课程名称︰个体经济学二 课程性质︰经济系必修 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）︰100年6月20日 考试时限（分钟）：100分钟 是否需发放奖励金：是~ （如未明确表示，则不予发放） 试题 : 总分39分。答题皆须附说明，未做解释的答案概不计分。 1. A competitive firm pollutes the air. The following graph shows the demand for the firm's product and the private and social marginal cost curves. The numbers in the graph represent areas. price │ MC social MC private │ ／ ／ │ ／ 7 ／ ├────┬──┬────── demand │8 ／│5 ／│ │ ／ │／ │ │ ／ ／ │ │／12 ／│ │ │ ／ │ │ │ ／ │ │ │／ │ │ │ │ │ └────┴──┴──────── quantity 70 80 (a) (2 points) Suppose there are no transaction costs, that there 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 struck between the firm and the neighbors. (b) Suppose transaction costs are so high that negotiation is impossible, and that it would cost the neighbors $6 to move. Under each of the following scenarios, determine wheather or not the neighbors move, and determine how much the firm produces. i. (2 points) The firm faces no penalty for pollution. ii. (2 points) The firms pays an excise tax equal to the amount of the externality it causes; all tax revenue is paid to people who live 3,000 miles away (and hence not affected by the pollution). iii. (2 points) The firm must reimburse the neighbors for all pollution damage. iv. (2 points) Reconsider scenarios i-iii. Which one is the most efficient? 2. Reconsider the aquarium problem in the textbook. The value of a visit to the aquarium, AV, is the same for every one, and it depends on the number of visitors in the aquarium, n. AV(n) = 240 - n. If a citizen decides not to visit the aquarium, he/she will enjoy a picnic in the park. The value of a picnic varies among people, and it is worth $i to the i-th person in the town, i = 1,2,3,... (a) (2 points) If the admission to aquarium is free, how many people will visit the aquarium in equilibrium? (b) (4 points) According to the efficiency criterion, how many visitors should be allowed to visit the aquarium? And how much should we charge a visitor to achieve this result? (c) (4 points) If a single owner could decide the ticket price of the aquatium, what is the market demand curve that the owner faces? When the owner maximizes the total ticket revenue, will he maximize the social gains at the mean time? 3. (4 points) Suppose that it is known for certain that the demand for wheat this year is identical to the demand for wheat next year. This year's wheat crop of 100 tons has just been harvested. Everybody believes that the next year's wheat crop, which has already been planted, will also be 100 tons. A speculator alone thinks differently. He believes the next year's crop will be only 80 tons. Assume that interest rate is 0% and wheat can be storeed costlessly. What will the speculator do? And what will happen to this year's wheat supply as a result? 4. A competitive firm has the following production function: 1/3 Y = ( KL ) In short-run, K is a fixed factor and K = 27; while L is a varible factor. The unit price of L is $1 and the unit price of output Y is $4. (a) (2 points) What is the marginal revenue product of L? (b) (2 points) How many units of L will this firm purchase in the short run? (c) (2 points) Are K and L complements or substitutes in production? 5. Consider the capital asset pricing model. There are only two stocks in the market: a and b. On the other hand, an investor could borrow/lend at a risk -free rate rf. The risk-free loan will be enforced to be paid back. The rates of return of two stocks depend on which event Ei occurs. The probability of each event and the stocks' rates of returns, ra and rb, in each event is as follows. ─────────────────── probability ra (%) rb (%) ─────────────────── E1 1/8 3 3 E2 3/4 5 7 E3 1/8 7 11 ─────────────────── (a) (2 points) Please calculate the expected value and standard deviation of ra. (b) (2 points) Please prove that the correlation coefficient of ra and rb is 1. (c) (3 points) If an investor spends $50 purchasing stock a, and another $50 purchasing stock b, what is his expected rate of return of this investment? What is the standard deviation of the rate of return? (d) (2 points) Please calculate rf. Exam201106.ctx --

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