# Homework 3

```NAME_______________________________________________________________
FE461 Practice Problem
Third Problem Set
Due March 6th
1. (50 points) Most wireless packages include cell phone minutes and text messages.
Suppose AT&amp;T wireless (the wireless provider previously known as Cingular, that was
previously known as AT&amp;T) has determined that six people purchase cell phone minutes
and text messages (you can interpret them as six equally represented types). The
following table represents the willingess to pay for cell phone minutes and the
willingness to pay for text messages for the six different people (Bob, Bill, Tom, Sue,
Julie, and Mary). The marginal cost to AT&amp;T for cell phone minutes is 3; the marginal
cost to AT&amp;T for a text message is 2.
Person
Willingness to pay
Willingness to
Combined WTP
for telephone
pay for a text
minutes
message
Bob
10
15
25
Bill
5
10
15
Tom
20
0
20
Sue
18
2
20
Julie
11
9
20
Mary
10
10
20
a) (10 points) What price will AT&amp;T charge for cell phone minutes if it can only set a
uniform price (and it does not bundle)?
b) (10 points) What price will AT&amp;T charge for text messages if it can only set a uniform
price (and it does not bundle)?
c) (10 points) What price will AT&amp;T charge for a pure bundle (cell phone minutes and text
messaging)?
d) (10 points) What price will AT&amp;T charge for a mixed bundle (cell phone alone, text
messaging alone, and bundling cell phone minutes and text messaging)?
e) (10 points) Which is more efficient, no bundling (parts a and b), the pure bundle (part c),
or the mixed bundle (part d)? Explain.
Steerage
2. (15 points) The following game has two players, Steerage and Drydock. On a Tuesday
night, King Hall is serving meatloaf. Most Mids don’t like meatloaf, so no one is
planning to eat in King Hall. Steerage and Drydock realize the consequences of bad
King Hall food, and each plan to start cooking food early in order to manage the huge,
disgusted crowd. Assume Steerage and Drydock will each only prepare one menu item
in advance, and will offer a special deal to get Mids to choose that item over the rest of
the menu. They can choose one of the three most popular menu items: Pizza, Mike
Schwobs, or Wraps. The payoffs are listed below. Identify all Nash pure strategy
Equilbria.
Drydock
Pizza
Mike Schwobs
Wraps
Pizza
7500, 7500
11000, 10000
10000, 7000
Mike Schwobs
13000, 9500
10500, 6500
14000, 5500
Wraps
2500, 9250
6250, 9000
6500, 6500
3. (10 points) In your own words, what makes a static game a “prisoner dilemma” game?
4. (25 points) Two firms face a market demand of P = 300 – 10Q. Firms face identical
marginal costs equal to 60.
a) (5 points) Find each firm’s best response function – be sure to solve for these through
profit maximization.
b) (10 points) Graph the best response functions – indicating the axis (so you need qmonopoly
and qperfect competition).
c) (10 points) Find the profit maximizing (Cournot-Nash equilibrium) quantities for each
firm.
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