2010：NFL的利润最大化

The Journal of Applied Business Research – January/February 2010 Volume 26, Number 1 45 Profit Maximization In The National Football League John P. Brunkhorst, Colorado College, USA Aju J. Fenn, Colorado College, USA ABSTRACT This paper investigates if NFL teams maximize profits with respect to ticket price. We modify Ferguson et al’s (1991) NHL paper as it pertains to the NFL. A profit function incorporating variable revenue and cost factors such as gate receipts and player expenses is employed. A systems model is used as the estimation procedure to identify the determinants of ticket prices for NFL franchises. The model implies a Kuhn-Tucker based cross equation parameter restriction that result from attendance capacity constraints. Results from the regression are then used in conjunction with other data to numerically test the first order necessary profit maximization conditions. The results indicate that over 80% of NFL teams set ticket prices in a manner consistent with gate receipt and profit maximization. Keywords: National Football League, Profit Maximization, Ticket Price Determination INTRODUCTION he theory of profit maximization has been a key economic concept for almost a century, Knight (1921). Profit maximization occurs when firms adjust either the quantity or price of the goods they produce in order to maximize the gap between revenues and costs. Professional sporting contests have been one of the most significant branches of the entertainment industry. Szymanski (2003) reports that in 1997 the U.S. Census Bureau found 41% of the population, roughly 110 million people, attended a spectator sporting event each year. He also states that Kagan Media estimated the annual household television viewing of sports events to be 77 billion hours per year. According to Scully (1995) the National Football League (NFL) is an economic enterprise where every single team in the league is consistently profitable. Zimbalist (2003) states that individual owner’s economic objectives differ due to the unique way each owner defines profit maximization. Some owners focus simply on money, while others believe the best way to maximize profits is to maximize the number of wins. Even though research conducted by Forbes shows that each team in the NFL makes a significant profit, it does not mean that each team maximizes potential profits. i Constant sellouts and scalpers selling tickets above face value point to the fact that NFL franchises could raise ticket prices in order to increase profits. Perhaps some owners are more interested in winning championships than making the most money. As long as franchises are not losing money, their ultimate goal could be the glory and prestige accompanying a Super Bowl victory. On the other hand, constantly increasing ticket prices and television blackouts in local areas during non-sellout games all point to profit maximization as the main objective. These conflicting empirical findings and stylized facts prompt the question: Do NFL franchises conform to the practices of profit maximization? This paper will strive to answer that question. The purpose of this study is to determine whether NFL franchises set ticket prices in a manner consistent with the first order necessary profit maximizing conditions. The first section will provide a review of the pertinent empirical literature on profit maximization. The second section will outline the modifications to the methodology employed by Ferguson et al. (1991) and will develop empirical models for the maximization of gate receipts with respect to ticket prices. Section three addresses the profit maximizing necessary conditions and presents the numerical equations used to test whether these conditions hold. The fourth section will present the data and regression model. The fifth section discusses the results for both the empirical model and the numerical testing of T The Journal of Applied Business Research – January/February 2010 Volume 26, Number 1 46 profit maximization. Finally, the implications of the results are presented in the concluding section. CURRENT RESEARCH ON PROFIT MAXIMIZATION While the theory of profit maximization has been around since the beginning of the 20 th century there have been relatively few studies that adapt this theory to professional sports leagues. Several studies have focused on the economic design of these leagues and the relationship between variables affecting the business side of professional sports. There is a copious literature that covers studies on attendance, revenue, competitive balance, etc. Brook (2006) provides an excellent summary of the literature on profit maximizing models and inelastic ticket pricing. El- Hodiri & Quirk (1971, 1974, and 1975) present the first model of a sports league. Like us they focus on gate receipts alone. Additional work by Heilmann & Wendling (1976) extended the El-Hodiri and Quirk effort to include additional revenue streams. Marburger (1997) has modeled sports teams as multi-product monopolists that sell both admission and concessions. Another vein of the literature examines the connection between ticket pricing and home field advantage. The reader is directed to Brook (2006) for a review of these studies. None of the above studies account for the fact that attendance constraints in the NFL are often binding. In 2006 the NFL set a record with every game for every team selling out through the eleventh week of the season. Studies on game day attendance like the one by Welki and Zlatoper (1994) fail to account for the impact of such a constraint in their empirical specifications. However, a study by Ferguson et al. (1991) examines if NHL teams maximized profits with respect to ticket prices given a seating constraint. Ferguson et al. (1991) investigate the issue of profit maximization in the National Hockey League (NHL) by looking at the ticket pricing behavior of teams given a stadium capacity constraint. Their study asserts that pricing differences between various packages of seating support the idea that owners use sophisticated practices to earn profits. They assume that each team considers the fan’s willingness to pay for attendance. The team then maximizes profits by setting seat prices accordingly to maximize its gate receipts. Each team will have a different method for price setting due to unique franchise