Boston University Professor Todd IdsonEC385 Economics of Sports Spring 2018, Midterm #1SolutionsInstructions: 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. 1. Discuss the central issues raised in the Krautmann, Anthony and David J. Berri, “Can We FindIt 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 is needed 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. 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 andconcessions, they derived the relationship between the profit-maximizing price, , and the ticket-only price, .Model:PQDMRElasticity = 1Elasticity < 1Elasticity > 1Let 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, andis the fixed costs of the team.Then, we can find the optimal quantity and price for ticket-only case as follow:Since , marginal revenue is also positive, and it means that profit maximizing team does not set ticket prices in the inelastic range of demand.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, marginal revenue is Note that profit maximizing team satisfies the optimal condition of MR=MC, i.e.Rearranging above equation: If , then the profit-maximizing team can set the price such that (i.e. inthe inelastic range of demand). Moreover, if we assume that (i.e. marginal cost of admitting another fan into the stadium is zero), then the marginal revenue ofticket is always negative since is positive. i.e. profit-maximizing team set the price in the inelastic range of demand. Solving above equation for the profit-maximizing quantity and price, and , we get:As we can see above, the profit-maximizing price is less than the ticket only price since is positive. In other words, profit-maximizing teams can set their price in theinelastic range of demand if they also consider concession revenues as their total revenues.2. 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 (P up below) from the upstream firms and treat this as the marginal cost and then price accordingly, charging P down. If it was vertically integrated, i.e. one firm in the bottom diagrams, then the media outlet would cost the games at marginal cost (i.e., P up would be treated as the MC at the second stage) and hence charge a lower pricefor the broadcast.3. 4. Omitted variable misspecification is when a variable is not taken into account, i.e. included in the regression, but it does affect the dependent variable. This will bias the estimated effect of any included variables that are correlated with the omitted variable. The example focused on in this paper is estimating an attendance function. Turnover was always ignored in the earlier models when we estimate attendance function. However fans care about roster stability, i.e. form attachments to players.Attendance is negatively correlated with turnover. Thus, turnover should belong in the regression. So firstly, the author measure the degree of roster turnover (different ways to measure this, but they opt for weighting by salary to give name players a greater weight/importance) and tests whether they have a statistically and quantitatively significant effect on attendance. As a result, the coefficient of turnover is negative and significant. Then author pointed out, if we omitted the turnover variable, it will cause misspecification problem here: (1) winning percentage has a positive effect on attendance, (2) roster turnover has a negative effect on attendance, and (3) winning percentage and roster turnover are negatively correlated. As a result, if you omit roster turnover from the attendance regression, the effect of roster turnover on attendance will be partly reflected in the estimated winning percentage effect ofturnover, acting to upwardly bias the estimated effect of winning percentage on attendance. To see thisnote that “low” turnover yields higher attendance, and low turnover is associated with higher winning percentage, and higher winning percentage leads to higher attendance, i.e. part of the estimated positive effect of winning percentage on attendance will also be reflecting the fact that when winning percentage is “high” turnover tends to be low which in itself is exerting a positive effect on attendance. If turnover was included in the regression, then the estimated winning percentage effect would fall. More specifically, consider simple estimation model as follow:True model: Misspecification: Note that is negative, is also negative, and is always positive. i.e. is positive and it means that the coefficient of winning percentage is upwardly biased if turnover is omitted in the