EC 301, Spring 2015. Problem set 6 Page 1 of 2

EC 301, Spring 2015. Problem set 6 Page 1 of 2 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 seven 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. A few sample questions and answers are posted on ANGEL to give you hints on how to solve some of these problems. Questions from Chapter 19 1. Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each earn as profit? How does the price compare to the marginal cost? 2. Consider question 1 again but assume that Joe’s and Rebecca’s firms compete in prices rather than in quantities. Consumers perceive the ready-mix concrete produced by the two firms as identical products. Find the Nash equilibrium prices when the two firms set their prices simultaneously. Questions from Chapter 20 3. Two hundred paper mills compete in the paper market. The total cost of production (in dollars) for each mill is given by the formula TC = 500Qmill + (Qmill)2 where Qmill indicates the mills annual production in thousands of tons. The marginal cost of production is MC = 500 + 2Qmill. The external cost of a mill’s production (in dollars) is given by the formula EC = 40Qmill + (Qmill)2 and the marginal external cost of production is MEC = 40 + 2Qmill. Finally, annual market demand (in thousands of tons) is given by the formula Qd = 150,000 – 100P where P is the price of paper per ton. Using algebra, find the competitive equilibrium EC 301, Spring 2015. Problem set 6 Page 2 of 2 price and quantity, as well as the efficient quantity. Calculate the magnitude of the deadweight loss resulting from the externality. Illustrate your solution with graphs. 4. Three stores have a problem with theft, and security is a public good. Let’s use S to stand for the number of person-hours of security patrols per week. The marginal benefit of security patrols to each of the stores is given by the formula MB = 100 – 2S, and the cost of patrols is $30 per hour. What is the socially efficient level of security? If security is left to the independent decisions of the stores, what will they choose? How would your answer change if there were 5 stores? 5. Students receive two types of benefits from standardized test preparation services: first, they learn useful material; second, they score better on the test relative to other students. Because relative performance matters, their improved performance creates a negative externality for other students. Suppose that the market demand function for test preparation services is Qd = 30 – P/2, where Qd is millions of hours of services and P is the price per hour. Suppose also that the market for these services is competitive and that the market supply function is Qs = 2P – 30. Finally, suppose that the marginal external cost of test preparation is given by MEC = 5 + 1.5Q. Find the socially efficient level of test preparation, the competitive equilibrium, and the deadweight loss created by the externality. Draw a figure to illustrate your answer. 6. Consider the same market described in Q. 5 above, but now assume that test preparation services are monopolized. Also assume that the monopolist’s marginal cost curve coincides with the market supply curve in the last problem. How does the monopoly output compare with the socially efficient output? Calculate the deadweight loss of monopoly. 7. Fifty residents of a college dorm all like espresso. An espresso machine costs $1,000. Each dorm resident is willing to pay up to $50 for the machine. However, the resident’s willingness to pay is their “private information.” One resident, Eugene, decides to take up a collection. Assuming there is no way to make other residents contribute (and Eugene does not know what the residents’ willingness to pay is), is Eugene likely to raise the necessary $1,000? Why or why not? What could be done to improve his chances of success? [Hint: a simple argument can be made in the lines of the “non-excludability” nature of a public good. If one student pays for the coffee maker in the pantry, all will use it! Eugene can do better by ensuring this does not happen.]