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 profit per customer compared to when it charges $0.25 per minute and the largest fixed fee that it can at that price? A) Profit per customer is the same in both cases, and it is equal to zero. B) Profit per customer is the same in both cases, and it is positive. C) Profit is $3.13 per customer higher at a price of $0.50. D) Profit is $3.13 per customer higher at a price of $0.25.

Question

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To find the profit per customer at each price, we need to use the following formula: Profit = Total Revenue - Total Cost At a price of $0.50 per minute, we first need to find the quantity demanded by customers. We can do this by setting Q^d equal to 0.50 and solving for Q: 200 - 100P = 0.50Q 100P = 200 - 0.50Q P = 2 - 0.005Q Now we can plug this price and quantity into the profit formula: Total Revenue = Price * Quantity = $0.50 * Q Total Cost = Marginal Cost * Quantity + Fixed Fee We know that the fixed fee charged must be the largest possible at this price, meaning that it must be high enough to make it just barely worthwhile for the customer to sign up. In other words, the fixed fee must be equal to the monopoly rent at this price. The monopoly rent is the amount that the customer is willing to pay above and beyond the cost of production, and it can be calculated as the area between the demand curve and the marginal cost curve up to the quantity demanded. To find the quantity demanded, we can plug in the price of $0.50 into the demand equation: Q = (200 - 100P) = 100 Now we can calculate the monopoly rent: Monopoly Rent = (1/2) * (200 - 0.25Q - 0.5Q) * Q = $37.50 This means that the fixed fee charged must be $37.50 per customer per month. Now we can calculate the profit per customer: Profit = Total Revenue - Total Cost = ($0.50 * Q) - ($0.25 * Q + $37.50) Profit = ($0.25 * Q) - $37.50 We know that Q = 100, so: Profit = ($0.25 * 100) - $37.50 = -$12.50 This means that Always There is actually losing money on each customer at a price of $0.50 and the maximum fixed fee. Now let's repeat the calculation for a price of $0.25 per minute: Q = (200 - 100P) = 150 Total Revenue = Price * Quantity = $0.25 * 150 = $37.50 Total Cost = Marginal Cost * Quantity + Fixed Fee = ($0.25 * 150) + $18.75 = $56.25 Profit = Total Revenue - Total Cost = $37.50 - $56.25 = -$18.75 Again, Always There is losing money on each customer. The difference in profit per customer between the two prices is: Profit at $0.50 - Profit at $0.25 = (-$12.50) - (-$18.75) = $6.25 So the correct answer is C, profit is $3.13 per customer higher at a price of $0.50.

Always There Wireless Is Wireless Monopolist in a Rural Area