# solution

The managers of Rooseveltâ€™s (a local yet upscale bar) are considering charging

an admission fee on Thursday nights. They contemplate how to charge.

Should they Option 1. Use just a beverage charge per beverage ordered or

Option 2. Use an admission charge (a fee to enter the establishment) and

a beverage charge per beverage ordered? There are two types of people who frequent Rooseveltâ€™s: Over 21 Students (S) and Over 21 Student Wannabees (W). Each Student has a demand for beverages of P = 8 â€“ QS where QS is the quantity of beverages demanded if the price of a beverage is P. Each Wannabee has a demand for beverages of P = 8 – 2QW

where QW is the quantity of beverages demanded if the price of a beverage is P.

The marginal cost of serving a beverage is a constant \$2.

For simplicity, assume there is one demander of each type. Rooseveltâ€™s

must (by law) charge all customers the same admission charge and the same

per beverage charge. Beverages do not have to be sold in integer amounts and

prices do not have to be in integer amounts.

a. Under option 1, what is the profit maximizing price per beverage?

b. Under option 2, what is the profit maximizing two-part tariff?

c. What is Rooseveltâ€™s profit under Rooseveltâ€™s best choice?

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