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課程名稱︰個體經濟學下
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）︰2011.4.18
考試時限（分鐘）：100
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Suppose the market is contestable. Each producer has the same total cost
function: TCi(qi)=100+qi^2. The market demand is: q=100-p
(a) (2 points)What is the equilibrium price?
(b) (2 points)How many producers will remain in the market in the long run?
2. Consider a merchant who sells high quality E-book readers and monopolizes
the market of E-books. The marginal cost to produce an E-book reader is
$2000 and the marginal cost to allow a customer to download an E-book is
zero. There are 100 customers who have the same income($50000 per person)
and the same utility function: (200-x)x
u(x,y)=------------ +y
2
where x(a continuous variable) is the number of E-books that a customer
reads and y is the money he could spend on food. The merchant wishes to
maximize profit.
(a) (2 points) How much will the merchant charge a customer to download one
E-book?
(b) (2 points) How many E-books will a customer purchase?
(c) (2 points) How much will the merchant charge for an E-book reader?
3. The products made by A and B are similar, but not quite the same. A and B
consider how to set the price for his own product. The sales will depend on
their prices:
QA=100-2PA+PB
QB=100-2PB+PA
where Pi is the price of i's product and Qi is i's sales quantity, i=A, B.
The productioncost is zero and each person wishes to maximize his own
profit.
(a) (2 points) Given PB, what is the optimal price PA?( The answer is a
function of PB.)
(b) (2 points) If A and B determine the price simultaneously, what is the
Nash equilibrium?
(c) (3 points) If B sets the price first and A shall decide on PA after
observing PB, what is the optimal PB?
4. N art lovers attend an (English) auction to purchase a painting. Let vi
denotes i's personal value of this painting, and vi is only known to i and
no one else. The auctioneer will raise the price continuously. If a bidder
loses interest in the auction when the price is too high for him, he will
leave. Let p denote the price that triggers the N-1th person to leave. The
painting will then be sold to the only remaining bidder at price p.
(a) (2 points) What is the optimal timing for a bidder to drop out?
(b) (2 points) Is the result of this auction efficient?
5. A monopoly has two types of customers whose individual inverse demand is as
follows:
│ A B
-------------
1 │10 12
2 │ 8 7
3 │ 6 2
There are 100 type A customers and 100 type B customers. There is no
production cost so the monopoly considers to maximize the total revenue.
(a) (3 points) If the monopoly sets a single price for all units, what is
the optimal price?
(b) (3 points) Now suppose the monopoly coulde offer quantity discounts and
practice the second-degree price discrimination. Let pi denote the
total price for a customer who purchase i units, i=1,2,3. (So if a
customer purchase 3 units, he pays p3 and the implied unit price is
p3/3.) Is it optimal if each customer is induced to purchase 2 units?
Why?
6. A and B, two enemies, will have a duel. Each person holds a gun with only
one bullet. When the duel starts, the distance between them is D and as
time passes by, they will start to walk towards each other. Hence the
distance between them decreases with time. The probability to kill the
enemt with the only bullet is Pi(d), i=A,B, where d is the remaining
distance. Pi'<0, and Pi(0)=1. Each persons strongly prefers himself to
survive and wishes for the other party;s death.
(a) (1 point) If A fires and A misses B, when should B fire?
(b) (4 points) Each person has to decide when to fire. Let di denote the
remaining distance at which player i will fire if his opponent has not
fired yet, i=A,B. Please prove that in a Nash equilibrium, dA=dB.
Exam201104.ctx
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