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： 社科院
開課系所︰ 經濟系
考試日期（年月日）︰ 2017/04/24
考試時限（分鐘）： 100 min
試題 :
總分31分。答題皆須附說明，未作解釋的答案概不計分。
1. (3 points) In the following game, the first element of the payoff vector
denotes the row player's payoff, and the second element of the payoff
vector denotes the column player's payoff. Please find all the Nash
equilibria.
│ t1 t2 t3
─────────────
s1 │1, 3 100,2 0, 2
s2 │0. 2 200,1 1, 3
2. A monopolist produces and distributes his products in market A and
market B in which it is possible to set different prices. The market
demand for these two markets are:
Q_A = 20 - 2P_A
Q_B = 40 - 8P_B
where Q_i and P_i denote quantity and price in market i, i = A, B.
(a) (1 point) If the monopolist only sells in market A, please derive
the marginal revenur function MR_A(Q_A)
(b) (2 points) Actually when Q units are produced, they will be
distributed to two markets to maximum total revenue. Please
derive the marginal revenue function MR(Q), and caculate
MR(4) and MR(10).
(c) (4 points) The total cost function is: TC(Q) = Q^2/10. Please
solve for the optimal prices in two markets, P_A and P_B.
3. A monopolist has two retailers to sell his products. The market
demand is:
q = 120 - p
where q is the quantity and p is the price. Given the whole price θ set
by the monopolist, a retailer could obtain at θ any unit she wishes.
The two retailers will engaged in a Cournot competition.
(a) (2 points) If θ = 30, what will be the equilibrium retail price
p?
(b) (2 points) There is no production cost for this monopolist.
Please determin the optimal whole price for him.
4. In a village, there is only one amusement park which is the position
to set the price. It is costless to run the rollercoaster, so the park
owner simply wishes to maximize revenue. Every customer has the
same demand:
q = 50 - p
where p is the ticket price of a ride.
(a) (2 points) If the park owner considers only sll ride tickets,
please decide the optimal price for him.
(b) (2 points) If the park owner turns to consider to set a two-part
tariff: an admission fee to the park and a ticket price per ride,
what is the optimal two-part tariff?
(c) New people move into this village, their individual demand,
different from an old resident's, is:
q = 75 - 1.5p
The number of these new resident is the same as the number
of old residents. The park owner reconsiders the situstion and
designs a two part tariff to attract both types of customers.
i. (1 point) Under the optimal two-part tariff, what is the
consumer's surplus of an old resident?
ii. (2 points) What is the ticket price per ride under the opti-
mal two-part tariff?
iii. (1 point) Under the scheme of a two-part tariff, is it better
to attract both types of customers or to attract only one
type of customers?
5. A competitive firm facing a price of $20 per unit for his product
pollutes the air when producing for the market. His own marginal
production cost is:
MC(q) = q
where q denotes his production units. At the mean time, the pollu-
tion harms his neighbors's health and consequently increases neigh-
bors's medical expenses. The more he produces, the larger their
medical bills become and the marginal medical expenses are:
ME(q) = q.
(a) (2 points) Supposr there are no transaction costs, that ther 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 struct between
the firm and the neighbors.
(b) Suppose transaction cost are so high that negotiation is impos-
sible, and that it would cost the neighbors $90 to move. Under
each of the following scenarios, determine whether or not the
neighbors move, and determine how much the firm produces.
i. (1 point) Ther firm faces no penalty for pollution.
ii. (2 points) The firm must reimburse the neighbors for all
pollution damage.
iii. (2 points) Reconsider scenarios i and ii. Which one is more
efficient?
6. There are several piles of matchsticks. Two players alternate in
moving. When it is your turn to move, toy must select one of the
piles and remove at least one matchstick from that pile. The last
player to take a matchstick is the winner.
In the following games, you move first, and try to make sure you
will win.
(a) (1 point) If there are 2 piles. The 1st pile has 1 matchstick and
2nd pile has 2 matchsticks. What is your first move?
(b) (2 points) If there are 3 piles. The 1st pile has 1 matchstick, the
2nd pile has 2 matchsticks, and 3rd pile has 4 matchsticks.
What is your first move?