Question

Joe has just moved to a small town with only one golf​ course, the Northlands Golf Club. His inverse demand function is pequals200minus2​q, 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 ​$40​, which is the marginal cost his round imposes on the Club. What membership fee would maximize profit for the​ Club? The manager could have charged Joe a single price per round. How much extra profit does the Club earn by using​ two-part pricing? The​ profit-maximizing membership fee​ (F) is ​$ nothing. ​(Enter your response as a whole​ number.)

Answer 1

$3200

Step-by-step explanation:

MC = Marginal Cost

MR = Marginal Revenue

p = 200 – 2q

The profit-maximizing membership fee​ is equal to the total surplus

So, Number of rounds played by joe,

P = MC = 40 = 200 - 2q

40 = 200 - 2q

q = 160/2 = 80

and, T.S = 1/2*(vertical intercept of demand curve - MC)*Quantiy of rounds

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

= 6400

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

If Firm Charge singe price , then it will provide rounds such 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 charge single price = TR - TC = PQ - MC*Q = (P-MC)*Q = (120-40)*40 = $3200

So, Increase in Profit = Membership fee - Profit if charge single price

= $6400 - $32000

= $3200