03 Jun Question Question If you choose to work in groups, each student must hand in their own problem set. When I say “brie?y”, I mean one or two sentences. I don’t expect (or want) an es
Question
Question
If you choose to work in groups, each student must hand in their own problem set.
When I say “brie?y”, I mean one or two sentences. I don’t expect (or want) an essay.
Vertical Di?erentiation
Consider again Comcast, the monopoly broadband internet provider in state college. Comcast is deciding how many di?erent download speeds to o?er to consumers. The highest they can o?er is 70Mbps and the lowest they can o?er 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 ?ip 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 Mbps by $2. Comcast would like to know if it is more pro?table to o?er two types of service or only one.
(a) Write down and brie?y explain the constraints that must be satis?ed for Comcast to be able to sell two di?erent speeds (zL , zH ) at two di?erent 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 )? Brie?y explain why it is a function of both speeds.
(d) What is the pro?t as a function of zH , zL , NL and NH ?
(e) Given your pro?t function, what is the optimal level of zH ? Why?
(f) Assume NH = 1, 000 and NL = 500, is it pro?table for Comcast to sell two di?erent speeds? Why or why not?
(g) Solve for zL , pL , and pH .
Bundling
Direct TV has four types of channels that they can o?er: movie channels, sports channels, news channels and variety channels. Assume that the cost of providing service for the di?erent types of channels is equal to $20. There are 3 types of consumers which Direct TV faces with the following preferences for the di?erent types of channels:
Jocks
Nerds
Others
Movies
30
35
25
Sports
70
5
30
News
8
60
25
Variety
20
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 pro?t do they earn in total?
(b) What is the optimal pure bundling price?How much pro?t do they earn in total?
(c) What is the optimal mixed bundling strategy? How much pro?t do they earn in total? Note that since there are 4 types of channels, they could o?er di?erent 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.)
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 a monopoly in the credit card market but not in the debit card market (most
banks o?er 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 pro?t 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 pro?t would they make?
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 ?rms. Demand for bootlegged whiskey in Atlantic City is given by:
P (Q) = 200 ? Q
(a) Write down the pro?t functions for each ?rm.
(b) Find the best response functions for each ?rm.
(c) Find the equilibrium quantities ordered for each store, total quantity, price and pro?ts for each ?rm.
(d) How much deadweight loss is there?
(e) How much money would Nucky be willing to pay to someone to ‘o?’ Gyp?
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