EC 301, Spring 2015. Problem set 5 Page 1 of 2/EC 301 Spring 2015: Problem set 5

EC 301, Spring 2015. Problem set 5 Page 1 of 2/EC 301 Spring 2015: Problem set 5 Note: Your score will be based on your overall performance in answering all questions in this problem set. Answers to specific questions will not be individually graded. Show all logical steps in your arguments. Answers without any explanation will get zero credit. You must work in groups of two and you can consult any other resources (internet, other text books, etc.). You need to turn in one home work per group. Make sure you write the names of all group members on your home work. There are eight problems in total. Several questions are from your text book “Microeconomics” by Bernhiem and Whinston. A remark on plagiarism: While you are allowed to use any resource you like to solve these problems, please note that each group must write their answers in their own words. Copying from other groups’ work or from any document that you have not produced by yourself is considered to be a case of plagiarism and may result in a ZERO grade. Questions from Chapter 17 1. Kalamazoo Competition-free Concrete (KCC) is a local monopolist of ready-mix concrete. Its annual demand function is Qd = 16,000 – 200P, where P is the price, in dollars, of a cubic yard of concrete and Q is the number of cubic yard sold per year. Suppose that Kalamazoo’s marginal cost is $20 per cubic yard and its avoidable fixed cost $100,000 per year. What is its profit-maximizing sales quantity and price? How would your answer change if Kalamazoo had an avoidable fixed cost of $200,000 a year? What if that $200,000 fixed cost were instead sunk? [Hint: Recall that when the fixed cost is sunk, the monopolist has to pay $200,000 in cost even if he decides to shut down.] 2. Kalamazoo Competition-free Concrete (KCC) is a local monopolist of ready-mix concrete. Its annual demand function is Qd = 16,000 – 200P, where P is the price, in dollars, of a cubic yard of concrete and Q is the number of cubic yard sold per year. Suppose that Kalamazoo’s marginal cost is MC = 20 + 0.02Q. What is its profit-maximizing sales quantity and price? [Note that in this problem the total cost function of the monopolist is not given. Hence, it is difficult to check the shut-down condition (however it can still be done, as will be discussed in the answer key). So, to keep things simple, just calculate the monopoly price and quantity using only the quantity rule.] 3. What is the deadweight loss from monopoly pricing in Problem 1 above? [Hint: In order to calculated the deadweight loss you also need to calculate what price and quantity would have prevailed in this market under perfect competition.] EC 301, Spring 2015. Problem set 5 Page 2 of 2 Questions from Chapter 18 4. Clearvoice is a wireless telephone monopolist in a rural area. There are 100 consumers, each of whom has a monthly demand curve for wireless minutes of Qd = 100 – 100P, where P is the per-minute price in dollars. The marginal cost of providing wireless service is 10 cents per minute. Suppose that Clearvoice charges 30 cents per minute. How large a fixed fee can Clearvoice charge and still persuade consumers to buy the service? What will be its profit from each consumer? What will be it total profit, and how will this amount compare to its total profit with a per-minute charge of 10 cents? [Hint: recall the class discussion on twopart tariff. The maximum fixed-fee the company can charge is the consumer surplus of each consumer at the price of 30 cents/minute.] 5. Clearvoice is a wireless telephone monopolist in a rural area. There are 100 consumers, each of whom has a monthly demand curve for wireless minutes of Qd = 100 –100P, where P is the per-minute price in dollars. The marginal cost of providing wireless service is 10 cents per minute. Suppose that Clearvoice charges 40 cents per minute. How large a fixed fee can Clearvoice charge and still persuade consumers to buy the service? What will be its profit from each consumer? [Hint: recall that the largest fixed fee is equal to the consumer surplus of each customer at the price of 40 cents/minute.] 6. A movie monopolist sells to college students and other adults. The demand function for students is Qd S = 800 –100P and the demand function for other adults is Qd A = 1800 –100P. Marginal cost is $2 per ticket. What prices will the monopolist set when she can price discriminate? What will be the monopolist’s profit from the price discrimination? Questions from Chapter 12 7. Bob and Brian square off for the World Rock Paper Scissors Championship. The winner will take home $5,000, the loser receives nothing, and they split the prize in the event of a tie. Draw a table (as discussed in Lecture slide 24) showing the player’s possible choices, and the payoffs that result from each pair of actions. [Recall that Paper beats Rock, Rock beats Scissors, and Scissors beat Paper.] 8. Consider the game shown in Figure 12.7. What is Myrna’s best response when Susan plays “Down”? What is Myrna’s best response when Susan plays “Up”? Does Myrna have a dominant strategy? What are the Nash equilibria in this game? If there is more than one, which do you think is the most plausible? Why?