Fall 2011 wikihomework Solutions, Chapters 1-4

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1 Fall 2011 wikihomework Solutions, Chapters 1-4 Professor John R. Crooker, Ph. D. September 14, 2011 Instructions Answer each of the following questions from chapter 1 material. Chapter 1 Problems 1. Is the following statement made by a college athlete true or false? Explain your reasoning. I am attending college on a full athletic scholarship, so the opportunity cost of attending college is zero for me. 2. The term figure skating refers to the shapes that skaters used to trace in the ice as part of skating competitions. In the 1970s, this aspect of the sport was deemphasized and eventually eliminated. Use the theory of comparative advantage to show why eliminating this part of the competition has led skaters to perform much more difficult and sophisticated jumps and spins. Chapter 1 Solutions 1. Is the following statement made by a college athlete true or false? Explain your reasoning. I am attending college on a full athletic scholarship, so the opportunity cost of attending college is zero for me. False. All choices require an opporunity cost and the decision to attend college on a full athletic scholarship or not is no different. There are several examples of prominent athletes who have skipped college even though they would have received a full athletic scholarship to attend college. Notable examples include LeBron James, Kobe Bryant, and Bubba Starling (2011 #1 draft pick by the Kansas City Royals). As these athletes received several millions of dollars to turn pro out of high school, clearly a decision to go to college on a full athletic scholarship would have been quite financially costly. Even athletes who do not have opportunities in the professional sport s ranks still have an opportunity cost. Spending time at practices likely has implications on available time to study or work and earn income. Practice and game preparation also takes the athlete away from family and friends. 1

2 Certainly, there are sacrificed opportunities when a student decides to accept a full athletic scholarship. 2. The term figure skating refers to the shapes that skaters used to trace in the ice as part of skating competitions. In the 1970s, this aspect of the sport was deemphasized and eventually eliminated. Use the theory of comparative advantage to show why eliminating this part of the competition has led skaters to perform much more difficult and sophisticated jumps and spins. In competition, skaters would be expected to master and exhibit performances that score more points from the judges. A move that is perceived to be more difficult and sophisticated and scored as such will invite skaters to develop and refine this move. As skaters compete, those that excel in events will have established a comparative advantage in executing the more difficult and spohisticated moves. Skaters are then forced to practice the more difficult moves so as to maintain or earn a comparative advantage against others. To the extent that skating literal shapes and figures on the ice is less complex or difficult, the elimination of these moves as worthy of points has instigated the chase for enjoying comparative advantages in more difficult maneuvers. Chapter 2 Problems 1. Suppose the market demand for tickets to see a University of Tennessee women s basketball game is Q d = 40, 000 1, 000p, and the supply is Q s = 20, 000. Identify the equilibrium price and quantity of tickets exchanged. What would happen to the market for tickets if the university set a price ceiling on tickets of $10/ticket and if Tennessee had strict antiscalping laws? What would happen if the price ceiling was $30/ticket instead? 2. The major North American sports leagues prohibit teams from locating within a specfic distance of an existing team. Why do they have such a rule? 3. Suppose the St. Louis Cardinals sign a star pitcher from Japan to a fiveyear $120 million contract. What is likely to happen to ticket prices in St. Louis for Cardinal s games? Why? Five years later, suppose the Cardinals re-sign the pitcher to another five-year contract this time for $150 million. What is likely to happen to ticket prices in St. Louis now? Why? Chapter 2 Solutions 1. Suppose the market demand for tickets to see a University of Tennessee women s basketball game is Q d = 40, 000 1, 000p, and the supply is Q s = 20, 000. Identify the equilibrium price and quantity of tickets exchanged. What would happen to the market for tickets if the university set a price ceiling on tickets of $10/ticket and if Tennessee had strict antiscalping laws? What would happen if the price ceiling was $30/ticket instead? 2

