Question

Assume a firm faces two customers in the market. Customer 1 has an inverse demand of p=100−q1​, and Customer 2 has an inverse demand of p=180−q2. Marginal cost per unit is constant and equal to ​$50. Determine the profit the firm could make if it could charge each customer a different access fee. When charging different access fees to both​ customers, profit equals ______ ​(Enter a numeric response using a real number rounded to two decimal​ places.) Assume the​ profit-maximizing price is $90.00 and the access fee charged to these two customers is ​$ 50.00. Determine the profit the firm would make if it charged this same access fee to both customers. The profit the firm could earn if it charged the same access fees is _____ (Enter a numeric response using a real number rounded to two decimal​ places.)

Answer 1

Answer :

(a) :-  

For Customer 1:

P = 100 - q1

Total Revenue = P*q1 = (100 - q1)*q1

MR = 100 - 2q1

MC = 50

Optimal condition : MR = MC

100 - 2q1 = 50

100 - 50 = 2q1

q1 = 25

P = 100 - 25 = 75

Profit from customer 1 = (75 - 50)*(25) = 625

For Customer 2:

P = 180 - q2

Total Revenue = P*q2 = (180 - q2)*q2

MR = 180 - 2q2

MC = 50

Optimal condition: MR = MC

180 - 2q2 = 50

q2 = 65

P = 180 - 65 = 115

Profit from customer 1 = (115 - 50)*(60) = 3900

Total profit with different prices = 625 + 3900 = 4525

(b) :-  Profit with price of 95 and access fee of 50 :

2*(50) + (90 - 50)*(100 - 90) + (90 - 50)*(180 - 90)

= 100 + 400 + 3600 = 4100