<p><span class="math-container">$\pi _{i}=p_{i}. q_{i}-c_{i}. q_{i}$</span>
Do you talk about this equation ?</p>
<p>This is a very traditional equation for profit. It just means that the profit of a firm <span class="math-container">$i$</span> is given by the difference between revenues and costs. The revenues are linked to the quantity <span class="math-container">$q$</span> of goods sold at price <span class="math-container">$p$</span>. Thus <span class="math-container">$p\times q$</span> is the total revenue of the firm here.
For the cost, each quantity of goods need to buy some intermediate goods, or to pay employees, etc, thus generate a cost <span class="math-container">$c$</span> for each good. Thus, <span class="math-container">$q\times c$</span> reprersent the total cost. Now, we have the total equation for profit.</p>
<p>The objective of the firm in most models is to maximize its profit. In other words, the firm wants to maximize the profit function. Maximization problem heavily relies on derivatives, but here it's a very simple problem. The optimum (max ou min) of a function is when the first derivative of the function is equal to 0. In some cases (perfect competition), firms can't change the prices <span class="math-container">$p$</span>, they can only change the quantity produced. Thus, the firm wants to maximize profit with respect to (w.r.t) quantities, which can be written like that :
<span class="math-container">$\begin{equation} \frac{\partial \pi}{\partial q_i}=0 \end{equation}$</span></p>
<p>Now, you need to calculated the derivative of the profit function w.r.t to quantites, which gives  :</p>
<p><span class="math-container">$\begin{equation}\max {\pi} \equiv \frac{\partial \pi}{\partial q_i}= p_i -c_i =0 \end{equation}$</span></p>
<p>Note that you can rewrite it like that : <span class="math-container">$p_i =c_i$</span>
What does it mean ? It means that in perfect competition, firms that want to maximize its profit will have to equalize price and marginal costs. In other words, in perfect competition, marginal revenue (price) = marginal cost. This is a very important result !</p>

CC BY-SA 4.0
2024-05-30T14:45:13.370Z
No, not that one. That one is easy to solve. I am talking about the inequality of what look like second derivatives.
DanceroftheStars
CC BY-SA 4.0
2024-05-30T14:50:07.930Z
This one ? $\frac{\partial^2 R}{\partial Q^{2}}< \frac{\partial^2 C}{\partial Q^2}$. It means that cost functions grows faster than revenue function I guess, so you know that profit can be maximized
justaneconomist
CC BY-SA 4.0
2024-05-30T10:06:18.890Z
2024-05-30T10:06:18.890Z
justaneconomist
<p>So, I found a formula for Profit Maximization on this page.</p>
<p><a href="https://en.m.wikipedia.org/wiki/Profit_maximization" rel="nofollow noreferrer">https://en.m.wikipedia.org/wiki/Profit_maximization</a></p>
<p>Listed in the <strong>Marginal Revenue- marginal cost perspective</strong> section.</p>
<p>My question is, what exactly do the different variables mean in the given equation. (I looked at the sources, and it was a book, so I can't easily access it). And how would I go about solving it. As I am bad at derivates and can't find any information on how to solve one without it proceeding any formula.</p>
<p>Like, I can solve a derivative of x^2, but I have no clue how to handle it if it is the derivative of nothing. I also have no clue what the variable by the top d is.  Please display through an example, if possible.</p>
<p>I am sorry for being a bother. I just am having trouble finding any way for this to be solvable. I feel I am misunderstanding something somewhere.</p>

CC BY-SA 4.0
2024-05-30T06:03:23.857Z
Can you write out the actual question you'd like help with?
I can't really tell from the link you give.
matthewoulton
CC BY-SA 4.0
2024-05-31T11:55:01.820Z
@DanceroftheStars You should write explicitely in the question the equations you want to be clarified, otherwise people don't understand what they should answer.
BakerStreet
<mathematical-economics><profit-maximization>
Confusion on the Profit Maximization Equation
DanceroftheStars
# Confusion on the Profit Maximization Equation

(Asked by: username_0 on 2024-05-30)

So, I found a formula for Profit Maximization on this page.

<https://en.m.wikipedia.org/wiki/Profit_maximization>

Listed in the **Marginal Revenue- marginal cost perspective** section.

My question is, what exactly do the different variables mean in the given equation. (I looked at the sources, and it was a book, so I can't easily access it). And how would I go about solving it. As I am bad at derivates and can't find any information on how to solve one without it proceeding any formula.

Like, I can solve a derivative of x^2, but I have no clue how to handle it if it is the derivative of nothing. I also have no clue what the variable by the top d is. Please display through an example, if possible.

I am sorry for being a bother. I just am having trouble finding any way for this to be solvable. I feel I am misunderstanding something somewhere.

**Tags:** mathematical-economics, profit-maximization

> **Comments:**
> **username_1**: Can you write out the actual question you'd like help with? I can't really tell from the link you give.  
> **username_2**: @username_0 You should write explicitely in the question the equations you want to be clarified, otherwise people don't understand what they should answer.  

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## 1 answers

### Answer by username_3 on 2024-05-30. Score: 1

$\pi \_{i}=p\_{i}. q\_{i}-c\_{i}. q\_{i}$
Do you talk about this equation ?

This is a very traditional equation for profit. It just means that the profit of a firm $i$ is given by the difference between revenues and costs. The revenues are linked to the quantity $q$ of goods sold at price $p$. Thus $p\times q$ is the total revenue of the firm here.
For the cost, each quantity of goods need to buy some intermediate goods, or to pay employees, etc, thus generate a cost $c$ for each good. Thus, $q\times c$ reprersent the total cost. Now, we have the total equation for profit.

The objective of the firm in most models is to maximize its profit. In other words, the firm wants to maximize the profit function. Maximization problem heavily relies on derivatives, but here it's a very simple problem. The optimum (max ou min) of a function is when the first derivative of the function is equal to 0. In some cases (perfect competition), firms can't change the prices $p$, they can only change the quantity produced. Thus, the firm wants to maximize profit with respect to (w.r.t) quantities, which can be written like that :
$\begin{equation} \frac{\partial \pi}{\partial q\_i}=0 \end{equation}$

Now, you need to calculated the derivative of the profit function w.r.t to quantites, which gives :

$\begin{equation}\max {\pi} \equiv \frac{\partial \pi}{\partial q\_i}= p\_i -c\_i =0 \end{equation}$

Note that you can rewrite it like that : $p\_i =c\_i$
What does it mean ? It means that in perfect competition, firms that want to maximize its profit will have to equalize price and marginal costs. In other words, in perfect competition, marginal revenue (price) = marginal cost. This is a very important result !

> **Comments:**
> **username_0**: No, not that one. That one is easy to solve. I am talking about the inequality of what look like second derivatives.  
> **username_3**: This one ? $\frac{\partial^2 R}{\partial Q^{2}}< \frac{\partial^2 C}{\partial Q^2}$. It means that cost functions grows faster than revenue function I guess, so you know that profit can be maximized  

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