Final answer:
Calculating the monopolist's total profit via perfect price discrimination involves finding the quantity where the demand curve meets the monopolist's cost. The profit is the total revenue (area under the demand curve) minus the total cost. None of the provided answer choices match the calculated profit of 975.
Step-by-step explanation:
The question involves a monopolist practicing perfect price discrimination with a given inverse demand curve p(y) = 150 - 4y and a cost function c(y) = 10y. To find the monopolist's total profit, we need to understand that perfect price discrimination allows the monopolist to capture the entire area under the demand curve down to its cost curve. Thus, the total profit is the integral of the difference between the price customers are willing to pay and the cost of production, all the way from zero production to the quantity where price equals marginal cost (where demand meets the cost curve).
First, we determine the quantity where the monopolist no longer makes a profit, which is where p(y) = c(y). Solving 150 - 4y = 10y gives y = 15. The total revenue then is the area under the demand curve from y = 0 to y = 15, calculated by the integral ∫015(150 - 4y)dy, which results in 2250 - 30y2/2 evaluated from 0 to 15, yielding 2250 - 30(15)2/2 = 2250 - 3375 = -1125 (as a total revenue figure, we take the absolute value, making it 1125). As the monopolist captures all surplus, this is also the profit before accounting for cost.
The total cost of producing 15 units is 10y, so for y = 15, it is 10 * 15 = 150. Subtracting this total cost from the total revenue gives us 1125 - 150 = 975 in profit, indicating that the correct answer is none of the above as none of the provided options match our calculation.