课程名称︰个体经济学下 课程性质︰必修 课程教师︰古慧雯 开课学院：社会科学院 开课系所︰经济系 考试日期（年月日）︰2011.4.18 考试时限（分钟）：100 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1. Suppose the market is contestable. Each producer has the same total cost function: TCi(qi)=100+qi^2. The market demand is: q=100-p (a) (2 points)What is the equilibrium price? (b) (2 points)How many producers will remain in the market in the long run? 2. Consider a merchant who sells high quality E-book readers and monopolizes the market of E-books. The marginal cost to produce an E-book reader is $2000 and the marginal cost to allow a customer to download an E-book is zero. There are 100 customers who have the same income($50000 per person) and the same utility function: (200-x)x u(x,y)=------------ +y 2 where x(a continuous variable) is the number of E-books that a customer reads and y is the money he could spend on food. The merchant wishes to maximize profit. (a) (2 points) How much will the merchant charge a customer to download one E-book? (b) (2 points) How many E-books will a customer purchase? (c) (2 points) How much will the merchant charge for an E-book reader? 3. The products made by A and B are similar, but not quite the same. A and B consider how to set the price for his own product. The sales will depend on their prices: QA=100-2PA+PB QB=100-2PB+PA where Pi is the price of i's product and Qi is i's sales quantity, i=A, B. The productioncost is zero and each person wishes to maximize his own profit. (a) (2 points) Given PB, what is the optimal price PA?( The answer is a function of PB.) (b) (2 points) If A and B determine the price simultaneously, what is the Nash equilibrium? (c) (3 points) If B sets the price first and A shall decide on PA after observing PB, what is the optimal PB? 4. N art lovers attend an (English) auction to purchase a painting. Let vi denotes i's personal value of this painting, and vi is only known to i and no one else. The auctioneer will raise the price continuously. If a bidder loses interest in the auction when the price is too high for him, he will leave. Let p denote the price that triggers the N-1th person to leave. The painting will then be sold to the only remaining bidder at price p. (a) (2 points) What is the optimal timing for a bidder to drop out? (b) (2 points) Is the result of this auction efficient? 5. A monopoly has two types of customers whose individual inverse demand is as follows: │ A B ------------- 1 │10 12 2 │ 8 7 3 │ 6 2 There are 100 type A customers and 100 type B customers. There is no production cost so the monopoly considers to maximize the total revenue. (a) (3 points) If the monopoly sets a single price for all units, what is the optimal price? (b) (3 points) Now suppose the monopoly coulde offer quantity discounts and practice the second-degree price discrimination. Let pi denote the total price for a customer who purchase i units, i=1,2,3. (So if a customer purchase 3 units, he pays p3 and the implied unit price is p3/3.) Is it optimal if each customer is induced to purchase 2 units? Why? 6. A and B, two enemies, will have a duel. Each person holds a gun with only one bullet. When the duel starts, the distance between them is D and as time passes by, they will start to walk towards each other. Hence the distance between them decreases with time. The probability to kill the enemt with the only bullet is Pi(d), i=A,B, where d is the remaining distance. Pi'<0, and Pi(0)=1. Each persons strongly prefers himself to survive and wishes for the other party;s death. (a) (1 point) If A fires and A misses B, when should B fire? (b) (4 points) Each person has to decide when to fire. Let di denote the remaining distance at which player i will fire if his opponent has not fired yet, i=A,B. Please prove that in a Nash equilibrium, dA=dB. Exam201104.ctx --

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