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
