Answer to Question #276065 in Economics for DANDAN

Question

Problem 1:

A perfectly competitive firm has total revenue and total cost curves given by:

TR = 100Q

TC = 5,000 + 2Q + 0.2Q 2

a. Find the profit-maximizing output for this firm. Show the solution. (5 points)

b. Find the profit the firm makes. Show the solution. (5 points)

Problem 2:

A perfectly competitive firm has the cost function TC=1,000 + 2Q + 0.1Q 2 .

a. What is the marginal cost (MC) of the firm? (3 points)

b. What is the average cost (AC) of the firm? (3 points)

c. What is the lowest price at which this firm can break even? Show the solution. (5 points)

Problem 3:

Market price is $50. The firm’s marginal cost curve is given by MC = 10 + 2Q. Find the profit-

maximizing output for the firm. Show the solution. (5 points)

Problem 4:

What does it mean to say that a perfectly competitive firm is a price taker? Can’t a firm set any

price it chooses? Explain. (5 points)

Answer 1

Problem 1:

a. Profit is maximized when MR = MC = P, so:

MR = TR'(Q) = 100.

MC = TC'(Q) = 2 + 0.4Q,

2 + 0.4Q = 100,

Q = 245 units,

P = MR = 100.

b. The profit the firm makes is:

$TP = TR - TC = 100×245 - (1,000 + 2×245 + 0.1×245^2) = 17,007.5.$

Problem 2:

a. What is the marginal cost is:

MC = TC'(Q) = 2 + 0.2Q.

b. The average cost is:

AC = TC/Q = 1,000/Q + 2 + 0.1Q.

c. The lowest price at which this firm can break even is:

P = AVC = VC/Q = 2 + 0.1Q.

Problem 3:

The profit-maximizing output is:

MC = P,

10 + 2Q = 50,

Q = 20 units.

Problem 4:

A perfectly competitive firm is known as a price taker because the pressure of competing firms forces them to accept the prevailing equilibrium price in the market. If a firm in a perfectly competitive market raises the price of its product by so much as a penny, it will lose all of its sales to competitors.