from the empirical data. We think this measurement problem is related with our understanding or interpretation of social and psychological forces underlying bandwagon-like behaviors. For example, it might be that bandwagon effects are the results of identity confirming behaviors of consumers. If identity confirming behavior enhances consumers utilities and identity confirming is made by mimicking the behaviors of others(of same social identity group) as postulated by Akerlof and Kranton(2000), then bandwagon effects in this study could be explained as behaviors of regional identity confirmation. Under this situation, the strength of bandwagon effects would be partly determined by the historical process under which local professional sports club has been related to local identity of the region. 15

17 Footnotes. (1) Becker s postulation is analyzed in a game theory framework by Karni and Levin(1994), for which Plott and Smith(1999) indicate behavioral inconsistencies of basic assumptions they adopted. (2) The demand curve in Figure 2 shows the relation between the market demand and the reservation price of the marginal attendant, which is somewhat different from the ordinary demand curves representing the sum of individual demands for given prices. We think this raises some confusion among the researchers. For example, Gisser et.al.(2009) wrote, if the zigzagged curve that Becker(1991) labeled d shown in Figure 1 is not really a demand curve then the question becomes: What is it?. (3) In this study, we explain the excess demand and excess supply as phenomena observed under market equilibrium equilibrium in the sense that producer s profit and consumers utilities are maximized. (4) The data for England Premier League is from BBC SPORT football(2016) and the data for J1 League is from Football GEIST(2016). (5) The data for Italian Serie A is from Serie A Transfer and Wage Budgets, REALSPORT(Nov. 11, 2016) and the for stadium sizes are from BBC SPORT football(2016) and List of English Football Stadiums by Capacity(Wikipedia). 16

18 References. Akerlof, G. A. and Kranton, R.E.(2000). Economics and Identity. Quarterly Journal of Economics, 115, Becker, Gary(1991). A Note on Restaurant Pricing and Other Examples of Social Influences on Price. Journal of Political Economy, 99, Gisser, M., J. McClure, G. Okten, and G. Santoni(2009). Some Anomalies Arising from Bandwagons that Impart Upward Sloping Segments to Market Demand. Economics Journals Watch, Karni, Edi and Dan Levin(1994). Social Attitudes and Strategic Equlibrium:A Restaurant Pricing Game, Journal of Political Economy, 102, Kesenne, Stefan(2007). The Economic Theory of Professional Team Sports, Edward Elgar Publishing Leibenstein, H(1950). Bandwagon, Snob and Veblen Effects in the Theory of Consumers Demand, Quarterly Journal of Economics, 64, Nuffer Gerd and Jan Fischer(2013). Ticket Pricing in European Football- Analysis and Implications. Sports and Arts, Pepall, Lynne and Joseph Reiff(2016). The Vebeln Effect, Targeted Advertising and Consumer Welfare. Economics Department Working Paper, Tufts University. Plott, Charles R. and Jared Smith(1999). Instability of Equilibria in Experimental Markets: Upward-sloping Demand Externalities. Southern Economic Journal,