Andy Anderson is the only supplier of email updates on avalanche conditions in the mountains above the two towns of Vanee and Keno. The marginal cost of producing these updates is zero (with zero fixed costs) and the inverse demand for these updates in Vanee is p = 52 - q and p = 11 - q in Keno. Suppose that in each of the two towns, all of the demand comes from one customer. Andy cannot identify which customer is which. To get around this, he creates two kinds of packages, one containing 52 updates and one containing 11. He allows his customers to simply buy one and only one of the kind of package that they prefer. What is the maximum price Andy could charge for the large package if he wants the Vanee customer to buy the package of 52 and the Keno customer to buy the package of 11?
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