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Suppose the Total Cost function of a firm in Perfect Competition is given by: $$C(q) = 450 + 15q + 2q^2$$

The market price is $P = 15$ per unit

Determine the optimal quantity produced by the firm

The trouble I'm having with this is a friend suggests the optimal quantity is q = 25 but that doesn't make sense to me.

Because when we calculate Marginal Cost = Marginal Revenue we get:

$$4q + 15 = 15$$

Which will yield an optimal quantity of 0 and not 25 when we solve for q.

The only way I can see it being equal to 25 is if the price is 115 and not 15 because of some typo. Any thoughts?

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    $\begingroup$ I am not sure what you are asking here. You give a very good explanation yourself: there is a typo in your question, or $q = 25$ is not the optimal quantity. $\endgroup$ – Giskard Jul 15 '18 at 18:14
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A typo seems very probable; more importantly, your procedure and concepts of setting MC=MR to solve for profit maximisation is definitely correct, regardless of the numbers being plug into the question.

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