Question: A monopoly firm faces the following estimated demand and average variable cost functions:

Q = 800,000 – 2,000P + 0.7M + 4,000P_R AVC = 500 – 0.03Q + 0.000001Q²

Where Q is quantity, P is price, M is income, and P_R is the price of a related good.

The firm expects income to be $40,000 and P_R to be $53. Total fixed cost is $2,6000,000.

a. Determine whether the firm should produce or shut down. Show how this decision was made.

b. If the firm produces, what is the profit maximizing level of output and the price it should charge?

c. What will be the firm’s profit?