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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morgan8002
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You haven't calculated total revenue and total cost properly. They should be the integrals with respect to quantity of price and marginal cost respectively.
If you do this, the partial derivatives cancel with the integrals and you're left with the equation that you used in the beginning.
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