Question

STC = 40 + 10Q + 0.1Q^2 . SMC = 10 + 0.2Q. The market price is $20.

a. Find the profit maximizing Q.

b. Calculate the maximum profit.

c. Find the average variable cost.

d. In the short run, at what price will this firm close?

e. Find the firm’s short run supply curve and express it as a function of price: Qs (P) = ?

Answer 1

a) Profit maximizing condition; MR = MC

TR = PQ = 20Q

MR = 20

MC = 10 + 0.2Q

MR = MC

20 = 10 + 0.2Q

0.2Q = 10

Q = 10/0.2

Q = 50 units

b) Profit = PQ - (40 + 10Q + 0.1Q²)

Profit = 20 x 50 - 40 - 10(50) - 0.1(50)² = 1000 - 40 - 500 - 250 = 1000 - 790

Profit = 210

c) TC = 40 + 10Q + 0.1Q²

TVC = 10Q + 0.1Q²

AVC = TVC/Q = (10Q + 0.1Q²)/Q

AVC = 10 + 0.1Q

AVC = 10 + 0.1(50) = 10 + 5 = 15

d) Firm will choose to close the firm when firm is not able to cover all its variable costs.

AVC is 15 so when price is less than 15 then firm will choose to close the firm.

e) Supply curve is the upward sloping MC curve of firm.

P = 10 + 0.2Q