課程名稱︰個體經濟學
課程性質︰必修
課程教師︰江淳芳
開課學院：社會科學院
開課系所︰經濟系
考試日期（年月日）︰2013/04/18
考試時限（分鐘）：9:20-12:00
試題 :
Microeconomics 2013 Spring Midterm Exam
1. (20%) Suppose that in a monopoly market, the demand curve in market
segment 1 is Q_1 = 200 - 2P_1 and the demand curve in market segment 2 is
Q_2 = 250 - P_2. The marginal cost of selling in each market segment is $10 per
unit. The monopoly firm can engage in third-degree price discrimination.
(a) What are the profit-maximizing quantities and prices in each market
segment?
(b) In many setting in which firms engage in third-degree price discrimination,
firms face constraints on how many customers can be served in a given period.
Examples would include airlines, rental car companies, and hotels. Suppose that
the firm's overall capacity is 150 units. What are the profit-maximizing
quantities and prices in each market segment?
2. (25%) An industry consists of two Cournot firms selling a homogeneous
product with a market demand curve given by P = 100 - Q_1 - Q_2. Each firm has
a marginal cost of $10 per unit.
(a) Find the Cournot equilibrium quantities and price.
(b) Find the quantities and price that would prevail if the firms acted "as if"
they were a monopolist (i.e., find the collusive outcome).
(c) Suppose firms 1 and 2 sign the following contract. Firm 1 agrees to pay
Firm 2 an amount equal to T dollars for every unit of output it (Firm 1)
produces. Symmetrically, Firm 2 agree to pay Firm 1 an amount, Tdollars, for
every unit of output it (Firm 2) produces. The payments are justified to the
government as a cross-licensing agreement whereby Firm 1 pays a royalty for the
use for the use of a patent developed by Firm 2, and similarly, Firm 2 pays a
royalty for the use of a patent developed by Firm 1. What value of T results in
the firms achieving the collusive outcome as a Cournot equilibrium?
(d) Draw a picture involving reaction functions that shows what is going on in
this situation.
3. (15%) Consider a market in which the market demand curve is given by
P = 18 - X - Y, where X is Firm 1's output, and Y is Firm 2's output. Firm 1
has a marginal cost of 3 while Firm 2 has a marginal cost of 6.
(a) Find the Stackelberg equilibrium in which Firm 1 acts as the leader. How
much profit does each firm make?
(b) Suppose now that the marginal cost of Firm 1 goes down, but the marginal
cost of Firm 2 stays the same. Will Firm 1 increase its quantity? Will Firm 2
increase its quantity?
4. (20%) In a World Series Game, Tim is pitching and Joe is batting. The count
on Joe is 3 balls and 2 strikes. Tim has to decide whether to throws a fastball
or a curveball, Joe has to decide whether to swing or not swing. If Tim throws
a fastball Joe doesn't swing, the pitch will almost certainly be strike, and
Joe will be out. If Joe does swing, however, there is a strong likelihood that
he will get a hit. If Tim throws a curve and Joe swings, there is a strong
likelihood that Joe will strike out. But if Tim throws a curve and Joe doesn't
swing, there is a good chance that it will be a ball four and Joe will walk
(assume that a walk is as good as a hit in this instance).
The following table shows the payoffs from each pair of choices that the two
players can make:
Joe
Swing Do not swing
┌────────┬────────┐
Fastball │ -100, 100 │ 100, -100 │
Tim ├────────┼────────┤
Curveball │ 100, -100 │ -100, 100 │
└────────┴────────┘
(a) Is there a Nash equilibrium in pure straegies in this game?
(b) Is there a mixed strategy Nash equilibrium in this game? If so, what if it?
5. (20%) Consider a buyer who, in the upcoming month, will make a decision
about whether to purchase a good from a monopoly seller. The seller
"advertises" that it offers a high-quality product (and the price that is has
set is based on that claim). However, by substituting low-quality components
for higher-quality ones, the seller can reduce the quality of the product it
sells to the buyer, and in so doing, the seller can lower the variable and
fixed costs of making the product. The product quality is not observable to the
buyer at the time of purchase, and so the buyer cannot tell, at that point,
whether he is getting a high-quality or a low-quality good. Only after he
begins to use the product does the buyer learn the quality of the good he has
purchased.
The payoffs that accure to the buyer and seller from this encounter are as
follows:
┌─────────────────────┐
│ Seller │
├─────────────────────┤
│ Sell High-Quality Sell Low-Quality │
│ │
│ product product │
┌──────┬────────┼──────────┬──────────┤
│ │Purchase │ $5, $6 │ -$4, $12 │
│ buyer │ ├──────────┼──────────┤
│ │Do Not Purchase │ $0, -$4 │ $0, -$1 │
└──────┴────────┴──────────┴──────────┘
(a) Suppose that the game is played just once. What are the Nash Equilibrium
strategies for the buyer and seller in this game?
(b) Let's again suppose that the game is played just once. But suppose that
before the game is played, the seller can commit to offering a warranty that
gives the buyer a monetary payment W in the event that he buys the product and
is unhappy with the product he purchases. What is the smallest value of W such
that the seller chooses to offer a high-quality product and the buyer choose to
pruchases?