Answer to Question #42217 in Microeconomics for JoJo

Question

A firm produces gardening services in a competitive industry and has a total cost function C=50+4Q+2Q².

a) At the given market price of $20, find the profit maximizing level of output in the short run.

b) What is the producer surplus at the profit maximizing level of output?

c) What is the difference between profit and producer surplus?

d) If the market price and the cost function does not change in the long run, should this firm continue to produce or exit the industry?

Answer 1

TC=50+4Q+2Q².

a) Pe = $20.

To find the profit maximizing level of output in the short run, we should calculate the quantity, for which marginal revenue equals marginal cost and price MR = MC = P
MC = TC' = 4 + 4Q
4 + 4Q = 20
4Q = 16
Qe = 4 units

b) What is the producer surplus at the profit maximizing level of output?

Producer surplus is an economic measure of the difference between the amount that a producer of a good receives and the minimum amount that he or she would be willing to accept for the good. To find it we need to know the supply function, which is equal MC. This curve intersects y-axis in point P = 4 + 4*0= $4.

So, the producer surplus equals PS = 0.5*(Pe - P0)*Qe = 0.5*(20 - 4)*4 = $32

c) What is the difference between profit and producer surplus?

Profit is the difference between total revenue and total cost TP = TR - TC =P*Q - TC = 20*4 - (50 + 4*4 + 2*4^2) = 80 - 98 = -18, so the firm faces losses
PS - TP = 32 - (-18) = $50

d) This firm should continue to produce, if AVC < P < ATC.

ATC = TC/Q = 50/4 + 4 + 2*4 = $24.5
AVC = VC/Q = (4Q+2Q^2)/Q = 4 + 2Q = 4 + 2*4 = $12
As 12 < 20 < 24.5, the firm should continue to produce.