3 Consider a perfectly firm who has a cost function of cQ 34

3 Consider a perfectly firm who has a cost function of c(Q) 3+40+602 a) Solve for the firm\'s supply function. b) If Price is $60, what are the firm\'s profits? Do they want to produce in the short run? c) If price is $10, what are the firm\'s profits? Do they want to produce in the short run?

Solution

Firm\'s supply function is the same as its marginal cost curve:

a) P = MC = 4 + 12Q

P = 4 + 12Q

b)

when P = $ 60

4 + 12Q = 60

Q = 4.67

Profit = P x Q - (3 + 4Q + 6Q²)

Profit = 127.67

AVC = VC/Q = 4 + 6Q

min AVC = 4

Yes, they would want to produce in the short run as firm earns a positive profit. ( P > min AVC)

c)

when P = $ 10

4 + 12Q = 10

Q = 0.5

Profit = P x Q - (3 + 4Q + 6Q²)

Profit = -1.5

Yes, they would want to produce in the short run as P > min AVC