In: Economics
OU Country Club is estimated yearly demand schedule for each customer’s in the golf club is P = 100-2Q with a constant marginal cost of 20 per customer per play and a yearly fixed cost of $500,000. The marketing manager projected that there are 500 identical customers. They are going to use a two-part pricing strategy, where F is the country club membership and r is a usage charge per customer. (10 points)
a) What is the optimal F and r for each customer? What is their total profit?
(a)
In order to maximize profit under two part pricing a firm produces that quantity at which P = MC and charge per unit (i.e. r) = MC where MC = Marginal Cost. By buying at this price whatever consumer surplus buyers receive, he will charge that at Membership Fee(F)
So, P = MC => 100 - 2Q = 20 => Q = 40 So, r = MC = 20.
So, r = 20
Consumer surplus is the area above price line(P = 20) and below demand curve.
Area of a triangle = (1/2)*base*height
So, Consumer surplus = (1/2)*40*(100 - 20) = 1600
So, Member ship fee(F) = $1600
Profit = Total Revenue - Total Cost.
Total Revenue from one buyer = r*Q + F = 20*40 + 1600 = 2400
So, Total Revenue from 500 Consumers = 2400*500 = 1,200,000
Total Cost = Fixed Cost + Variable cost = 500,000 + Market quantity*MC = 500,000 + (500*40)*20 = 900000
Thus, Profit = Total Revenue - Total Cost = 1,200,000 - 900,000 = 300000
Hence, Profit = $300000