1: Table Separating the Market
McGraw Hall
Microeconomics Macroeconomics
Microeconomics
5,5
10,10
Prentice Hill
Macroeconomics
10,10
5,5
Table 2: Pursuing Macro Market
McGraw Hall
Microeconomics Macroeconomics
Microeconomics
10,10
5,15
Prentice Hill
Macroeconomics
15,5
8,8
Homework #5
Due Date: Friday, April 29th
Note: Only one randomly selected question will be graded.
Question 1
There are two textbook publishers, Prentice Hill and McGraw Hall. They can make
only one kind of textbook among Microeconomics or Macroeconomics. They should
make a decision without knowing the opponents decision. Consider the Table 1.
The rst gure is a payo for Prentice Hill and the second gure is for McGraw Hall
in each cell.
(a) List the strategies of Prentice Hill.
(b) What is the best response of McGraw Hall when Prentice Hill chooses Microeconomics?
(c) Find all possible Nash equilibrium. A Nash equilibrium is written like (Prentice
Hills strategy, McGraw Halls strategy).
Now, Macroeconomics becomes very popular, but it needs a pre-requisite Microeconomics class. That is, if a publisher makes Microeconomics textbook, then
Macroeconomics textbook becomes very popular. Although students can take Macroeconomics without taking Microeconomics, the popularity is not high enough without
Microeconomics class. The Table 2 shows payos for both publishers.
(d) What is the best response of McGraw Hall when Prentice Hill chooses Microeconomics?
(e) Find all possible Nash equilibrium. Can we reach to (10,10) payo combination
1
Table 3: Repeated Game
McGraw Hall
Microeconomics Macroeconomics
Microeconomics
10,10
8,8
Prentice Hill
Macroeconomics
8,8
8,8
at the equilibria?
(f) Does Prentice Hill have a dominant strategy? If yes, what is a dominant strategy
for Prentice Hill? Does McGraw Hall have a dominant strategy? If yes, what is a
dominant strategy for McGraw Hall?
Now, the publishers take this game every year. That is, they have a repeated
game. Consider the Table 3.
(g) What is the best response of McGraw Hall when Prentice Hill chooses Microeconomics?
(h) Find all possible Nash equilibrium. Can we reach to (10,10) payo combination
at the equilibria?
(i) Does Prentice Hill have a dominant strategy? yes, If what is a dominant strategy
for Prentice Hill? Does McGraw Hall have a dominant strategy? If yes, what is a
dominant strategy for McGraw Hall?
Question 2
Apple decides the price of iPhone. Apples possible choice is a high price or a low
price. If Apple makes a high price, then Apple can get a high prot, but it may
attract Samsungs entry in the smart phone market. If Apple makes a low price,
it can deter Samsungs entry, although it gives a low prot to Apple. Consider the
Figure 1. Each branch represents each players actions. And upper number of payo
implies Apples prot and lower number of payo implies Samsungs prot.
(a) List the actions and strategies of Samsung.
(b) What is the best response of Samsung when Apple takes $400?
(c) Find all possible (subgame perfect) Nash equilibrium. A Nash equilibrium is
written like (Apples strategy, Samsungs strategy).
(d) Samsung announced that they will enter the market, regardless of Apples pricing policy. An economist argued that this is a just empty threat. Explain why the
2
Figure 1: Entry Deterrence Game
APPLE
$600
$400
SAMSUNG
Enter
20M
20M
SAMSUNG
Not
40M
0M
Enter
Not
10M
-10M
30M
0M
economist can argue like that.
Question 3
Jacob dug wells and began to sell water. In the neighborhood, Jacob was the only
seller. Jacobs marginal cost function is M C = 5 + 0.01Q. The inverse demand
function of the neighborhood is P = 10 0.02Q. Then, the total revenue of Jacob
is T R = P Q = (10 0.02Q)Q = 10Q 0.02Q2 . The marginal revenue curve is
M R = T R (Q) = 10 0.04Q.
(a) Draw the demand curve, the marginal cost curve, and the marginal revenue
curve in (Q, P ) plane.
(b) Calculate the prot maximizing Q, denoting Q .
(c) At Q , calculate the equilibrium price, denoting P .
(d) What is the consumer surplus and producer surplus?
(e) Assume that this market is perfectly competitive and the total supply function is
same with Jacobs marginal cost function. Then, what is the equilibrium quantity,
denoting QP and the equilibrium price, denoting P P ?
(f) Calculate the consumer and producer surplus at the perfectly competitive market.
3
(g) Calculate the deadweight loss induced by the monopolist, Jacob.
4