(5 Points) A consulting firm estimates the demand by local businesses for attendance at a pro sports team’s games: PB = $140 – 4AB where PB is the ticket price paid by businesses, measured in dollars, and AB is their attendance measured in thousands of fans. a. Draw this attendance demand function with the traditional P on the vertical axis, and Q/A on the horizontal axis. b. Using this demand function, find the total revenue function. What is the shape of the total revenue function? What is the highest possible total revenue that the team can hope to collect? At what level of attendance? At what price? c. Using this demand function and your answer to part (b), what is the elasticity of demand at the revenue maximizing attendance level (hint: if your calculations are correct, there is only one answer you should get for this0? d. Using your answers to a-c, if capacity at the team’s stadium is 25,000 seats, should the team owner fill the stands with business buyers? Why or why not? 2. (5 Points) The same consulting firm also estimates that the demand by families for attendance at the same games and the same seat-types is as follows: PF = $80 – (2/3)AF where PF is the price of a ticket for individual family members, measured in dollars, and AF is the attendance by individual family members, measured in thousands. a. Explain, comparing the elasticity of demand found in 1C with that found using the above equation, why individual family members will be charged a different price than business buyers for the same game and seat-type. What is the ratio of business buyer to family member price (PB/PF) if the team owner cares about the bottom line (you will need to calculate PF in much the same way as you calculated PB in question 1. Is this price discrimination? b. Calculate both the business buyers consumer surplus and family members consumer surplus given your answers to questions 1 and 2a. What does this number represent? 3. (2.5 Points) The NFL’s Houston Oilers left Texas to become the “Tennessee Oilers” for the 1997 season. They changed their name to the Tennessee Titans and moved into their new Adelphia Stadium for the 1999 season. Interestingly, their lowest-priced individual tickets were priced at $12 while their lowest-priced season ticket cost $250. Given that there are only 8 home games, why didn’t fans just buy individual tickets rather than season tickets? Is this price discrimination or not? Explain. 4. (5 Points) a. Using MLB ticket price (on blackboard) and attendance data (at https://umich.app.box.com/s/41707f0b2619c0107b8b), produce a spreadsheet for the year 2001 with the following columns: team name, attendance, and ticket price. Scale attendance in 100,000 for charting purposes. Sort the data by attendance in ascending order. Produce a scatter chart with attendance on the x-axis and ticket prices on the y-axis (include the scatter chart with your homework). Do your results support or reject the theory of demand? Explain. What other variables would you like to have to more accurately depict demand? b. Using MLB ticket price and attendance data (from the same sources as part a), produce a spreadsheet for the San Diego Padres, 1998-2003, with the following columns: year, attendance, ticket price. Scale attendance in 100,000 for charting purposes. Sort the data by attendance in ascending order. Produce a scatter chart with attendance on the x-axis and the two ticket prices on the y-axis (include scatter chart with your homework). Do your results support or reject the theory of demand? Explain. If you include 2004 and 2005 to the 1998-2003 data does your answer change? Why or why not? 5. (5 Points) a. The Yankees typically dominate the top of the payroll distribution in MLB, while the Expos/Nationals are usually towards the bottom. On blackboard, I have given you two spreadsheets, one for each of these teams, with the following columns: year, team payroll, ticket price, real team payroll, and real ticket price (real means inflation adjusted). Adjust payrolls to $millions for charting by dividing each payroll by 1,000,000. Sort the data by team payroll in ascending order, and for each team, produce a separate scatter chart with team payroll on the x-axis and ticket prices on the y-axis to include with your homework. For these unadjusted dollar values, calculate the correlation coefficients between payroll and ticket price for each of the three teams (in a blank cell type =CORREL(__,__) where for each __ you select the column with payroll and the column for ticket prices respectively). b. Now sort the data by real team payroll in ascending order. For each team, produce a separate scatter chart with real team payroll on the x-axis and real ticket prices on the y-axis to include with your homework. Calculate the correlation coefficients between real payroll and real ticket price for each of the three teams. c. What conclusions can you draw from this regarding the relationship between payrolls and ticket prices? What would you say to the fan who complains that ticket prices are too expensive because team payrolls are out of control? 6. (2.5 Points) Consider Coke and Pepsi’s decision of whether to advertise during the Super Bowl or not. If neither company advertises during the Super Bowl, the two companies split the market and earn $50 million each. If they both advertise, they again split the market, but profits are lower by $10 million since each company must bear the cost of advertising. Yet if one company advertises while the other does not, the one that advertises attracts customers from the other. In this case, the company that advertises earns $60 million while the company that does not advertise earns only $30 million. Given this information, what is each company’s dominant strategy? What level of profits will following this strategy lead to for both firms? Will both firms advertise or not? What would have to happen to change your answer? Here are some suggested things to collect for your paper due at the end of the term (not due with your homework, just a suggestion to make the actual “writing” of the paper at the end easier): ï‚· Collect pricing, attendance and winning percentage data for your chosen franchise over at least a five year period (ticket pricing information is provided for the NFL, NBA, NHL and MLB on blackboard under the data section, the other variables can be collected from a variety of sources, but I recommend you start at https://umich.app.box.com/s/41707f0b2619c0107b8b). Graph both attendance and prices over time…what does this graph tell you about your franchise’s demand curve over time? Then follow the instructions on blackboard for running a regression to estimate your team’s actual demand (including any variable which should impact attendance), which will allow you in your paper to discuss your franchise’s demand elasticity, optimal pricing policy, consumer surplus, etc). If you have trouble getting Excel to run this regression (which often happens if you are using a Mac) let me know and I can do it for you, as the point is to be able to have your team’s demand curve and use it (you aren’t being graded on whether you can generate it or not). ï‚· Collect information for your chosen franchise regarding their revenues from broadcast rights both nationally and locally. If you cannot find this information (which may very well be the case for some franchises), determine how many games are shown locally on television and draw conclusions about the value of their broadcast rights.
