推 TINTINH :已收精華區:) 05/31 19:09
課程名稱︰個體經濟學二
課程性質︰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）︰99.05.31
考試時限（分鐘）：13:20-14:20(後延至14:35) (60+15min)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
15 points in total. You have to state your reasoning clearly. No points will
be given to an unexplained answer.
1. A and B are roommates. A loves music and his utility function is:
UA = mbA ,
where m is the number of different music disks he could play in the room
(via a loud speaker), and bA is the amount of bread that he could consume.
B hates music and his utility function is:
UB = bB-m ,
where bB is the amount of bread that B consumes. A and B have $12 each to
purchase music disks and bread. The price of a music disk is $2 and the
price of a loaf of bread is $1.
(a) Suppose A has the right to play as many disks as he likes in the room.
i. (1 pts) How many disks will A purchase if he and B can make no
negotiation?
ii. (2 pts) Now consider that A and B could negotiate. For instance, B
could give A some money and ask A to return some disk to the shop
for a full refund. In this case, how many disks will A decide to
keep?
(b) (2 pts) What happen if A has no right to bombard B with music? B's
utility level is 12 if he completely bans A playing music. Suppose A
and B could negotiate and for every new disk A plays, A has to
compensate B so that after receiving A's payment, B's utility level
remains 12. (B's utility function is publicly known.) In this case, how
many disks will A purchase and play?
2. Reconsider the previous problem: everything stays the same expect that B
loves music, and B's utility function is:
UB = bB+m
In this case, music disks become public goods in the room.
(a) (1 pts) Suppose A and B consider how many disks to purchase
independently without discussion. In a Nash equilibrium, how many disks
will A purchase?
(b) (2 pts) Now suppose they could discuss how many disks to purchase, and
the result of their discussion is Pareto effecient. Let m* denote the
total number of disks they will purchase, and bA* the amount of bread
that A will consume. Please compare m* and bA*.
3. (3 pts) A monopolist has the following production function:
_
y = √x
The market demend for his product is:
y = 100 - py
He is a price taker in the factor market of x. What is his demend for x?
(The answer should be a function of the price of x, px.)
4. A fair coin will be flipped: half of the time its head will turn up and
half of the time its tail will turn up. A has a chance to gamble on the
head. If A bets $m, when the head comes up, A will get his $m back and in
addition to that A will receive $1.1m. On the other hand, when the tail
comes up, A loses $m. A has $100 in the pocket now. Put A's wealth in the
state that a head (tail) turns up on the horizontal (vertical) axis.
(a) (1 pts) What is the slope of A's budget line?
(b) (1 pts) If A is risk neutral, will A he bet any money?
(c) (2 pts) If A is risk averse, will A he bet any money?
(編註:暗字為下標)
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