The managers of Roosevelt'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 Roosevelt's: Over 21 Students (S) and Over 21 Student Wannabe (W). Each Student has a demand for beverages of
P = 8 - QS
where QS is the quantity of beverages demanded if the price of a beverage is P. Each Wannabe 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. Roosevelt'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 Roosevelt's profit under Roosevelt's best choice?