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Answer to Question #58499 in Microeconomics for Gracey

Question #58499
Assume the current price of maize K70 per 100 kg and the short run cost function, where Q represents bags of maize per year is:
TC = 800 + 16Q - Q^2
a) What is the profit maximizing output?
b) Calculate the profit for the output you got in (a) above?
c) Based on the rule that a firm should produce only if it covers its variable costs of production, what quantity should be produced to cover variable costs?
d) How much are the fixed costs of this business?


Expert's answer
P = 0.7, TC = 800 + 16Q - Q^2.
a) The profit maximizing output is in the point, for which MC = MR = P.
MC = TC' = 16 - 2Q, so:
16 - 2Q = 0.7
Q = 7.65 kg.
b) The maximum profit is TP = TR - TC = P*Q - TC = 0.7*7.65 - 800 - 16*7.65 + 7.65^2 = -858.5, so the firm face losses.
c) As a firm should produce only if it covers its variable costs of production, the firm should produce the quantity, for which P = AVC = (16Q - Q^2)/Q = 16 - Q = 0.7 to cover variable costs. So, Q = 15.3 kg.
d) The fixed costs of this business are FC = 800.

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