Scenario 10.2:
A monopolist faces the following demand curve, marginal revenue curve, total cost curve and marginal cost curve for its product:
Q = 200 - 2P
MR = 100 - Q
TC = 5Q
MC = 5
-Refer to Scenario 10.2. How much profit does the monopolist earn?

Question

Quizplus · Accepted Answer

The monopolist's profit is equal to total revenue minus total cost. Total revenue is equal to price times quantity, and price is equal to marginal revenue. So, total revenue is equal to marginal revenue times quantity. Marginal revenue is equal to 100 - Q, and quantity is equal to 200 - 2P. So, total revenue is equal to (100 - Q)(200 - 2P).Total cost is equal to 5Q. So, the monopolist's profit is equal to (100 - Q)(200 - 2P) - 5Q.Substituting Q = 200 - 2P into the profit equation, we get:profit = (100 - (200 - 2P))(200 - 2P) - 5(200 - 2P)profit = (100 - 200 + 2P)(200 - 2P) - 1000 + 10Pprofit = (-100 + 2P)(200 - 2P) - 1000 + 10Pprofit = -20000 + 400P - 4P^2 - 1000 + 10Pprofit = -4P^2 + 410P - 21000To find the monopolist's profit-maximizing quantity, we set marginal revenue equal to marginal cost. Marginal revenue is equal to 100 - Q, and marginal cost is equal to 5. So, we have:100 - Q = 5Q = 95Substituting Q = 95 into the profit equation, we get:profit = -4(95)^2 + 410(95) - 21000profit = -4(9025) + 38950 - 21000profit = -36100 + 38950 - 21000profit = $1850So, the monopolist earns a profit of $1850.

Scenario 10.2: A Monopolist Faces the Following Demand Curve, Marginal Revenue Curve