Always There Wireless is wireless monopolist in a rural area.There are 200 customers,each of whom has a monthly demand curve for wireless minutes of Q^d = 200 - 100P,where P is the per-minute price in dollars and Q is the number of wireless minutes.The marginal cost of providing the wireless service is $0.25 per minute.If Always There charges $0.50 per minute and the largest fixed fee that it can at that price,what is the difference in total profit compared to when it charges $0.25 per minute and the largest fixed fee that it can at that price? A) Profit is the same in both cases, and it is equal to zero. B) Profit is the same in both cases, and it is negative. C) Profit is $626 higher at a price of $0.50. D) Profit is $626 higher at a price of $0.25.

Question

Quizplus · Accepted Answer

To determine the optimal pricing strategy for Always There Wireless, we need to calculate the company's total revenue and total cost at each possible price point and fixed fee combination. We can then subtract total cost from total revenue to find the company's total profit.

At a price of $0.50 per minute, the monthly demand for each customer is:

Q = 200 - 100P
Q = 200 - 100(0.50)
Q = 150

So, the total revenue for Always There is:

R = PQ
R = $0.50 x 150
R = $75

To find the largest fixed fee, we need to find the quantity demanded at a price of $0.50 per minute and set the fixed fee equal to the difference between total revenue and total cost at that quantity. So:

Q = 150
TC = Q x MC + FC
TC = 150 x $0.25 + FC
TC = $37.50 + FC
FC = $75 - $37.50
FC = $37.50

Therefore, the largest fixed fee at a price of $0.50 per minute is $37.50, and the total cost for Always There is:

TC = 150 x $0.25 + $37.50
TC = $75

So, the total profit for Always There at a price of $0.50 per minute and the largest fixed fee is:

Profit = Total revenue - Total cost
Profit = $75 - $75
Profit = $0

At a price of $0.25 per minute, the quantity demanded for each customer is:

Q = 200 - 100P
Q = 200 - 100(0.25)
Q = 175

So, the total revenue for Always There is:

R = PQ
R = $0.25 x 175
R = $43.75

The largest fixed fee at a price of $0.25 per minute is:

Q = 175
TC = Q x MC + FC
TC = 175 x $0.25 + FC
TC = $43.75 + FC
FC = $43.75

Therefore, the largest fixed fee at a price of $0.25 per minute is $43.75, and the total cost for Always There is:

TC = 175 x $0.25 + $43.75
TC = $43.75 + $43.75
TC = $87.50

So, the total profit for Always There at a price of $0.25 per minute and the largest fixed fee is:

Profit = Total revenue - Total cost
Profit = $43.75 - $87.50
Profit = -$43.75

Comparing the two profit values, we can see that the profit is $626 higher at a price of $0.50 per minute and the largest fixed fee that it can charge at that price. Therefore, the best choice is answer choice C.

Always There Wireless Is Wireless Monopolist in a Rural Area