Sports Economics 3123 Sample Second Midterm Exam Cheap calculators only Part A Question 1 The NFL is taking bids for one new franchise Suppose that the diagram below measures the annual demand for NFL games by the cities of San Antonio population 1 7 million and Orlando population 1 6 million These are aggregated demand curves combining all local benefits direct ripple externality intangible that come with an NFL franchise Assume that according to league rules only whole franchises 8 home games per season are available Annual Demand for NFL games million game 16 Demand Orlando 14 12 Demand San Antonio 10 8 6 4 2 0 0 4 8 12 16 home games a b What is the maximum amount that San Antonio would rationally offer for an 8 home game franchise What is the maximum for Orlando Illustrate your answer Which city has the highest maximum Discuss the considerations that might lead to an expansion outcome other than that suggested by a 2 Question 2 The chart below plots competitive balance ratios R for Major League Baseball since its founding in 1871 solid dots for the National League and open dots for the American League MLB Competitive Balance Ratio R 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 0 5 0 0 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 a The lowest R is 1 14 for the AL in 1974 marked as a diamond above 12 teams played 162 games this year the table below shows the final standings City Baltimore Oakland New York Texas Boston Minnesota Chicago Cleveland Kansas City Milwaukee Detroit Los Angeles Team Orioles Athletics Yankees Rangers Red Sox Twins White Sox Indians Royals Brewers Tigers Angels Winning percentage 0 562 0 556 0 549 0 525 0 519 0 506 0 500 0 475 0 475 0 469 0 444 0 420 Explain how these numbers are used to calculate R do not actually do the calculation Interpret the meaning of the result R 1 14 b The objective of competitive balance according to Bud Selig is that fans want to begin each season with hope and expectation of a championship Discuss whether a league would achieve Selig s goal if R 1 Is a R less than 1 possible 3 c The table below is a regression analysis of these statistics The dependent variable is R The independent variables are NL 1 a dummy variable equal to 1 for the National League and 0 for the American League and time which equals 0 in 1900 increasing to 106 in 2006 The season length variable is the number of games played by each team in the season The number of teams variable is the number of teams in the league SUMMARY OUTPUT Regression Statistics Multiple R 0 604 R Square 0 365 Adjusted R Square 0 354 Standard Error 0 509 Observations 242 ANOVA Df SS MS F Regression 4 35 290 8 823 34 027 Residual 237 61 449 0 259 Total 241 96 740 Coefficients Standard Error t Stat P value intercept 2 327 0 366 6 359 0 000 NL 1 0 064 0 069 0 932 0 352 time 0 013 0 002 6 880 0 000 number of teams 0 017 0 020 0 849 0 397 season length 0 003 0 002 1 326 0 186 Write down the regression equation and evaluate its goodness of fit d The NL began with a 27 game season in 1871 and expanded several times to a 162 game season for both the NL and AL after 1962 The NL began with 9 teams in 1871 dropped to 6 teams in 1877 and expanded eventually to 16 teams in the NL and AL each after 1998 What does statistical theory say about the affect of season length and number of teams on the competitive balance ratio Use the regression output above to test of this theory 4 Question 3 The basketball coaches of BYU and Utah are both trying to recruit the same local high school star LeBron Bryant Both estimate that LeBron will generate 3 million in revenue after deducting the cost of his scholarship over the next two years LeBron has declared that he does not want to leave the state that he wants to play in the MWC and that he will not join the NBA draft before his junior year due to NBA regulations However before committing LeBron demands that the coach arrange for a secret deposit of 1 million into his Swiss bank account Of course this bribe would be against NCAA recruiting rules and punishable by sanctions worth 10 million However each coach knows that there is zero chance that the NCAA will detect the violation a wealthy but discreet booster will make the deposit Each coach also knows that he is certain to sign LeBron if he pays the bribe and his rival refuses to bribe Each coach knows that his chance of signing is even 50 50 when both rivals follow the same strategy Each also knows that if both attempt to bribe then the losing school will not pay the bribe The payoff table below describes the situation payoffs BYU violate rules violate rules obey rules Utah expects 1 million BYU expects 1 million University of Utah obey rules a Fill in the missing payoffs in the matrix Explain b Does either coach have a dominant strategy What is the Nash equilibrium of this game Explain 5 Part B Mark the best answer 1 In game theory a dominant strategy is one where a a player s strategy is depends on the strategy of the other player b a player s strategy is randomized c a player s strategy leads to the worst outcome d a player s strategy is independent of the choice made by her opponent e a player s strategy is to maximize the worst case 2 A comparison of the competitive balance statistics across leagues reveals that a the NFL is one of most balanced according to the balance ratio R of standings and the least balanced according to HHI of championships b the MLB is one of the most balanced according to the R of standings and the HHI of championships c the NBA is the one of the least balanced according to the R of standings and the most balanced according to the HHI of championships d the English Premier League is one of the most balanced according to the R of standings and one of the least balanced according to the HHI of championships e none of the above is correct 3 The Competitive Balance Ratio R a is a sum of squares of championship shares b derives from Markov chain theory c is the area under the Lorenz curve d has been used to measure competitive balance in terms of the number championships over many seasons e is measured as the ratio of the observed standard deviation to its ideal 4 If the marginal propensity to consume MPC is 3 4 and the fraction spent locally is …