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Unformatted text preview: Economics 104B Solution for Final Exam Spring 2010 1. A private golf club has two types of members. Serious golfers each have the demand curve D s ( p ) = 350- 10 p , where D s ( p ) denotes the number of rounds demanded at the per-round price p . Casual golfers each have the demand curve D c ( p ) = 100- 10 p . The club has 10 serious and 100 casual golfing members and has a constant marginal cost of $5 per round played by either type of member. a) (5pt) If the club can engage third-degree price discrimination, what price should it charge to the two types of members? Answer: The inverse demand curve by the serious golfers is p s ( Q s ) = 35- 1 10 Q s and that by the casual golfers is p c ( Q c ) = 10- 1 10 Q c . Thus, the MR s curve from the serious golfers all to- gether is MR s ( Q s ) = 35- 1 5 Q s and that from the casual golfers is MR c ( Q c ) = 10- 1 5 Q c . Thus, with third-degree price discrimina- tion, optimal quantities are determined by 35- 1 5 Q s = 5 and 10- 1 5 Q c = 5 . Solving these equations, we get Q * s = 150 and Q * c = 25. Thus the prices the club should charge to the two types are p * s = 20 to the serious type and p * c = 7 . 5. b) (7pt) Suppose the club can use a two-part pricing scheme but must charge all members the same membership fee. What membership fee and per-round price should the club charge? Answer: With two-part pricing, the optimal variable part (the per-round price) is p * = MC = 5. The fixed part (e.g., the membership fee) is determined by each members surplus at price p * . Since there are two demand curves and since the club must charge the same fixed fee, there are two candidates for the optimal fixed fee. One is the amount by which the club can keep all the golfers. From the demand curves, this amount is the CS at price p * according to each casual golfers demand curve. It is given by 125 1 per golfer. With this fixed fee, the clubs total profit is 125per golfer....
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- Fall '09