A supplier is selling chairs to two cities, Southshore and Northshore. The cost of producing and handling one chair is $6. It is safe to assume that customers would not bother traveling to another city to purchase a chair, so the supplier implements the price discrimination. Let p1, p2 denotes the prices of chairs for Southshore and Northshore. Then the demand would be d1(p1) = (10000 − 1000p1) + for Southshore and d2(p2) = (8000 − 500p2) + for Northshore.

(a) What should be the optimal p1, p2 if the supplier would like to maximize the profit? What is the best total profit that the firm can earn?

(b) Now there is an enterprising arbitrager that finds a way to ship the chairs from Southshore to Northshore at the cost of $1 per chair. The arbitrager then buys chairs from Southshore at price p1 and sells them at the Northshore at the price of p2. Suppose p1 and p2 are the same as those computed in part (a). Now the arbitrager and the supplier charge the same price in Northshore, so half of the customers would buy chairs from the supplier and another half will buy chairs from the arbitrager. How many chairs should the arbitragers buy from Southshore? What would be the profit for the arbitrager? What would be the profit for the supplier?

(c) After a while, the supplier realizes that their is an arbitrager and set p1 = 9.5 and p2 = 10 instead. In this case, can the arbitrager takes the advantage? What would be the profit for the supplier in this case?

(d) If the supplier simply set the price to be 9 for both p1 and p2, what would be the profit?

(e) Compare the profits of the supplier in part (b), (c) and (d). Comment on your findings.