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The following payoff table lists the profits of a buyer and a seller. The seller acts first by choosing a sale price ($9, $8, or $6). The buyer then decides the quantity of the good to purchase (two units, four units, six units, or eight units).
a. Suppose the buyer and seller transact only once. Does the buyer have a dominant strategy? Depending on the price quoted, what is his best response? What price should the seller set? Explain carefully.
Buyer Quantities
P = $9
Seller P = $8 Prices
2 Units 4 Units 6 Units 8 Units
10, 6
20, 5
30, 0
40, -8
8, 8
16, 9
24, 6
32, 0
4, 12
8, 17
12, 18
16, 16
P = $6
b. Suppose the seller and buyer are in a multiyear relationship. Each month, the buyer quotes a price and the seller selects her quantity. How might this change each player's behavior?
c. Now suppose the buyer and seller are in a position to negotiate an agreement specifying price and quantity. Can they improve on the result in part (a)? Which quantity should they set? What price would be equitable? Explain.
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