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# hw2a - Homework 2 ISyE 4803B 1 Given the following...

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Homework 2 – ISyE 4803B 1. Given the following price-response 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 2-part tariff scheme (so the price-response 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 non-linear program with multiple constraints, so you will need to apply the KT conditions.

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hw2a - Homework 2 ISyE 4803B 1 Given the following...

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