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Joe has just moved to a small town with only one golf course, the Northlands Golf Club

Economics Nov 25, 2020

Joe has just moved to a small town with only one golf course, the Northlands Golf Club. His inverse demand function is p= 120 – 2q, where q is the number of rounds of golf that he plays per year. The manager of the Northlands Club negotiates separately with each person who joins the club and can therefore charge individual prices. This manager has a good idea of what Joe's demand curve is and offers Joe a special deal, where Joe pays an annual membership fee and can play as many rounds as he wants at $40, which is the marginal cost his round imposes on the Club. Joe marries Susan, who is also an enthusiastic golfer. Susan wants to join the Northlands Club. The manager believes that Susan's inverse demand curve is p = 100 – 29. The manager has a policy of offering each member of a married couple the same two-part prices, so he offers them both a new deal. What two-part pricing deal maximizes the club's profit? Will this new pricing have a higher or lower access fee than in Joe's original deal? How much more would the club make if it charged Susan and Joe separate prices? The club maximizes profit subject to the policy by charging a per round price of p=$ and a lump-sum fee of F = $ (Enter your responses as whole numbers.)

Expert Solution

Hi

The answer of the following question is given below in a detailed manner as follows :

p = 200 - 2q

The membership fee that maximizes profit (F) equals the total surplus

So, Number of rounds played by Joe,

P = MC = 40 = 200 - 2q

40 = 200 - 2q

q = 160/2 = 80

y T.S = 1/2 * (vertical intersection of the demand curve - MC) * Number of rounds

T.S = 1/2 * (200-40) * 80

= 6400

So the maximum membership FEE (F) = $ 6400.

If Firm Charge only price then it will provide rounds like MR = MC

TR = P * Q = (200 - 2Q) * Q

MR = dTR / dQ = 200 - 4Q

Equating MR = MC

200 - 4Q = 40

Q = 160/4 = 40

P = 200 - 2Q = 200 - 2 * 40 = 120

So, Profit if you charge a single price = TR - TC = PQ - MC * Q = (P-MC) * Q = (120-40) * 40 = $ 3200

So double price gain increase = membership fee - gain if you charge single price

= $ 6400 - $ 3200

= $ 3200

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