Question

In: Economics

OU Country Club is estimated yearly demand schedule for each customer’s in the golf club is...

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?

Solutions

Expert Solution

(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


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