ECON 447: Economics of Sports Homework Assignment 1 To receive full credit, you must show your work. This homework is due on Wednesday, September 6th at 11:59pm in Canvas.

Problem 1: Math Review. Consider the function f (x) = 2x2 + 16x 10. a) Find the value of f (x) at the following points: x = 1, x = 3, x = 5, x = 7. b) Write down the first order condition, f (x) = 0. Use this to solve for the value of x that maximizes f (x). c) Calculate the maximum value of f (x). d) Graph f (x), labeling the values found in the previous parts.

Problem 2: Perfect Competition & Monopoly. Demand is given by Q(P ) = 225 1 2 P and the marginal cost of production is given by M C(Q) = 30 + 3Q. There are no fixed costs of production. 1. First, assume the market is perfectly competitive. a) Find P (Q), the inverse demand curve. b) Find the market price P ? and the market quantity Q?. c) What is producer surplus? What is consumer surplus? 2. Now, assume there is a single monopoly producer. a) Find M R(Q), the marginal revenue curve. b) Find the market price P m and the market quantity Qm. c) What is producer surplus? What is consumer surplus? What is deadweight loss? 1

Problem 3: Team Decisions. Suppose that all NBA teams have the same average revenue curve equal to P (W ) = AR(W ) = 160 2W where W represents the number of expected wins in the season. Half the teams are profit- maximizers and the other half are win-maximizers. 1. Suppose that all teams face the same constant marginal cost given by M C = 40. a) How many expected wins will each profit-maximizing team choose (W )? b) Calculate consumer surplus for each profit-maximizing team (CS). c) How many expected wins will each win-maximizing team choose (W )? d) Calculate consumer surplus for each win-maximizing team (CS). 2. Suppose the league wants all teams choose the same level of W . The league implements a tax of t per win on each win-maximizing team so that win-maximizing teams now face a higher marginal cost of M C = 40 + t. (Profit-maximizing teams still face the original M C = 40.) a) What tax t should the league choose so that all teams choose the same number of expected wins (W = W )? b) Calculate the profits of each win-maximizing team ().