Question #58191

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 - Q2
a) What is the profit maximizing output?

Expert's answer

The conditions seems inconsistent with the reality: that is, the Total Cost function becomes negative when Q becomes more than 37:

TC (0) = 800 + 16 * 0 - (0 * 0) = 800

TC (38) = 800 + 16 * 38 - (38 * 38) = -36

...

TC (100) = 800 + 16 * 100 - (100 * 100) = - 7600

which means that the cost become "revenue", in fact. Formally, based on the conditions, the answer would be infinity, which is obviously impossible.

TC (0) = 800 + 16 * 0 - (0 * 0) = 800

TC (38) = 800 + 16 * 38 - (38 * 38) = -36

...

TC (100) = 800 + 16 * 100 - (100 * 100) = - 7600

which means that the cost become "revenue", in fact. Formally, based on the conditions, the answer would be infinity, which is obviously impossible.

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