3 The equilibrium quantity requires: Q d = 40, 000 1, 000p = 20, 000 = Q s Solving for p, we see p = 20. That is, at a price of $20 per ticket, 20,000 tickets will be exchanged for a University of Tennessee women s basketball game. The equilibrium price is $20 per ticket and the equlibrium quantity is 20,000. If we suppose that antiscalping laws prohibit any secondary market for bsketball games, we expect the price to be $10/ticket. As the availability of the tickets is likely limited by the capacity of the stadium at 20,000 seats, only 20,000 tickets will be sold. There would be a shortage of 10,000 tickets as the quantity demanded of tickets at $10 is 30,000. While ticket prices may appear cheaper, fans would be forced to wait in lines for tickets and possibly not get tickets. Thus, non-monetary costs of acquiring tickets would go up. If the price ceiling was $30/ticket, the price ceiling would not impact the market. This is because the market reaches equlibrium below the price ceiling. 2. The major North American sports leagues prohibit teams from locating within a specfic distance of an existing team. Why do they have such a rule? This rule is designed to protect the market power of existing teams. If teams in the same league are permitted to spring up within the limits of an existing teams market, the team would create a substitute as multiple producers in the league compete for existing fan base. Without these rules, the value of a franchise is reduced. Formally, the monopoly pricing power of a league and subsequent profits in a particular market is greater when the franchise has no close substitutes. If a substitute is introduced into the market, the demand curve shifts to the left and becomes more elastic. As a result, the teams profits are eroded. As teams become less profitable, the interest in owning a team in the league wanes. As team owners can control this rule by participating in the league, we would anticipate that they would collectively agree to protect the markets of each other owner. This would ensure their own profits as well. 3. Suppose the St. Louis Cardinals sign a star pitcher from Japan to a fiveyear $120 million contract. What is likely to happen to ticket prices in St. Louis for Cardinal s games? Why? Five years later, suppose the Cardinals re-sign the pitcher to another five-year contract this time for $150 million. What is likely to happen to ticket prices in St. Louis now? Why? The knee-jerk reaction of most fans is that when a star player is signed, the ticket prices will go up. This is not necessarily the case. It depends on what happens to the demand for tickets. If the team is relatively loaded with talent and another star player fails to generate more interest in attending the game in person (or subscribing to some satellite plan that 3

4 enriches the owner), ticket prices would not rise. On the other hand, if the star player generates more interest in the game, we would anticipate the team would enjoy greater pricing power and raise ticket prices. If five years later, the same concepts are relevant. If re-signing the same star player causes new fans to come out to games more or existing fans to come out more often, we would anticipate the team enjoying greater pricing power. On the other hand, if re-signing the player will not cause new fans to come out to games or induce existing fans to come out more frequently, the re-signing will not have an impact on the ticket prices. Of course, if the team fails to sign the player and existing fans come less frequently and new fans are not attracted, we would expect a loss in pricing power and a subsequent reduction in ticket prices. Chapter 3 Problems 1. Draw a graph (you can attach an image to your wikipage by clicking the image icon in the toolbar that appears above when you begin editing your page) that shows the demand for seats at an NFL stadium. Show how demand for attendance at a given game would be affected if: a) The prices of parking and food at the games increase but quality does not; b) Televised games switch from free TV to pay-per-view only; c) A new league forms with a team that plays nearby; d) The quality of the team decreases dramatically; e) The length of the season is increased. 2. True or False; explain your answer: If all teams are of equal quality, it doesn t matter whether they share gate receipts or not revenue will be the same for all teams. 3. Suppose an owner pays $500 million to purchase a hockey team that earns operating profits of $50 million per year. The new owner claims that $200 million of this prices is for the players, which he can depreciate using straight-line depreciation in five years. If the team pays corporate profit taxes of 40%, how much does the depreciation of the players save the owner? Chapter 3 Solutions 1. Draw a graph (you can attach an image to your wikipage by clicking the image icon in the toolbar that appears above when you begin editing your page) that shows the demand for seats at an NFL stadium. Show how demand for attendance at a given game would be affected if: a) The prices of parking and food at the games increase but quality does not; b) Televised games switch from free TV to pay-per-view only; c) A new league forms with a team that plays nearby; d) The quality of the team decreases dramatically; e) The length of the season is increased. The effects of (a), (c), and (d) are all the same. Specifically, these effects will result in a decrease in demand. I have diagrammed a decrease in demand below. 4

