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&T wireless (the wireless provider previously known as Cingular, that was
previously known as AT&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&T for cell phone minutes is 3; the marginal
cost to AT&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&T charge for cell phone minutes if it can only set a
uniform price (and it does not bundle)?
P = 20, Q = 1 and profits = 17 (P – MC)Q  (20 – 3)1
P = 18, Q = 2 and profits = 30
P = 11, Q = 3 and profits = 24
P = 10, Q = 5 and profits = 35
Optimal price is P =10
b) (10 points) What price will AT&T charge for text messages if it can only set a uniform
price (and it does not bundle)?
P = 15, Q = 1 and profits = 13 (P – MC)Q  (15 – 2)1
P = 10, Q = 3 and profits = 24
P = 9, Q = 4 and profits = 28
P = 2, Q = 5, and profits = 0
Optimal price is P = 9
Combined profits with uniform prices are 63 (35 + 28) (or if Pmin = 18  58 (30 + 28).
c) (10 points) What price will AT&T charge for a pure bundle (cell phone minutes and text
messaging)?
Possible bundle prices are Pbundle = 25, Pbundle = 20, and Pbundle = 15
Pbundle = 25, Qbundle = 1, profits = 20  (P – MCtext – MCphone)Q
Pbundle = 20, Qbundle = 5, profits = 75
Pbundle = 15, Qbundle = 6, profits = 60
Optimal Pbundle = 20, profits = 75
d) (10 points) What price will AT&T charge for a mixed bundle (cell phone alone, text
messaging alone, and bundling cell phone minutes and text messaging)?
Key idea is to get those with WTP < MC to not buy the buy. Also – want to find a way to
get Bill to buy at least texting.
One option:
Ptelephone = 19.99, Tom only buys minutes. Q = 1, so profits(telephone) = (19.99 – 3)1 =
16.99
Ptext = 10 (Bill buys) Q = 1 so profits(text) = (10 – 2) = 8
Pbundle = 20, Q bundle = 4  profits(bundle) = 60
Combined profits are 84.99 (60 + 8 + 16.99)
Another option:
Ptelephone = 5, Tom and Bill only buy minutes. Q = 2, so profits(telephone) = (5 – 3)2 =
4
Ptext = 10 (Bill buys) Q = 1 so profits(text) = (10 – 2) = 8
Pbundle = 20, Q bundle = 4  profits(bundle) = 60
Combined profits are 72 (60 + 8 + 4)
Go with option One
NOTE: you have to make sure no one gets consumer surplus and switches to buying the
product and not the bundle. If Ptelephone = 19.99 everyone else but Tom has WTP less
than 19.99 so they would buy the bundle. If Ptext = 10, Bill will buy text and not be out
of the market, Mary is indifferent (she has CS = 0 regardless of buying the bundle or
not); likewise Bob is indifferent (he has CS = 5 regardless of buying the bundle or not)
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.
Efficiency requires Q increases. With no bundling, Q = 5 for phone, Q = 4 for text. With
pure bundling Q = 5 for both phone and text, so this increases efficiency. With mixed
bundle, Q = 5 for both phone and text so improvement from pure bundling occurs with
leaving out the person who values less than it costs to produce.
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
Nash equilibria: (Mike Schwobs, Pizza) and (Pizza, Mike Schwobs)
3. (10 points) In your own words, what makes a static game a “prisoner dilemma” game?
Dominant strategy leads to pareto inferior outcome.
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.
MC = 60
TR1 = (300 – 10(q1 + q2))q1
MR1 = dTR1/dq1 = 300 –20q1 –10q2
Profit max  MC = MR  60 = 300 –20q1 –10q2
Finding firm 1’s best response function (solving for q1):
q1 = 240 – 10q2
20
Since this is symmetric: we can easily find firm 2’s best response function
q2 = 240 – 10q1
20
b) (10 points) Graph the best response functions – indicating the axis (so you need qmonopoly
and qperfect competition)
q2
240/10 =24
q1 = R1(q2) =240 – 10q2
20
240/(2*10)=12=q2m
240/(3*10)=8=q2c
q2 = R2(q1)= 240 – 10q1
20
8=q1c q1m=12
24
q1
c) (10 points) Find the profit maximizing (Cournot-Nash equilibrium) quantities for each
firm.
To find the Cournot-Nash equilibrium – we simultaneously solve the two equations
q2 = 12 
1
q1
2
(plugging in q1 = 12 
q2 = 12 
1
q2
2
1
1
1
* (12  q 2 ) = 6  q 2  q2 = 8
2
2
4