Question

A firm has

MC = 10 + Q and AVC = 10 + Q / 2

If FC = 5,000 and the market price is 100, findthe firm’s maximum profit. Will the firm continue to operate in the SR? In the LR? Explain

Answer 1

Solution:

Derive ATC:

ATC = AFC + AVC

AFC = $\frac{FC}{Q} = \frac{5,000}{Q}$

ATC = $\frac{5,000}{Q} + 10 + \frac{Q}{2}$

TR = P $\times$ Q = 100 $\times$ Q = 100Q

MR = $\frac{\partial TR} {\partial Q}$ = 100

 

Maximum profit: MR = MC

100 = 10 + Q

100 – 10 = Q

Q = 90

Profit = TR – TC

TC = $\frac{Q^{2} }{2} + 10Q + 5000 = \frac{90^{2} }{2} + 10(90) + 5,000$ = 4,050 + 900 + 5,000 = 9,950

TR = 90 $\times$ 100 = 9,000

Profit = 9,000 – 9,950 = (950)

 

The firm cannot operate in the short run since it is making losses.

The firm can operate in the long run.