A nightclub serves both student and non-student customers.

A nightclub serves both student and non-student customers. An individual student has a demand for drinks given by QS = 18 − 3P . The drink demand for a non-student is QN = 10 − 2P . There are equal numbers of students and non-students. The marginal cost of a drink is $2. Suppose the club can “card” patrons and determine who is a student and who is not. The club offers a cover charge, which may be different for students and non-students, and in exchange for the cover charge, a patron receives some drink tokens. The number of tokens given to students may be different than the number given to non-students.

(a) What is the cover charge for students and the number of tokens they receive? What is the cover charge and number of tokens for non-students? How much profit does the club receive?

(b) If the club cannot tell students from non-students, and it would like to continue using its “cover plus tokens” pricing strategy you identified in part (a), is it worthwhile to continue serving both types of consumers?

(c) Now, suppose that the club cannot tell students from non-students, but it is committed to continue serving both types of consumers. It will set a cover charge and give some number of tokens to all consumers who pay the cover charge. The club will then offer additional tokens at a price of P per token. Can you identify a cover charge, number of tokens included with the cover, and a price P such that profit is better than giving all customers the non-student cover/token pair that you identified in part (a)?