<p>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.</p>

CC BY-SA 4.0
2018-07-17T16:02:36.380Z
2018-07-17T16:02:36.380Z
J Tg
<blockquote>
  <p>Suppose the Total Cost function of a firm in Perfect Competition is
  given by: $$C(q) = 450 + 15q + 2q^2$$</p>
  
  <p>The market price is $P = 15$ per unit</p>
  
  <p><strong>Determine the optimal quantity produced by the firm</strong></p>
</blockquote>

<p>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.</p>

<p>Because when we calculate <strong>Marginal Cost = Marginal Revenue</strong> we get:</p>

<p>$$4q + 15 = 15$$</p>

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

<p>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?</p>

CC BY-SA 4.0
2018-07-15T18:14:06.230Z
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.
Giskard
<microeconomics><general-equilibrium><competitive-equilibrium><producer-theory>
MICROECONOMICS: Optimal quantity produced in a Perfect Competition Market
Metrician
# MICROECONOMICS: Optimal quantity produced in a Perfect Competition Market

(Asked by: username_0 on 2018-07-15)

> 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?

**Tags:** microeconomics, general-equilibrium, competitive-equilibrium, producer-theory

> **Comments:**
> **username_1**: 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.  

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## 1 answers

### Answer by username_2 on 2018-07-17. Score: 1 | Accepted answer

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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