5 Price < D1 D Quantity The original demand curve is labled D0 above. A decrease in demand is depicted as a leftward shift. I have illustrated the decrease in demand as a movement from D0 to D1. Prices of parking and food at the game increasing without any improvement in quality are likely to impact the demand for game attendance because these items are complement goods. That is, these goods are used together with game attendance. When the price of complement goods rise, the demand for the related complement good declines. If a new league forms nearby, we would anticipate a decrease in the demand for games for the incumbent team. This is because a new league with a team would constitute a substitute good. As the price of a substitute goes down, the demand for the related substitute good declines. So, given the new league has a team viewed by fans in the market as a substitute game experience, the demand would decrease. A loss of team quality would also cause demand to decrease. Provided fans enjoy the quality of play, a decrease in quality holding all else constant is going to result in less fan interest and fewer fans willing to pay the same price for the same number of games attended. Thus, a decrease in demand. Part (b) supposes the impact of switching televsied games from free TV to pay-per-view. As watching the games on TV is a substitute for attending the game, making the substitute price more expensive is likely to increase the demand for game attendance. Thus, we anticipate a rightward shift of the demand curve as illustrated here. 5

6 Price D1 D Quantity The original demand curve is denoted D0 in the graph above. As a result of the change, demand increases to D1. Let s consider part (e). If the length of the season is increased, this is likely equivalent to an increase in the supply of games. We would anticipate that more opportunities to go out to a game results in a smaller demand for tickets on any particular game day. For the picture I have illustrated below, the increase in the length of season will likely cause ticket prices to fall. As ticket prices go down, we anticipated the quantity demanded of tickets rising. 2. True or False; explain your answer: If all teams are of equal quality, it doesn t matter whether they share gate receipts or not revenue will be the same for all teams. False. While teams may be of equal quality, the problem does not state that all markets are the same. We know that some markets are bigger than others and some markets may have a different collection of entertainment options for people in that market. As the availability of other substitutes may differ across teams, the pricing power and subsequent revenue and profits are also likely to be heterogeneous even if the teams were homogeneous in quality. 3. Suppose an owner pays $500 million to purchase a hockey team that earns operating profits of $50 million per year. The new owner claims that $200 million of this prices is for the players, which he can depreciate using straight-line depreciation in five years. If the team pays corporate profit taxes of 40%, how much does the depreciation of the players save the owner? By claiming $200 million of the $500 million the owner paid for the hockey 6

7 team is for the players, the owner may subtract 1/5 of the amount in one year a depreciation expense. In this case, the depreciation expense is $40 million. As depreciation expense is a deductible expense, the owner will pay taxes on $50 million - $40 million, or $10 million. This means a tax bill of $4 million with the depreciation expense. Without depreciation for the players, the owner must presumably pay taxes on the entire $50 million in operating profit. Thus, the owner would pay $20 million in taxes if depreciation is not allowed. Thus, the owner saves $16 million in taxes per year if he is allowed to depreciate players. Chapter 4 Problems 1. An athletic director was once quoted as saying that he felt his school spent too much on athletics but that it could not afford to stop. Use game theory to model his dilemma. 2. Suppose that the demand curve for tickets to see a football team is given by Q = 100, p and marginal cost is zero. a) How many tickets would the team be able to sell (ignoring capacity constraints) if it behaved competitively and set price equal to marginal cost? b) How many tickets would it sell and what price would it charge if it behaved like a monopoly? (HINT: In this case the marginal revenue curve is given by MR = 1, Q). 3. Suppose the typical Buffalo Bills fan has the demand curve for Bills football games: p = G, where G is the number of games the fan attends. a) If the Bills want to sell the fan a ticket to all eight home games, what price must they charge? What are their revenues? b) Suppose the Bills have the chance to offer a season ticket that is good for all eight home games, a partial season ticket that is good for four home games, and tickets to individual games. What price should they charge? What is their revenue? Chapter 4 Solutions 1. An athletic director was once quoted as saying that he felt his school spent too much on athletics but that it could not afford to stop. Use game theory to model his dilemma. The game embodied in the table below represents a two-player simultaneous move game. The players are My U and Arch Rival. Each player may play the Spend Too Much strategy or Spend Little strategy. The pay-outs are listed with the row player s pay-out first followed by the column player s pay out. Upon examining the pay-out matrix, we see each University has a dominant strategy to Spend Too Much. That is, Spend Too Much always does better than Spend Little. If the Arch Rival Spends Too Much, My U does better by also choosing Spend Too Much. If the Arch Rival chooses Spend Little, My U does better by choosing Spend Too Little. 7

