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
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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