Boston University EC385 Economics of Sports Professor Todd Idson Summer 2016 Midterm 1 Solutions Instructions Answer all questions below in your blue books be sure to show all of your calculations Please label all parts of your diagrams and draw them large enough so that all aspects can be readily assessed Each question is worth 25 points 1 Suppose that each team in a league has a demand curve for generic advertising a league wide nonteam specific campaign equal to Q 1 000 10p If there are 25 teams in the league and ads cost 200 each how many ads will the teams want to purchase as a group Illustrate your result graphically 2 Would fans be better off if government prevented media outlets such as Disney or local cable companies from owning pro sports teams Be sure to fully articulate your answer and to illustrate your answer diagrammatically Answers Not necessarily The restriction will break a vertical integrated firm into separate upstream and downstream components This may actually worsen the well being of the consumer because the downstream firm will buy at an inflated monopoly price when it would buy at marginal cost if it were vertically integrated 3 Suppose the typical Buffalo Bills fan has the following demand curve for Bills football games P 120 10G where G is the number of games the fans 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 Answer If the Bills want to sell tickets to all 8 games by selling eight individual tickets they have to set the price P 120 10 8 120 80 40 This yields revenue of 40 8 320 from each fan 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 Answer If the Bills practice second degree price discrimination they can effectively charge P 120 10 1 120 10 110 for single games P 110 100 90 80 380 95 ticket for a 4 game package and P 110 100 90 80 70 60 50 40 600 75 ticket for an 8 game package Revenues are clearly much higher for the price discriminating example than one where the team wishes to sell as many as 8 tickets to some fans but must sell tickets individually 4 Discuss the central issues raised in the Krautmann Anthony and David J Berri Can We Find It at the Concessions Understanding Price Elasticity in Professional Sports and their key theoretical results Be sure to work out their analytic model in detail not just describe in words their results Answer more than you need for full points Many studies have shown that teams price their tickets in the inelastic range of demand which implies that teams are not profit maximizing The authors attempt to explain these results by considering the complementarity between tickets sold and concessions P Elasticity 1 Elasticity 1 Elasticity 1 MR D Q As you can see in the above figure if teams price their tickets in the inelastic elasticity is less than 1 range of demand marginal revenue is less than zero Note that profit maximizing team should satisfy the condition of MR MC But marginal cost cannot be negative and it means that the team which price their tickets in the inelastic range of demand is not profit maximizing Using the fact that marginal revenue for teams include both revenue from tickets and concessions they derived the relationship between the profit maximizing price and the ticket only price Model Let the team s demand for tickets be given by i e Then the ticket revenue is Let the team s total cost TC be given by where is the marginal cost MC of admitting another fan into the stadium and is the fixed costs of the team Then we can find the optimal quantity and price for ticket only case as follow Since team does not set ticket prices in the inelastic range of demand marginal revenue is also positive and it means that profit maximizing Now also consider concession revenues i e total revenue is sum of ticket revenues and concession revenues Let concession revenues be given by where is the marginal revenue of concession Then total revenue is Thus margina revenue is Note that profit maximizing team satisfies the optimal condition of MR MC i e Rearranging above equation then the profit maximizing team can set the price such that If the inelastic range of demand Moreover if we assume that cost of admitting another fan into the stadium is zero then the marginal revenue of ticket is always negative since price in the inelastic range of demand is positive i e profit maximizing team set the i e marginal i e in Solving above equation for the profit maximizing quantity and price we get and As we can see above the profit maximizing price is less than the ticket only price since inelastic range of demand if they also consider concession revenues as their total revenues is positive In other words profit maximizing teams can set their price in the