8 Arch Rival Spend Too Much Spend Little My U Spend Too Much (-10, - 10) (+20, -20) Spend Little (-20, +20) (0, 0) In fact, this is the favorite outcome for My U. Unfortunately, we anticipate each University adopting the dominant strategy of Spend Too Much. As a result, each University experiences a -10 outcome. The dilemma is that we see that both schools do strictly better-off by both adopting a Spend Little approach. This outcome is not sustainable, however. If somehow the schools found themselves in this situation, both schools would have an incentive to switch to the Spend Too Much strategy. In the language of Game Theory, we would say that the Spend Too Much - Spend Too Much outcome is a Nash Equilibrium. 2. Suppose that the demand curve for tickets to see a football team is given by Q = 100, p and marginal cost is zero. a) How many tickets would the team be able to sell (ignoring capacity constraints) if it behaved competitively and set price equal to marginal cost? b) How many tickets would it sell and what price would it charge if it behaved like a monopoly? (HINT: In this case the marginal revenue curve is given by MR = 1, Q). If the team priced competitively and set price equal to marginal cost ($0), the number of tickets demanded with a price of $0 is 100,000. This would generate $0 in revenue. If the team, instead, behaved like a monopolist, the team would set: Solving for Q, we see: MR = 1, Q = 0 = MC. Q = 5, 000. We can identify the required ticket price by solving: or 5000 = 100, p p = $ Charging $950/ticket for 5,000 tickets generates $4,750, Suppose the typical Buffalo Bills fan has the demand curve for Bills football games: p = G, where G is the number of games the fan attends. a) If the Bills want to sell the fan a ticket to all eight home games, what price must they charge? What are their revenues? b) Suppose the Bills have the chance to offer a season ticket that is good for all eight home games, a partial season ticket that is good for four home games, and tickets to individual games. What price should they charge? What is their revenue? 8

9 If the Bills must charge a single game ticket price and use the ticket price for all games, the Bills must charge $40/ticket or less to induce the fan to purchase tickets to all eight games. A price of $40/ticket generates $320 in ticket revenue for the Bills from this fan. If we want to sell the fan a ticket all eight home games, we should calculate the individual s maximum willingness-to-pay for 8 games. This corresponds to the area under the demand curve from 0 to 8 Games. This region can be broken down into a triangle and a rectangle. The triangle has a height of $80/Game and a width of 8 games. The rectangle has a height of $40/Game with a width of 8 games. Price Games Thus, the indivdiual s maximum willingness-to-pay for 8 games is $320 + $320 = $640. Thus, selling a season ticket for all 8 games for just under $640 would entice the individual to purchase a season-ticket if he or she had no other alternatives. The individual has a maximum willingness-to-pay of $400 for a partial season ticket of 4 games. A single game revenue maximizing price would be $60/Game. Recall that the marginal revenue curve will have the same vertical axis intercept as the demand curve but with twice the slope. Thus, given p = G, we know MR = G. Hence, the revenue maximizing single game price is MR = G = 0 imples G = 6. The highest price the consumer would pay per game is p = (6) = 60. The fan would purchase 6 tickets spending $360 total. The Bills would do best by charging $ for a season ticket to all 8 gmaes. Pricing the partial season ticket (4 games) at $400 or more would dissuade the individual to purchase a partial season ticket to 4 games. Finally, charging $115 or more for a single game ticket would keep the fan from purchasing single game tickets. In this example and perhaps in the 9

10 limit, the fan is better-off by $0.01 by purchasing a full season ticket for $ This is the greatest revenue the Bills can raise from the fan. 10