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5.2 In a large economics class of 400 students, each student would buy either one copy of the textbook or would not buy it. Students with different reservation prices for the textbook can be grouped as below: Group Reservation Price ($) Number of students in IQ TMOODD the group 550 40 500 50 450 60 400 60 350 60 300 50 250 40 200 40 There are also a few sellers who are willing to sell the textbook at or above the following prices. The sellers are price takers Seller Reservation Price ($) Number of copies it sells 250 100 300 100 350 70 IV 400 50 450 100 (a) What are the possible factors that would affect each student's reservation price? (b) What are the equilibrium price and quantity of the textbook? (c) What are the consumer surplus and producer surplus in this equilibrium? (d) To encourage students to buy the textbook, a subsidy of $100 is given to the students who buy the textbook. What are the equilibrium price and quantity after the subsidy is imposed? (Note: the market price is the price paid by students including the subsidy.) (e) Following part (d), if there is indeed no externalities, is there any deadweight loss? If so, how much is the deadweight loss?5.4 Ms. Wong is a fitness trainer providing personal fitness training course to her customers. She can be taken as a monopoly in providing her unique way of training. The following table shows her customers' maximum price willing to pay for her weekly one-hour training course in two centers at Tsim Sha Tsui (TST) and Tai Po (TP) respectively. The rental cost of the center is fixed at $200 in total for Ms. Wong, while for each hour of course given, she needs to give up her work as a piano teacher that earns $290 per hour. Assume no other costs for simplicity. Customer Center Maximum Price Willing to Pay($) Z3X--IQTMOOOD TST 400 TST 390 TST 380 TST 370 TP 360 TST 350 TP 340 TP 330 TST 320 TP 310 TP 300 TST 290 TP 280 TP 270 (a) Suppose Ms. Wong charges one single price to all of her customers. What is the profit maximizing price she has to charge? What is the amount of her economic profit? S'how your calculation. (b) Suppose Ms. Wong knows that customers who go to different centers are likely to have different maximum price they are willing to pay on average. Therefore, she plans to charge one single price to customers in TST center and another single price to customers in TP center. What is the profit maximizing price for the TST customers and TP customers respectively? Will she serve more customers in this case? Can she earn more in total than charging a single price? Show your calculations. (c) Is the pricing strategy in part (b) likely to be successful? Why? (d) If Ms. Wong is able to carry out perfect price discrimination, how many customers will she serve? How large is the profit? In this context, what will make it more plausible?5.5 Consider that the two companies Moonbucks and Atlantic Coffee form a duopoly in the freshly brewed coffee market in a university a distance away from the city center. Let QA and Qs be the number of cups of coffee Moonbucks and Atlantic Coffee sold a day respectively. The market demand curve if the freshly brewed coffee is given by P = 50 - 0.1(QA + Q=) = 50 -0.1Q The cost function for Moonbucks is given by TCA(QA) = 8Q, and similarly the cost function for Atlantic Coffee is also given by TC;(Q:) = 80,. Moonbucks and Atlantic Coffee each can choose a high output level of 140 cups a day, or a low output level of 105 cups a day. (a) Complete the following table about the market quantity supplied (Q) and the price (P) that a cup of coffee can be sold under each possible scenario Atlantic Coffee QB = 105 QB = 140 Moonbucks QA = 105 (Q = P = P= QA = 140 (Q = , P = (Q = , P = (b) The payoff of each company is the profit they can earn each day. Complete the following payoff matrix about the payoff of each firm. Atlanctic Coffee QB = 105 QB = 140 Moonbucks QA = 105 (TIA = TTB = (TIA me = QA = 140 (TA = WB= (TIA = (Hint: As usual, profit for each firm is equal to its total revenue minus its total cost.) (c) Find the Nash Equilibrium. Show your reasoning. (d) Is it likely to be successful for them to collude to produce less output and earn a higher profit together? Explain using the logic of game theory
