[試題] 98上 陳添枝 個體經濟學一 期中考
課程名稱︰個體經濟學一
課程性質︰必修
課程教師︰陳添枝
開課學院：社會科學院
開課系所︰經濟系
考試日期（年月日）︰2009/11/05
考試時限（分鐘）：180 分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Answer all questions:
1. (20 points)
Suppose that there are 10 sudents who want to rent an apartment. Their
reservation prices are given below:
A B C D E F G H I J
100 90 85 80 77 65 55 45 40 30
(a) Suppose that there are 8 apartments available on the market and the market
is perfectly competitive, what is the equilibium price? (If there is more
than one possible price, give the maximum price). Who get the apartments?
(b) Suppose that all these apartments are owned by a single landlord, and
there is no extra cost in maintaining the apartment when it is rented out.
If the monopoly landlord can only charge one price, what price will he
charge and who will rent the apartment from him?
(c) If the same monopoly can charge different prices to different students
(perfect price discrimination), how many apartments will he rent out? What
will be his total revenue in this case?
(d) If the government imposes a price ceiling of 30 apartment rent, and
apartments are rented out by drawing. Suppose all students get the draws,
except students B and C. Now student B offers to sublet the apartment from
student J, what price is likely to be the sublet contract price?
(e) Let us go back to case (a) where the market is perfectly competitive and
there is no government intervention. Now suppose that we have towo new
students on the market, and their reservation prices are 100 and 90
respectively. What will happen to the equilibrium price? Who get the
apartments in this case?
2. (10 points)
Mr. Chang has 1200NT to spend each week and he plans to spend his entire
budget on two goods: hamburger and pizza. The price of hamburger is 60 NT, and
price of pizza is 100NT.
(a) Please draw a budget line to show his possible choice.
(b) In addition to the monetary constraint, he also faces a calorie constraint.
His doctor told him that he can take no more than 15,000 cal a week, and he
takes the doctor's words seriously. Each hamburger generates 1,000 cal and
each pizza generates 750 cal. Please show his possible choices of hamburger
and pizza if both monetary and calorie contraints are to be satisfied.
3. (10 points)
The government is debating about two alternative policies to help the
poor. One is to offer 3000 NT income subsidy to the poor. The other is to
provide a 50% subsidy (that is, the poor only pays half of the market price)
to his food consumption up to a maximum of 3000 NT. Without knowing the
preference of the poor, can you tell the government which policy is better?
4. (12 points)
Mr. Chang is preparing for the entrance exam of the graduate school. Two
subjects will be tested: economics and calculus. The rule of admission is that
the lower score of the two tests will be counted; the higher score will be
ignored. Mr. Chang has 21 hours remaining before the exam. For every 0.1 hour
he spends on economics, he will gain 1 point; for every 0.2 hour he spends on
calculus, he will gain 1 point. This productivity stay contant, i.e., if he
studies economics for 10 hours, he will score 100 points on this subject.
(a) Use indifference curves to portray his possible exam outcomes. Put his
score on economics on the horizontal axis and his score on calculus on the
vertical axis. Draw the possible combinations that give rise to an exam
outcome of 50 points (The school only counts the lower score of the two).
This will be the indifference curve for 50 points. Draw another curve for
60 points.
(b) Draw his time contraint (bidget line).
(c) Use the indifference curves and the time constraint to find out his
optimal choice (the allocation of time between economics and calculus, and
the scores of two subjects).
5. (8 points)
Mr. Chang hates study. The more he studies, the more he feels unhappy. Let
us draw an indifference curve to show his unhappiness. Assume he has to study
economics and history. If he studies economics for 1 hour (no history), his
unhappiness is the same as he studies history for 2 hours (no economics). But
he will be less unhappy if he studies economics for 0.5 hour and history for 1
hour at the same time. Please draw an indifference curve for the level of
unhappiness that pass through the point where he studies economics for 1 hour
without touching the history book. Draw another to show a higher level of
unhappiness.
6. (10 points)
Miss Chang has a typical utility function shich is convex. She has two
goods to consume, apple and orange. She went to the market and purchased 10
apples and 20 oranges for himself. The price of apple is 20 NT each, and the
price of orange is 5 NT each. At this point, her marginal rate of substution
(MRS) is 3 according to her utility function. That is, she is willing to
exchange three oranges for one apple. Draw an indifference curve and a budget
line to show this situation. Is she now in equilibrium? If not, what can she
do to make herself happier if the budget is unchanged?
7. (10 points)
Miss Chang views orange juice and grapefruit juice as perfect substitutes,
with her utility function shown below:
U(x1,x2)＝3x1+4x2,
where x1 stands for orange juice and x2 stands for grapefruit juice. Miss
Chang has 2400 NT to spend on these two juices. If the price for grapefruit
juice is 20 NT, can you write the demand equation for orange juice? (Hint:
Write quantity demanded for orange juice x1 as a function of the price of
orange juice p1). Is the demand curve downward sloping?
8. (10 points)
Mr. Gates' utility function is as follows:
U(x1,x2)＝3x1x2
He has 1500 NT to spend, and the price of x1 is 30 NT, the price of x2 is 50
NT. What bundle of x1 and x2 will he purchase? If the price of x1 increases
to 50 NT, and the price of x2 stays unchanged, what will be his consumption
bundle? How will the above answers change if the utility function is
U(x1,x2)＝3(x1^2)(x2^2)
instead?
9. (10 points)
The telephone company has two pricing plans for consumers to choose. Plan
A charges a monthly fee of 600 NT and allows consumers to make unlimited calls
(all-you-can-eat package). Plan B charges a monthly fee of 300 NT, and
consumers pay additional 2 NT for every minute of calls. Suppose a consumer
has a monthly budget of 1000 NT, and he spends all money on telephone calls
(x1) and other goods (x2). The price of other goods is 1 (numeraire). Draw the
budget lines for Plan A and B. Show the case where the consumer chooses Plan A
over B.
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