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Homework answers / question archive / Joe has just moved to a small town with only one golf course, the Northlands Golf Club
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.)
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
