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 $0.30 per minute.What is the highest fixed fee Always There Wireless could charge without losing the low-demand consumers?
A) $28.13
B) $56.26
C) $24.50
D) $49.00

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 $0.30 per minute.What is the highest fixed fee Always There Wireless could charge without losing the low-demand consumers?
A) $28.13 
B) $56.26 
C) $24.50 
D) $49.00

Quizplus · Accepted Answer

To find the maximum fixed fee that Always There Wireless could charge and still retain all of its low-demand customers, we need to compare the total consumer surplus of high-high and low-demand consumers with and without the fixed fee. If the fixed fee is too high, then the low-demand consumers will not buy any service (since they have relatively elastic demand) and Always There Wireless will lose their revenue. Without the fixed fee, the market equilibrium price and quantity for high-high demand consumers can be found by setting the marginal cost equal to the demand curve and solving for P: 0.25 = 11 - 0.00001Q, or Q = 750, P = 2 Similarly, the market equilibrium price and quantity for low-demand consumers will be: 0.25 = 3 - 0.00001Q, or Q = 250, P = 0.50 The total consumer surplus of high-high demand consumers will be: (1/2) x (11-2) x 750 = $2,812.50 The total consumer surplus of low-demand consumers will be: (1/2) x (3-0.50) x 250 = $312.50 Total revenue for Always There Wireless will be: ($2 x 750) + ($0.50 x 250) = $1,750 Now let's consider the case with a fixed fee. Assume that Always There Wireless charges F dollars as the fixed fee. Consumers who pay the fixed fee can use any amount of minutes they want, while consumers who do not pay the fixed fee will pay the per-minute price of $0.30. High-high demand consumers will still pay the per-minute price of $0.30, so their demand curve remains the same. Low-demand consumers who pay the fixed fee will have an unlimited demand curve: Q = infinity if P <= F, and Q = 0 if P > F. Low-demand consumers who do not pay the fixed fee will have the same demand curve as before: Q = 300 - 10,000P. To find the revenue function for Always There Wireless, we need to add up the revenue from high-high and low-demand consumers who pay the fixed fee, and the revenue from low-demand consumers who do not pay the fixed fee. We also need to subtract the fixed cost F. Total revenue R(F) = (0.3 x 100) + (F x 300) + (0.3 x Q), where Q = 300 - 10,000P for P <= F, and Q = 0 for P > F. To maximize R(F), we need to find the value of F that makes the demand curve of low-demand consumers who pay the fixed fee tangent to the demand curve of low-demand consumers who do not pay the fixed fee. This is because any higher fixed fee would cause the demand of low-demand consumers who pay the fixed fee to be lower than the demand of low-demand consumers who do not pay the fixed fee, resulting in lower revenue. Solving Q'(P) = -10,000 and Q(P) = 300 - 10,000P, we get: P* = $0.03 and Q* = 270 This means that if Always There Wireless charges $0.03 per minute for low-demand consumers who pay the fixed fee, 270 of them will do so. The total revenue from these customers will be $8.10. To find the highest fixed fee that Always There Wireless could charge without losing any low-demand consumers, we need to set Q = 300 - 10,000F = 0 at P = $0.30. Solving for F, we get: F = $24.50 Therefore, the highest fixed fee Always There Wireless could charge without losing the low-demand consumers is $24.50.

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