<p>As a counterexample to the statement, consider the following:</p>

<p>Let demand be <span class="math-container">$p=10-q$</span>, so that <span class="math-container">$MR=10-2q$</span>. Suppose there’s no cost, so that profit equals revenue. If the monopolist produces at <span class="math-container">$q=6$</span>, <span class="math-container">$MR=-2&lt;0$</span>, but <span class="math-container">$TR=(10-6)6=24&gt;0$</span>, thus contradicting the statement. </p>

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2019-01-26T21:11:01.197Z
thanks for answering. But am I allowed to just assume there are no costs? (context: this is a correct/incorrect question from a 2016 microeconomics exam)
zerohedge
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2019-01-26T22:59:30.967Z
@zerohedge: You can incorporate costs into this setup and the conclusion is not going to change.
Herr K.
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2019-01-22T22:16:45.960Z
2019-01-22T22:16:45.960Z
Herr K.
<p><strong>Statement:</strong> If a monopoly is producing a quantity for which its MR is negative, its total profit cannot be positive.</p>

<p>Is this statement correct or incorrect, and why?</p>

<p>I've read a lot about this, but sources tend to discuss maximizing profitability, while the question above presumes that MR &lt; 0 (and obviously smaller than MC) but wonders about profitability in this scenario.</p>

<p>My hunch is that yes, it is possible, but I'm struggling to prove it.</p>

<p>Edit: this getting downvoted is the reason why SE is deteriorating at the rate it is. I’ll go look for a more welcoming community.</p>

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2019-01-22T13:32:23.813Z
Hint: Suppose there's no cost, so that profit equals revenue. Is total revenue non positive when MR is negative?
Herr K.
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2019-01-22T13:54:41.813Z
@HerrK. I guess it’s not, but P > MR in monopolist markets?
zerohedge
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2019-01-22T14:25:03.337Z
Please clarify any constraints on the problem. Is this a question about a regulated monopolist? Price discriminating? Is this a question about equilibrium profit maximization? Of does it just have to be possible, in the sense of something in the choice set of the producer? Or does it have to be possible while profits are positive?
BKay
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2019-01-22T16:49:28.767Z
@BKay: if there were any additional constraints I would have specified them.
zerohedge
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2019-01-22T17:24:58.737Z
Given zerohedge's response, @HerrK's should write up his response as an answer. He provides an example that satisfies the question.
BKay
<microeconomics>
microeconmics: can a monopolistic firm be profitable if its marginal revenue is negative?
zerohedge
# microeconmics: can a monopolistic firm be profitable if its marginal revenue is negative?

(Asked by: username_0 on 2019-01-22)

**Statement:** If a monopoly is producing a quantity for which its MR is negative, its total profit cannot be positive.

Is this statement correct or incorrect, and why?

I've read a lot about this, but sources tend to discuss maximizing profitability, while the question above presumes that MR < 0 (and obviously smaller than MC) but wonders about profitability in this scenario.

My hunch is that yes, it is possible, but I'm struggling to prove it.

Edit: this getting downvoted is the reason why SE is deteriorating at the rate it is. I’ll go look for a more welcoming community.

**Tags:** microeconomics
> **Comments:**
> **username_1**: Hint: Suppose there's no cost, so that profit equals revenue. Is total revenue non positive when MR is negative?  
> **username_0**: @HerrK. I guess it’s not, but P > MR in monopolist markets?  
> **username_2**: Please clarify any constraints on the problem. Is this a question about a regulated monopolist? Price discriminating? Is this a question about equilibrium profit maximization? Of does it just have to be possible, in the sense of something in the choice set of the producer? Or does it have to be possible while profits are positive?  
> **username_0**: @BKay: if there were any additional constraints I would have specified them.  
> **username_2**: Given zerohedge's response, @HerrK's should write up his response as an answer. He provides an example that satisfies the question.  

---

## 1 answers

### Answer by username_1 on 2019-01-22. Score: 2 | Accepted answer

As a counterexample to the statement, consider the following:

Let demand be $p=10-q$, so that $MR=10-2q$. Suppose there’s no cost, so that profit equals revenue. If the monopolist produces at $q=6$, $MR=-2<0$, but $TR=(10-6)6=24>0$, thus contradicting the statement.

> **Comments:**
> **username_0**: thanks for answering. But am I allowed to just assume there are no costs? (context: this is a correct/incorrect question from a 2016 microeconomics exam)  
> **username_1**: @zerohedge: You can incorporate costs into this setup and the conclusion is not going to change.  

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