<p><span class="math-container">$max_p f(p)$</span> just means the maximal value of expression of <span class="math-container">$f(p)$</span> with regards to <span class="math-container">$p$</span> (meaning the value of <span class="math-container">$f(p)$</span> is checked over the whole range of <span class="math-container">$p$</span>'s possible values).</p>
<p>In your case it does indeed mean the maximal profit value the monopolist can attain.</p>
<p>The given first order condition is a derivative of the expression with respect to <span class="math-container">$p$</span>, divided by 3. Division by 3 is fine since the right hand side of the first order condition is 0, which divided by 3 will remain 0.</p>

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2023-07-27T14:18:03.087Z
how do they get 1 - 2p, then? and not just 1 - p?
andromeda
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2023-07-27T14:18:41.637Z
also, I hope you could explain the consumer surplus being (1-p)^2, please?
andromeda
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2023-07-27T19:27:46.007Z
1. This is the derivative of the function. 2. Please ask new questions as new questions.
Giskard
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2023-07-28T05:09:23.330Z
... I had already asked that in the original question lol. chill tho, thanks for your help.
andromeda
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2023-07-27T11:47:59.853Z
2023-07-27T11:47:59.853Z
Giskard
<p><a href="https://i.sstatic.net/57bzq.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/57bzq.png" alt="enter image description here" /></a></p>
<p>Hello. Someone sent this on a discord server that I am on, and I couldn't make heads or tails of this. I found the book it is from on studocu; solutions to Cabral's Industrial Organisations, 2nd Ed. The question has MC = 0.</p>
<p>Is max p just max profit? Because then it would make some sense for me. And how did they derive the first order condition from this? All I found was that (∂π / ∂q) = 0, but please do explain where this comes from? Also, why is consumer surplus just the square of the total demand from a type 1 consumer?</p>
<p>Thank you so much in advance!</p>

<microeconomics><monopoly><industrial-organisation><monopolistic-competition>
What is max here, and how did they derive the first order condition from it?
andromeda
# What is max here, and how did they derive the first order condition from it?

(Asked by: username_0 on 2023-07-27)

[![enter image description here](https://i.sstatic.net/57bzq.png)](https://i.sstatic.net/57bzq.png)

Hello. Someone sent this on a discord server that I am on, and I couldn't make heads or tails of this. I found the book it is from on studocu; solutions to Cabral's Industrial Organisations, 2nd Ed. The question has MC = 0.

Is max p just max profit? Because then it would make some sense for me. And how did they derive the first order condition from this? All I found was that (∂π / ∂q) = 0, but please do explain where this comes from? Also, why is consumer surplus just the square of the total demand from a type 1 consumer?

Thank you so much in advance!

**Tags:** microeconomics, monopoly, industrial-organisation, monopolistic-competition


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## 1 answers

### Answer by username_1 on 2023-07-27. Score: 1

$max\_p f(p)$ just means the maximal value of expression of $f(p)$ with regards to $p$ (meaning the value of $f(p)$ is checked over the whole range of $p$'s possible values).

In your case it does indeed mean the maximal profit value the monopolist can attain.

The given first order condition is a derivative of the expression with respect to $p$, divided by 3. Division by 3 is fine since the right hand side of the first order condition is 0, which divided by 3 will remain 0.

> **Comments:**
> **username_0**: how do they get 1 - 2p, then? and not just 1 - p?  
> **username_0**: also, I hope you could explain the consumer surplus being (1-p)^2, please?  
> **username_1**: 1. This is the derivative of the function. 2. Please ask new questions as new questions.  
> **username_0**: ... I had already asked that in the original question lol. chill tho, thanks for your help.  

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