Homework 2 – ISyE 4803B
1.
Given the following priceresponse functions for 2 independent markets:
2
2
1
1
70
)
(
2
100
)
(
p
p
m
p
p
m

=

=
where the incremental cost for an item in either market is $10, find the
optimal
prices.
2.
Assume now that we are going to use a 2part tariff scheme (so the priceresponse
functions above are for the individual (the “clone” notion we discussed in class)),
answer the following:
a.
If we can perfectly segment, what should the scheme(s) be?
b.
If we can’t segment and can only offer a single price and tariff to both
markets, what should the scheme be?
3.
Suppose in addition to the two price response functions given in problem 1, there
is a third market with:
3
3
4
100
)
(
p
p
m

=
in addition, suppose there is a person that has the ability to arbitrage by
buying
goods in a lower price market and selling them in a higher price market.
The cost
for them to move the item between markets is $2 per unit.
What would the
optimal prices be?
(Note:
This ends up being a constrained nonlinear program
with multiple constraints, so you will need to apply the KT conditions.
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 Spring '08
 Staff
 Economics, $2, $10, $8

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