ECN 100B study guide
ECN 100B WQ 2024 Midterm STUDY GUIDE Name: Student ID: TA Name: You have 50 minutes to complete this exam. The exam is closed book. No notes are allowed. Blue books are not required; you will write directly on this exam. You may use a non-graphing calculator. The exam has three sections: 1. Answer 2 of 3 short answers [approximately 10 minutes] 2. Answer 2 of 3 multi-part problems [approximately 40 minutes] IF YOU ANSWER MORE THAN THE REQUIRED NUMBER OF QUESTIONS IN A SECTION WE WILL GRADE ONLY THE REQUIRED NUMBER, IN THE ORDER THAT THEY SHOW UP ON THE EXAM. IF YOU WRITE IN THE ANSWER AREA FOR A QUESTION BUT DO NOT WANT IT GRADED, CROSS IT OUT CLEARLY AND ENTIRELY. In order to protect the integrity of a UC Davis degree and reward the sincere efforts of my students, academic dishonesty of any kind will not be tolerated. All violations of the Academic Code will be referred to Student Judicial Affairs for discipline and to impose the strictest sanctions. If you have to use the restroom during the exam, please leave your exam and your phone with Professor Rezaee or the TA. 1 1 Short answers Answer 2 out of 3. Please provide 2 to 3 sentences answering each question. 1.1 What is the optimal price cap for a government to impose on a monopoly? Why? 1.2 What is a potential problem that could arise when a government wants to regulate a monopoly with a price cap? 1 1.3 What three conditions must be met for a firm to profitably price discriminate? 2 Multi-part problems Answer 2 out of 3. Please answer all parts of the question. 2.1 Monopsony question Imagine that UC Bavis is a monopoly employer of labor in the city of Bavis. Suppose the firm faces an inverse supply curve of labor of w(L) = 36 + 6L. A. What is the marginal expenditure curve for the Bavis? 2 Now assume the monopsony has an inverse demand curve for labor of w(L) = 72 − 6L. B. What are the equilibrium wage and labor quantity? C. Show the equilibrium wage and equilibrium labor quantity graphically. Include the inverse demand curve and the firm’s supply and marginal expenditure curves. 3 D. What are Bavis’s surplus, workers’ surplus, and deadweight loss at the equilibrium? E. Now assume the City of Bavis wants to set a minimum wage to ensure zero deadweight loss in the Bavis labor market. What should the City of Bavis set as the minimum wage? D. What are Bavis’s surplus, workers’ surplus, and deadweight loss at the postminimum wage equilibrium? 4 2.2 Static game question Imagine an airline traveler and TSA are playing a simultaneous static game. The airline traveler has to decide whether to arrive at the airport early or late. TSA has to decide whether to make security lines short or long. If the traveler arrives early and the security line is short, the traveler will make his/her flight and will get a utility of 2. TSA will be happy the traveler made his/her flight but unhappy that its employees had to work hard so it will get a utility of 1. If the traveler arrives early and the security line is long, the traveler will still make his/her flight and will still get a utility of 2. TSA will be very happy because the traveler made his/her flight and its employees did not have to work hard so it will get a utility of 3. If the traveler arrives late and the security line is short, the traveler will just make his/her flight and will be happy to not have wasted time, so s/he will get a utility of 3. TSA will get a utility of 1. If the traveler arrives late and the security line is long, the traveler will miss his/her flight and get a utility of 0. TSA will be bummed to have a stranded traveler in the airport but otherwise happy and so will have a utility of 2. A. Draw the payoff matrix for this game, including the players, their possible actions, and the payoffs for each combination of actions. 5 B. Does the traveler have a dominated strategy? If yes, what is it? If no, why not? C. Does the TSA have a dominated strategy? If yes, what is it? If no, why not? D. What is the Nash equilibrium of this game? E. Is this a prisoners’ dilemma? 6 2.3 Sequential game question A hacker wants the contents of a computer (bitcoin) and is threatening the owner of the computer, the only person who knows the computer’s password, to log into the computer so the hacker can steal the bitcoin. The hacker cannot force his/her way into the computer without the password but can wipe the computer’s hard drive, destroying the bitcoin for everyone. Should the computer owner believe the threat and unlock his/her computer? This table shows the value that each person places on the various possible outcomes: Unlock the computer, hacker does not wipe hard drive Unlock the computer, hacker wipes hard drive Do not unlock computer, hacker wipes hard drive Do not unlock computer, hacker does not wipe hard drive A. Draw the game tree. Who moves first? B. What is the equilibrium? 