Econ 444: Problem Set #3
October 16, 2014
Due Date: Thursday October 23, by 5 PM. You can hand it in in class or to
my office.
Try your best at each problem. Problems sets will be weighted towards effort
and correct strategy, rather than the exact right answer.
Write clearly.
Show all your work and label graphs!
If you choose to work in groups, each student must hand in their own problem
When I say “briefly”, I mean one or two sentences. I don’t expect (or want) an
1 Vertical Differentiation
Consider again Comcast, the monopoly broadband internet provider in state
college. Comcast is deciding how many different download speeds to offer to
consumers. The highest they can offer is 70Mbps and the lowest they can
offer is 10Mbps. Assume the marginal cost of supplying broadband to a new
consumer is 0 no matter the download speed. This could be due to the fact
that the infrastructure is already in place and it only takes the flip of a switch
to provide access. Comcast knows they face two types of consumers, one who
values download speeds highly:
VH = 3(z ? 30) ? p
and those who do not:
VL = 2(z ? 20) ? p
where z is the download speed and p is the price per month. Comcast knows
there are NH high types and NL low types. The high types will not tolerate
download speeds less than 20Mbps and value each addition Mbps by $3. The
low types will tolerate the lowest download speed and value each additional
1Mbps by $2. Comcast would like to know if it is more profitable to offer two
types of service or only one.
(a) Write down and briefly explain the constraints that must be satisfied for
Comcast to be able to sell two different speeds (zL, zH) at two different prices
(pL, pH). Hint: there should be three.
(b) What is the price should Comcast charge for the slow speed (pL) as a
function of the slow speed, (zL)?
(c) What is the price Comcast should charge fast speed (pH) as a function
of the slow speed (zL) and the high speed (zH)? Briefly explain why it is a
function of both speeds.
(d) What is the profit as a function of zH, zL, NL and NH?
(e) Given your profit function, what is the optimal level of zH? Why?
(f) Assume NH = 1, 000 and NL = 500, is it profitable for Comcast to sell
two different speeds? Why or why not?
(g) Solve for zL, pL, and pH.
2 Bundling
Direct TV has four types of channels that they can offer: movie channels, sports
channels, news channels and variety channels. Assume that the cost of providing
service for the different types of channels is equal to $20. There are 3 types of
consumers which Direct TV faces with the following preferences for the different
types of channels:
Movies Sports News Variety
Jocks 30 70 8 20
Nerds 35 5 60 25
Others 25 30 25 40
Assume that there are 10 of each type.
(a) What is the optimal price for each type of channel if Direct TV does not
bundle? How much profit do they earn in total?
(b) What is the optimal pure bundling price?How much profit do they earn
in total?
(c) What is the optimal mixed bundling strategy? How much profit do they
earn in total? Note that since there are 4 types of channels, they could offer
different bundles of 1, 2 or 3 types in a mixed bundling strategy. (hint: the
optimal policy involves bundling of 3 types and bundling 4 types of channels.)
3 Tying
Suppose Mastercard sells both their Credit Card and Debit card service to
retailers. The marginal cost of providing credit card service to a retailer is
$200. The marginal cost of one debit card transaction is $2. Mastercard has
2a monopoly in the credit card market but not in the debit card market (most
banks offer debit cards). Additionally, there are two typos of retailers, large (aka
Wal-Mart) and small mom and pop stores. Each type decides whether or not
to buy credit card service and then decides how many debit card transactions
to buy. Assume there is only 1 of each type.
The demand for debit card transactions for Wal-Mart is:
Pw = 50 ? Qw
and mom and pop stores is:
Pm = 40 ? Qm
(a) If Mastercard does not use a tying strategy, how much would they charge
for each debit card transaction? How much would they charge for the credit
card service? How much profit would they make?
(b) Suppose Mastercard uses a tiring strategy by telling the retailer they can
only have use the credit card if they also use the debit card service. Assume
they charge $5 for debit card transactions. How much would they charge for
credit card servicer? How much profit would they make?
4 Cournot Competition
Nucky Thompson and Gyp Rosetti are the only two bootleggers in Atlantic City.
Assume they compete in quantities. Producing a case of bootlegged whiskey is
$20 for both firms. Demand for bootlegged whiskey in Atlantic City is given by:
P(Q) = 200 ? Q
(a) Write down the profit functions for each firm.
(b) Find the best response functions for each firm.
(c) Find the equilibrium quantities ordered for each store, total quantity,
price and profits for each firm.
(d) How much deadweight loss is there?
(e) How much money would Nucky be willing to pay to someone to ‘off’