characteristics. The econometric results, which use Kuhn-Tucker conditions through cross equation restrictions, offer considerable support for the notion that NHL teams do follow a profit maximizing procedure in setting ticket prices. The present study modifies the model proposed by Ferguson et al. (1991) to examine profit maximization as it applies to ticket pricing in the NFL. To the best of our knowledge no economic studies conducted on profit or revenue maximization pertaining to the NFL subject to seating capacity constraints exist. This study tests the necessary (first order) conditions of profit maximization to see if in the presence of a capacity constraint firms maximize gate receipts with respect to ticket prices. The following section outlines the mathematical models derived for both profit and ticket prices which will serve as the foundation for testing profit maximization in the NFL. PROFIT MAXIMIZATION: DERIVATION If owners maximize profits, they must pay close attention to the revenues generated and costs incurred throughout the season. The revenue that a team receives accrues in two main forms. The majority of revenue is collected from the gate receipts of each game. Additional revenues arise from the teams’ share of NFL broadcasts and merchandise sales. Even though revenue sharing from NFL broadcasts and merchandise does make up a fairly significant part of a team’s total revenue, it is approximately a fixed amount from team to team. The NFL signs contracts with national and local broadcasting agencies, Szymanski (2003). The NFL allots a share of the revenue produced from sales of NFL merchandise to be distributed among teams in the league. The revenues generated by these contracts are divided equally among all teams. The teams have virtually no control over the revenue they receive from league sharing. Therefore, owners focus on gate receipts, which they can control. Owners can set ticket prices to maximize profits for the season. The Journal of Applied Business Research – January/February 2010 Volume 26, Number 1 47 In keeping with Ferguson et al (1991), it is assumed that the costs varying with attendance at each individual game are so small that operating costs and stadium costs should not play a large role in profit maximization. The majority of costs for each team stem from factors such as players salaries. This implies that the owners’ sole objective is to maximize the difference between total gate receipts in each year and total player expenses. To do this owners will adjust ticket prices until they find a price that returns maximum profit, π, given the amount spent on players. The revenue generated by gate receipts is simply ticket price, p, multiplied by attendance, A. Equation (1) gives the profit maximization rule for NFL owners. Max π = p*A - E subject to A < C (1) E represents total player expenses. The maximum number of people that can attend any game is limited to the seating capacity, C, of the stadium. Ticket price itself is a function of other variables. In keeping with Ferguson et al (1991), this study will define ticket price as a function of attendance and a vector of other variables. However, it will also incorporate player expenses as a determinant of ticket price. Equation (2) gives the ticket price function. p x = ƒ (A, E, z;θ) (2) P x is ticket price raised to the power x, z is the vector of exogenous attributes of the team, and θ is the vector parameters. It is believed that both attendance and player expenses are endogenous variables. Instrumental variables will be used to handle this endogeneity to ensure that the estimates are unbiased and consistent. The instrumental variables will produce theoretical values for attendance and player expenses, which will be called and respectively. Therefore, the inverse demand function from equation (2) is represented by equation (3). (3) Combining equations (1), (2) and (3) yields the profit function presented in equation (4). Since profit maximization corresponds to revenue minus costs, equation (4) will be the basis for testing empirical hypotheses regarding profit maximization. EzEA xk   )1( 210 )(*  (4) PROFIT MAXIMIZATION: TESTING METHODOLOGY A first order necessary condition for profit maximization is that the first order derivative with respect to the choice variable equals zero. Equation (5) states that, the derivative of profit function with respect to attendance equals zero. (5) The second order condition states that the second derivative must be negative with respect to the choice variable attendance A. The derivative of ∂π/∂ must be taken with respect to attendance. The resulting expression is given by Equation (6). (6) The Journal of Applied Business Research – January/February 2010 Volume 26, Number 1 48 As noted previously, stadium capacity places a restriction on the number of people attending a game. This constraint must be taken into account. To do this a univariate Kuhn-Tucker approach is used. A maximum profit must be generated between zero and stadium capacity. Therefore at the profit maximizing attendance, the following Kuhn-Tucker conditions must hold. (7) These conditions imply the capacity constraint is binding unless local concavity exists. This study uses the third condition in (7) to represent the restriction on owners’ choices because it is able to represent both the first and second conditions simultaneously. Thus the restriction equation is given by equation (8). (8) Ferguson et al. (1991) use a similar restriction approach in their paper. The effects of the theoretical determinants on ticket prices in the NFL will be determined empirically by estimating the following system of equations (9) and (10) that are the empirical versions of equations (3) and (8): (9) (10) In equations (9) and (10) i represents the observation and and are unobservable errors terms. Using the coefficients and determinants from these equations the first and second order derivatives can be numerically calculated and evaluated for both sellout and non-sellout teams. The results of these calculations should shed some light on the maintained hypothesis of profit maximization, in the context of this paper, by NFL owners. DATA AND METHODS The dataset is comprised of all 32 NFL football teams over three regular seasons from 2003 to 2005. The unit of observation is a single regular season for each team. The