03 Jun Question If you choose to work in groups, each stu
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?
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