Ken Kalax
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Okay, so I have a business that is a price taker, and p=8 (horizontal price line).

The marginal cost function is 0.22222(q)^2 (no fixed costs)

On a graph, this means the cost curve intersects the price line at a quantity of 6, where profit is maximized. All good so far.

BUT

when I put this through the derivative method, I get a wacky answer

PROFIT = TR-TC

PROFIT = 8q - (0.22222(q)^2)

Differentiate using the power rule gives us .... -0.44444q +8

I then set the answer to zero, and the result for q comes out as

0, 36.00036

It should be 6! or damn near close! What am I doing wrong here?
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jpt4749
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Just set P = MC and you'll get Q=6

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