Question

1. A monopoly faces the following demand function: P=1200-Q. Variable production costs are VC(Q)=2Q^2. The firm also pays $50000 in costs that do not depend on production (even if q=0).

1. What are the sunk costs, the fixed (but not sunk) costs, and the variable costs for this firm?

2. Find the profit maximizing quantity and price, as well as profits.

2. Repeat question 1 above if the costs of the firm are now 0 if it does not produce, but 2Q^2+150000 if it produces any positive quantity

Answer 1

a.

Sunk Cost = $50000

Fixed (but not sunk) Cost = 0

Variable Cost = 2Q²

b.

Maximization requires:

Q = 200

P = 1200 - 200 = 1000

Profit = 1200(200) - 3(200)² - 50000 = 240000 - 120000 - 50000 = 70000

If the costs of the firm are now 0 if it does not produce, but 2Q^2+150000 if it produces any positive quantity:

a.

Sunk Cost = 0

Fixed (but not sunk) Cost = 150000

Variable Cost = 2Q²

b.

Maximization requires:

Q = 200

P = 1200 - 200 = 1000

Profit = 1200(200) - 3(200)² - 50000 = 240000 - 120000 - 150000 = - 30000 (Loss)