Final answer:
To calculate the monopolistic profit, you need to find the profit-maximizing quantity and price. The monopolist faces an inverse demand curve, p(y) = 150 - 4y, and a cost function, c(y) = 10y + 3y². Applying the necessary equations, we find that the monopolistic profit is $6000.
Step-by-step explanation:
The monopolistic profit can be calculated by finding the profit-maximizing quantity and price. In this case, the monopolist faces an inverse demand curve, p(y) = 150 - 4y, and a cost function, c(y) = 10y + 3y². To find the profit-maximizing quantity, we need to set marginal revenue equal to marginal cost. Marginal revenue is the derivative of the inverse demand curve, MR = 150 - 8y, and marginal cost is the derivative of the cost function, MC = 10 + 6y. Setting MR equal to MC gives: 150 - 8y = 10 + 6y. Solving for y, we get y = 10. Substituting y = 10 into the inverse demand curve gives the price, p(10) = 150 - 4(10) = 150 - 40 = 110. To find the monopolistic profit, we multiply the quantity sold by the difference between the price and average cost. Average cost is calculated by dividing the total cost function by the quantity, so AC = (10y + 3y²)/y = 10 + 3y. Now we can calculate the monopolistic profit: Profit = (110 - 10) * (110 - 10 - (10 + 3(10))) = 100 * 60 = 6000.