Suppose Always There Wireless serves 100 high-high demand wireless consumers,each of whose monthly demand curve for minutes of wireless service is and 300 low-demand consumers,each of whose monthly demand curve for minutes of wireless is ,where P is the per-minute price in dollars.Its marginal cost is $0.25 per minute.Suppose Always There Wireless charges $0.35 per minute.What is Always There Wireless's profit from sales for each high-demand consumer?
A) $27.63
B) $37.63
C) $21.13
D) $28.13

Question

Suppose Always There Wireless serves 100 high-high demand wireless consumers,each of whose monthly demand curve for minutes of wireless service is  and 300 low-demand consumers,each of whose monthly demand curve for minutes of wireless is  ,where P is the per-minute price in dollars.Its marginal cost is $0.25 per minute.Suppose Always There Wireless charges $0.35 per minute.What is Always There Wireless's profit from sales for each high-demand consumer?
A) $27.63 
B) $37.63 
C) $21.13 
D) $28.13

Quizplus · Accepted Answer

For high-demand consumers, the profit-maximizing output level is where marginal revenue equals marginal cost.
The marginal revenue can be found by taking the derivative of the demand function, which is MR=11.76-0.04Q. 
Setting MR equal to marginal cost of $0.25 gives 
11.76-0.04Q=0.25 
Q=293.5 
So, the profit-maximizing quantity for high-demand consumers is approximately 293.5 minutes.
Total revenue for each high-demand consumer is TR=P*Q=0.35*293.5=$102.73
Total cost for each high-demand consumer is MC*Q=$0.25*293.5=$73.38
Then, profit for each high-demand consumer is 
TR-TC=$102.73-$73.38=$29.35
Therefore, the profit from sales for each high-demand consumer is $29.35, which is closest to answer choice B ($37.63).

Suppose Always There Wireless Serves 100 High-High Demand Wireless Consumers,each