Can you please help me with the following question?
A monopolist has two plants with different marginal cost functions:
M C1(Q1) = 20 + 2Q1
M C2(Q2) = 10 + 5Q2
where Q1 is the amount of output produced in the first plant and Q2 is the amount of output produced in the second plant. The firm faces the following inverse demand curve: P = 84 - 3Q, where Q = Q1 + Q2.
(a) What is the total output that maximizes profit for this firm and how much of that output will be produced at each plant? Assuming there are no fixed costs, what is the firm's profit (Hint: the area under the MC curve is the TVC)?
(b) Suppose now that you expect a drop in demand that would shift it to be:
P = 20 - 3Q. How would the monopolist's optimal output allocation change? (Hint: drawing the marginal cost curves and the marginal revenue curve might help).