Answer to Question #273279 in Microeconomics for Linh

Question #273279

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


1
Expert's answer
2021-12-02T13:57:05-0500

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.


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