1. A night - club owner has both student and adult customers. The demand for drinks by a typical student is Q S = 18 - 3P. The demand for drinks by a typical adult is Q A = 10 - 2P. There are equal numbers of students and adults. The marginal cost of each drink is $2. (a). (10 points) If the club owner could separate the groups and practice third - degree price discrimination, what price per drink would be charged to members of each group? How many drinks are consumed by each consumer? What would be the consumer surplus of each group? What would be the club owner's profit in this case? (b). (10 points) Now consi der the night - club owner implements two - part pricing to charge an entry fee for student and adult. How should the owner of night - club design the two - part pricing? Namely, what are the entry fees charged to student and adult? Again, what price per drink wou ld be charged? H ow many drinks are consumed by each consumer? What would be the consumer surplus of each group? What would be the club owner's profit in this case?
2. Now consider block pricing. If the club owner in problem #1 can "card" patrons and determine who among them is a student and who is not and, in turn, can serve each group by offering a cover charge and a number of drink s to each group , i.e. the owner is going to design two packages for each consumer. (a). (10 points) Now help the owner of the night - club to design the pricing strategy. Namely, w hat will the cover charge and number of drink s be for students? What will be the cover charge and number of drink s given to adults? (b). (10 points) W hat is the club owner's profit under this regi me? W hat are consumer surpluses of student and adult?
3. (20 points) Now consider menu pricing (second degree price discrimination). Suppose the club owner in problem #1 cannot distinguish these two types of consumers: student and adult. How can you help the owner of the club to design the packages targeted to student and adult? What is the club owner ' s profit under this regime? What are consumer surpluses of student and adult? Explain what t he incentive compatibility constraint is in this example. (Hint: stu dent is willing to pay more. So, student is the high - type; adult is the low - type. As you design the menu pricing, start from the low - type, adult.