7 Hacker Computer’s owner 400 3 2 1 1 2 3 400 C. Does the computer’s owner believe the hacker’s threat? D. Does the computer’s owner unlock it? 8 3 Extra short answer problems 3.1 Is deadweight loss always zero under perfect competition? 3.2 Is there always deadweight loss in the case of a market with a monopoly? 3.3 Is a monopoly that conducts price discrimination better for producers and consumers than one that does not? 3.4 In the case of a static prisoners’ dilemma game, is the Nash Equilibrium identical to the subgame perfect Nash Equilibrium? 3.5 Are a market’s equilibrium price and equilibrium quantity always determined by the intersection of the market supply curve and the market demand curve? 3.6 Can a firm be a monopoly and a monopsony? 3.7 What are the five characteristics that ensure firms are price takers? 3.8 What are two reasons a market could have a monopoly? 3.9 What is the optimal minimum wage for a government to impose on a monopsony? 3.10 What is a dominant strategy? 3.11 What is a best response? 3.12 What is a Nash Equilibrium? 3.13 What is a subgame perfect Nash Equilibrium? 4 Extra multi-part problems 4.1 Perfect competition question Imagine many small farms selling usb charging cables on a large online marketplace, in a setting of perfect competition. Each individual firm faces costs C(q) = 3q 2 . A. Derive a firm’s supply curve. Now assume there are 300 firms selling usb cables on the same large online marketplace. B. Derive the market supply curve. Suppose the market demand curve is QD (p) = 1000 − 50p. 9 C. What are equilibrium price and equilibrium quantity? D. Graph the inverse demand and inverse supply curves for the market and indicate the equilibrium price and quantity. E. What are consumer and producer surplus? 4.2 Monopoly question Imagine a firm called Bapple that is the monopoly in the market for smartwatches, with cost-function C(Q) = 99Q2 + 20000. Imagine the inverse demand function for smartwatches is p(Q) = 2000 − Q. A. What are equilibrium price and equilibrium quantity? B. What is the monopoly’s profit at the equilibrium? C. Prove that this profit level is a global maximum. D. Show the equilibrium price and equilibrium quantity graphically. Include the inverse demand curve, firm’s marginal revenue curve, and firm’s marginal cost curve. E. What are consumer surplus, producer surplus, and deadweight loss at the equilibrium? 4.3 Specific tax of monopoly question Now imagine that the government decides to tax smartwatches using a specific tax of 200 per smartwatch produced and sold. A. What are the new post-tax equilibrium price and equilibrium quantity? B. What is Bapple’s new profit at the equilibrium? C. Prove that this new profit level is a global maximum. D. Show the new equilibrium price and equilibrium quantity graphically. Include the inverse demand curve, firm’s marginal revenue curve, and firm’s pre- and post-tax marginal cost curves. E. What are consumer surplus, producer surplus, and deadweight loss at the equilibrium? How have these quantities changed from the no-tax case in the monopoly question? 4.4 Price cap monopoly question Imagine a firm called Bapple that is the monopoly in the market for smartwatches, with costfunction C(Q) = 99Q2 + 20000. Imagine the inverse demand function for smartwatches is p(Q) = 2000 − 2Q. The government has decided it would ensure that there is no deadweight loss in this market for smartwatches by setting a price cap on Bapple. A. At what price should the government cap smartwatch sales? B. What are the new post-price cap equilibrium price and equilibrium quantity? C. What is Bapple’s new profit at the equilibrium? D. Prove that this new profit level is a global maximum. 10 E. Show the new equilibrium price and equilibrium quantity graphically. Include the original and regulated inverse demand curves, firm’s marginal revenue curve, and firm’s marginal cost curve. F. What are consumer surplus, producer surplus, and deadweight loss at the equilibrium? How do they compare to the case of perfect competition? 4.5 Price discrimination question Imagine a firm called Bapple that is the monopoly in the market for smartwatches, with costfunction C(Q) = 15Q2 . Imagine the inverse demand function for smartwatches is p(Q) = 2000 − 10Q. A. What are equilibrium price and equilibrium quantity? B. Show the equilibrium price and equilibrium quantity graphically. Include the inverse demand curve, firm’s marginal revenue curve, and firm’s marginal cost curve. Now assume that Bapple is able to perfectly price discriminate in the market for smartwatches. C. What three conditions must be true for this perfect price discrimination to be possible? D. What are the equilibrium prices and equilibrium quantity with perfect price discrimination? E. What are consumer surplus, producer surplus, and deadweight loss at the perfect price discrimination equilibrium? 11
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