[試題] 99下 古慧雯 個體經濟學二 期末考
課程名稱︰個體經濟學二
課程性質︰經濟系必修
課程教師︰古慧雯
開課學院：社會科學院
開課系所︰經濟系
考試日期（年月日）︰100年6月20日
考試時限（分鐘）：100分鐘
是否需發放獎勵金：是~
（如未明確表示，則不予發放）
試題 :
總分39分。答題皆須附說明，未做解釋的答案概不計分。
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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