After retiring from the National Basketball Association (NBA) as a player and co

Question

After retiring from the National Basketball Association (NBA) as a player and coach, Larry Bird has decided to move back to his home state of Indiana and open up a barbershop in the city of French Lick. Larry has proven to be as innovative in the barbershop as he was on the basketball court by selling haircutting services by the minute. Larry currently serves two types of customers. Type W customers do not really care much about their appearance. Known as "walk-ins" to those in the trade, they may spontaneously decide to drop in for a haircut while out shopping or enjoying the ambience of downtown French Lick. Each type W's demand for Larry Bird's services is q_w =30-4p, where q_w is denominated in minutes and p is price per minute. Type H customers, on the other hand, are more concerned about the appearance of their hair. They always phone Larry Bird in advance to book an appointment. Type H customers have a demand of q_H =30-2p. There are equal numbers of type W and type H customers in French Lick. Larry Bird cuts hair at a constant marginal cost of $2 per minute (which incidentally is roughly $866 per minute less than what he made as a coach in his final year in the NBA). Roughly sketch type W and type H demand curves on the same graph. Which type has the more elastic demand at p = 5? If Larry Bird could perfectly price discriminate between types, what price would he charge per minute of haircutting to type W customers? What price to type H customers? A law has been passed in the city of French Lick that prevents price discrimination between types. What price does Larry Bird charge per minute of haircutting?

Explanation / Answer

a) At p=5, qw = 10

qh = 20

Elasticity for w at p=5 is dqw/dp * p/qw = -4*5/10 = 2

Elasticity for H at p=5 is dqh/dp * p/qh = -2 * 5/20 = 1/2

Type w has higher elasticity

b) For W, MR =30 - 8p

To maximize profits, MR =MC => 30-8p = 2

pw = 7/2 = 3.5

For H, MR = 30 -4p

To maximize profits, MR =MC

30 - 4p = 2

ph = 7

c) Without price discrimination,

TR = p(30-4p +30-2p)

MR = 60 - 12p

Profit is maximized at MR=MC

60 - 12p = 2

p = 58/12 = 29/6 = 4.8

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