left hand side dependent variable in this model is the average ticket price by team for each season. ii Average ticket price was defined as a weighted average of season ticket prices for general and club-level seats for each team during a given season. The weights used were the proportion of seats in each pricing category. Ticket prices were then adjusted to 2003 dollars using the Consumer Price Index. The explanatory variables are summarized in equation (11) and briefly defined in Table 1. PRICE X = f(ATTEND, POP, WEALTH, PWIN, CWIN, ALTREC, STAR, PEXP, HHI, DIVISIONAL DUMMY VARIABLES, (11) YEAR DUMMY VARIABLES) s.t. [(β1ATTEND/X)*PRICE^(1-X)+ PRICE] [CAP-ATTEND] = 0 The definitions of the variables presented in the above model are displayed in Table 1. The Journal of Applied Business Research – January/February 2010 Volume 26, Number 1 49 Table 1: Variable Definitions Variable Definition X Exponent value that PRICE was raised by PRICE Average game ticket price for season in 2003 dollars ATTEND Season home attendance POP Population of franchise’s home city WEALTH Median income of franchise’s home city in 2003 dollars PWIN End-of-year winning percentage for previous year CWIN End-of-year winning percentage ALTREC Alternative forms of local recreation available in home city STAR Number of Pro Bowl selections PEXP Total player expenses in 2003 dollars HHI Yearly HHI in the NFL CAP Stadium Capacity NFCE Dummy for division NFC East NFCN Dummy for division NFC North NFCS Dummy for division NFC South NFCW Dummy for division NFC West AFCE Dummy for division AFC East AFCN Dummy for division AFC North AFCS Dummy for division AFC South YEAR03 Dummy for 2003 season YEAR04 Dummy for 2004 season Attendance is also believed to be an endogenous variable in the model, and is therefore dependent on the exogenous variables. The determinants that affect average ticket price also affect attendance. Attendance (ATTEND) is defined as the total number of spectators at an NFL team’s home games for a given year. All attendance data was found at the NFL’s website.iii Lower ticket prices will allow more people to attend games through the usual income and substitution effects. Therefore, the theoretical prediction is that attendance will have a negative relationship with price. The costs of running a professional football team are not small. Most of these costs are either operating expenses or player expenses. We assume that operating costs, such as stadium operation and general management costs, do not vary by large amounts across NFL teams. Since these costs are assumed to be fixed, and that data for them is not readily available, they are excluded from the model. However, expenses such as player and coach salaries, benefits, and bonuses do differ throughout the league. Even though there is a salary cap in the NFL, player expenses (EXP) vary significantly for each team. Like attendance, player expenses are believed to be endogenous in the model. Player expense data was collected from the NFL Team Valuations conducted by Forbes. iv They were then adjusted to 2003 dollars using the Consumer Price Index. When teams spend more on their players and staff they should theoretically have to bring in more revenue to offset the increased cost. To accomplish this ticket prices should increase. This is why we expect average ticket price and player expenses to be positively related. El-Hordiri (1971) says that the league typically gives exclusive rights to organize a team in a 35-75 mile geographical area around the home playing field. Particular demographics in each territory represented by a NFL team are potential determinants of NFL ticket prices and other endogenous variables. The total population (POP) of a territory should directly affect the number of fans wanting to attend home games. A larger population creates a greater demand for tickets, allowing owners to raise prices, leading to greater revenue. Population may be positively correlated with ticket prices in the NFL. Populations of the various NFL territories were collected from the US Census Bureau’s 2000 census.v Ferguson et al. (1991) find per capita income and ticket prices to be positively correlated in the NHL, showing attending NHL games to be a normal good. We also expect wealth to have a positive correlation with ticket prices because NFL tickets should be a normal good. Median income (WEALTH) data was collected from the US Census Bureau’s 2000 census and then adjusted to 2003 dollars using the Consumer Price Index.vi The Journal of Applied Business Research – January/February 2010 Volume 26, Number 1 50 The number of different professional sports teams in each territory (ALTREC) represents the possible substitutes for attending an NFL football game. Multiple sports teams may act as substitutes for each other. NFL football games are a source of entertainment and compete with other local entertainment for people’s time and money. If this is the case the greater the number of sports teams in an area the lower the attendance of NFL games. On the other hand multiple sports teams may be evidence of complementary preferences of consumers. Cities with more sports teams may have a larger demand for sports and ceteris paribus, attendance at NFL events may be higher. A priori it is uncertain as to what type of impact the number of sports teams in an area will have on the ticket prices and revenue in the NFL. The measure of alternative forms of recreation is captured by the number of major league teams in a particular territory from the four major U.S. professional sports leagues: MLB, NBA, NHL, and the NFL. There is a significant literature on the connection between winning and attendance. People prefer to watch winning teams because they attract attention. A winning team should have not only a consistent fan base but a growing one because current fans will continue to support their team and people who were not previously fans might now be attracted to the team. The success of an individual team should play a significant role in determining the prices charge for game day attendance. In any given year, the greater the success of a team, the more people will want to attend games. The performance of a team in the previous year will also affect attendance for the current year. If a team did well last year, people will expect another good season and eagerne