Question

Joe has just moved to a small town with only one golf​ course, the Northlands Golf Club. His inverse demand function is pequals=140140minus−22​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 ​$2020​, which is the marginal cost his round imposes on the Club. What membership fee would maximize profit for the​ Club? The manager could have charged Joe a single price per round. How much extra profit does the Club earn by using​ two-part pricing? The​ profit-maximizing membership fee​ (F) is ​$nothing. ​(Enter your response as a whole​ number.)

Answer 1

Answer: $1800

Explanation:

Here is the correct question:

Joe has just moved to a small town with only one golf​ course, the Northlands Golf Club. His inverse demand function is p=140-2q, 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 ​$20, which is the marginal cost his round imposes on the Club. What membership fee would maximize profit for the​ Club? The manager could have charged Joe a single price per round. How much extra profit does the Club earn by using​ two-part pricing? The​ profit-maximizing membership fee​ (F) is ​$nothing. ​(Enter your response as a whole​ number.)

Answer:

p = 140 - 2q

The profit-maximizing membership fee​ will be equal to total surplus

Therefore, the number of rounds that Joe played will be,

P = MC

20 = 140 - 2q

2q = 140 - 20

2q = 120

q = 120/2

q = 60

Total surplus = 1/2 × (vertical intercept of the demand curve - marginal cost) × the quantiy of rounds.

Total surplus = 1/2 × (140 - 20) × 60

= 1/2 × 120 × 60

= 3600

Therefore, the maximum membership fee will be = $3600.

If the firm charge Joe a single price , then the rounds provided will be such that MR = MC

Total revenue = price × quantity

TR = (140 - 2q) × q

TR = 140q - 2q²

MR = dTR/dQ = 140 - 4q

We then equate MR = MC

140 - 4q = 20

4q = 140 - 20

4q = 120

q = 120/4

q = 30

P = 140 - 2q

P = 140 - (2 × 30)

P = 140 - 60

P = 80

Therefore, the profit if a single price is charge will be:

= TR - TC = pq - MC×q = (P-MC)×Q

= (80-20) × 30

= $1800

Therefore, the increase in the profit by two-par pricing will be:

=Membership fee - Profit of single price charge

= $3600 - $1800

= $1800