课程名称︰ 个体经济学二 课程性质︰ 必修 课程教师︰ 古慧雯 开课学院： 社科院 开课系所︰ 经济系 考试日期（年月日）︰ 2017/04/24 考试时限（分钟）： 100 min 试题 : 总分31分。答题皆须附说明，未作解释的答案概不计分。 1. (3 points) In the following game, the first element of the payoff vector denotes the row player's payoff, and the second element of the payoff vector denotes the column player's payoff. Please find all the Nash equilibria. │ t1 t2 t3 ───────────── s1 │1, 3 100,2 0, 2 s2 │0. 2 200,1 1, 3 2. A monopolist produces and distributes his products in market A and market B in which it is possible to set different prices. The market demand for these two markets are: Q_A = 20 - 2P_A Q_B = 40 - 8P_B where Q_i and P_i denote quantity and price in market i, i = A, B. (a) (1 point) If the monopolist only sells in market A, please derive the marginal revenur function MR_A(Q_A) (b) (2 points) Actually when Q units are produced, they will be distributed to two markets to maximum total revenue. Please derive the marginal revenue function MR(Q), and caculate MR(4) and MR(10). (c) (4 points) The total cost function is: TC(Q) = Q^2/10. Please solve for the optimal prices in two markets, P_A and P_B. 3. A monopolist has two retailers to sell his products. The market demand is: q = 120 - p where q is the quantity and p is the price. Given the whole price θ set by the monopolist, a retailer could obtain at θ any unit she wishes. The two retailers will engaged in a Cournot competition. (a) (2 points) If θ = 30, what will be the equilibrium retail price p? (b) (2 points) There is no production cost for this monopolist. Please determin the optimal whole price for him. 4. In a village, there is only one amusement park which is the position to set the price. It is costless to run the rollercoaster, so the park owner simply wishes to maximize revenue. Every customer has the same demand: q = 50 - p where p is the ticket price of a ride. (a) (2 points) If the park owner considers only sll ride tickets, please decide the optimal price for him. (b) (2 points) If the park owner turns to consider to set a two-part tariff: an admission fee to the park and a ticket price per ride, what is the optimal two-part tariff? (c) New people move into this village, their individual demand, different from an old resident's, is: q = 75 - 1.5p The number of these new resident is the same as the number of old residents. The park owner reconsiders the situstion and designs a two part tariff to attract both types of customers. i. (1 point) Under the optimal two-part tariff, what is the consumer's surplus of an old resident? ii. (2 points) What is the ticket price per ride under the opti- mal two-part tariff? iii. (1 point) Under the scheme of a two-part tariff, is it better to attract both types of customers or to attract only one type of customers? 5. A competitive firm facing a price of $20 per unit for his product pollutes the air when producing for the market. His own marginal production cost is: MC(q) = q where q denotes his production units. At the mean time, the pollu- tion harms his neighbors's health and consequently increases neigh- bors's medical expenses. The more he produces, the larger their medical bills become and the marginal medical expenses are: ME(q) = q. (a) (2 points) Supposr there are no transaction costs, that ther is no legal penalty for polluting, and that it is impossible for the neighbors to move. What quantity does the firm produce? Give a concrete description of a deal that might be struct between the firm and the neighbors. (b) Suppose transaction cost are so high that negotiation is impos- sible, and that it would cost the neighbors $90 to move. Under each of the following scenarios, determine whether or not the neighbors move, and determine how much the firm produces. i. (1 point) Ther firm faces no penalty for pollution. ii. (2 points) The firm must reimburse the neighbors for all pollution damage. iii. (2 points) Reconsider scenarios i and ii. Which one is more efficient? 6. There are several piles of matchsticks. Two players alternate in moving. When it is your turn to move, toy must select one of the piles and remove at least one matchstick from that pile. The last player to take a matchstick is the winner. In the following games, you move first, and try to make sure you will win. (a) (1 point) If there are 2 piles. The 1st pile has 1 matchstick and 2nd pile has 2 matchsticks. What is your first move? (b) (2 points) If there are 3 piles. The 1st pile has 1 matchstick, the 2nd pile has 2 matchsticks, and 3rd pile has 4 matchsticks. What is your first move? --

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