<p>Here's how I would solve it : </p>

<p>Finding Q, P, and $\pi$</p>

<p>$AR = 20 - 2Q$</p>

<p>Know : $AR = \frac{R}{Q}$ and $R = PQ$</p>

<p>Therefore : </p>

<p>$R = 20Q - 2Q^2$</p>

<p>$PQ = 20Q - 2Q^2$</p>

<p>$\Rightarrow$ $ P = 20 - 2Q$ $\hspace{22mm} (1)$</p>

<p>$\Rightarrow$ $ Q = \frac{P - 20}{2}$ $\hspace{28mm} (2)$</p>

<p>$\Rightarrow$ $ \pi = 20Q - 2Q^2 - C$ $\hspace{8mm} (3)$</p>

<p>Additional Information : </p>

<p>$AC = 3Q$ and $MC = MR$</p>

<p>Know : $AC = \frac{C}{Q}$ </p>

<p>Therefore : </p>

<p>$C = 3Q^2$ </p>

<p>Max $\pi$</p>

<p>$ \pi = 20Q - 2Q^2 - 3Q^2$</p>

<p>$\frac{\partial \pi}{\partial Q} = 20 - 4Q - 6Q = 0$</p>

<p>Solve for Q then plug into (1) to find P:</p>

<p>$Q = 2$ and $P = 16$</p>

<p>Plug P and Q into $\pi$</p>

<p>$\pi = 20(2) - 2(2^2) - 3(2^2)$</p>

<p>$\pi = 20$</p>

<p><img src="https://i.sstatic.net/CXWyR.png" alt="enter image description here"></p>

CC BY-SA 3.0
2015-01-11T18:21:35.480Z
And in case there are extra conditions: **AC=3Q** and **MC=MR** I get results Q=2, P=16, TP=20. Dont ask me how I get it :D Are the results OK?
Luxqs
CC BY-SA 3.0
2015-01-11T18:51:02.510Z
I think you're missing some other information.  Did you get those answers from a solutions manual?  Is this from a book?
Amstell
CC BY-SA 3.0
2015-01-11T18:57:48.770Z
Consider that the company maximizes profit. That is only extra information. Someone else calculated it. If you got some other results, let me know. Thanks.
Luxqs
CC BY-SA 3.0
2015-01-11T19:01:29.363Z
Ok....it looks good then.  Please mark as answered :)
Amstell
CC BY-SA 3.0
2015-01-11T19:02:09.570Z
Sorry but how do they get it?
Luxqs
CC BY-SA 3.0
2015-01-11T19:13:59.663Z
I've updated the answer....let me know if you have questions....i think I got all the equations formatted correctly
Amstell
CC BY-SA 3.0
2015-01-11T18:11:12.747Z
2015-01-11T19:13:06.093Z
2015-01-11T19:13:06.093Z
Amstell
<p>Only data I have is Average Revenue: <strong>AR=20-2Q</strong> </p>

<p>How can I calculate <strong>Q</strong> - Quantity, <strong>P</strong> - Price and Total Profit - <strong>TP</strong>?</p>

<p>Thanks for help</p>

CC BY-SA 3.0
2015-01-11T17:48:01.393Z
This is not mathematical economics but homework, so please change the tagging. Also, what exactly is "Total Price"?
Alecos Papadopoulos
CC BY-SA 3.0
2015-01-11T17:50:49.960Z
Sorry its Total Profit
Luxqs
CC BY-SA 3.0
2015-01-12T05:02:04.480Z
This question does not meet the standards for homework question as spelled out in the relevant meta posts (see [here](http://meta.economics.stackexchange.com/questions/24/how-should-we-deal-with-homework-questions)).
jmbejara
CC BY-SA 3.0
2015-01-12T06:50:35.410Z
Sorry, it was the fastest way to help my girlfriend for tomorrow's exam. Next time I will do my best :)
Luxqs
<industrial-organisation>
How can I calculate Q, P, TP from AR=20-2Q?
Luxqs
# How can I calculate Q, P, TP from AR=20-2Q?

(Asked by: username_0 on 2015-01-11)

Only data I have is Average Revenue: **AR=20-2Q**

How can I calculate **Q** - Quantity, **P** - Price and Total Profit - **TP**?

Thanks for help

**Tags:** industrial-organisation
> **Comments:**
> **username_1**: This is not mathematical economics but homework, so please change the tagging. Also, what exactly is "Total Price"?  
> **username_0**: Sorry its Total Profit  
> **username_2**: This question does not meet the standards for homework question as spelled out in the relevant meta posts (see [here](http://meta.economics.stackexchange.com/questions/24/how-should-we-deal-with-homework-questions)).  
> **username_0**: Sorry, it was the fastest way to help my girlfriend for tomorrow's exam. Next time I will do my best :)  

---

## 1 answers

### Answer by username_3 on 2015-01-11. Score: 4 | Accepted answer

Here's how I would solve it :

Finding Q, P, and $\pi$

$AR = 20 - 2Q$

Know : $AR = \frac{R}{Q}$ and $R = PQ$

Therefore :

$R = 20Q - 2Q^2$

$PQ = 20Q - 2Q^2$

$\Rightarrow$ $ P = 20 - 2Q$ $\hspace{22mm} (1)$

$\Rightarrow$ $ Q = \frac{P - 20}{2}$ $\hspace{28mm} (2)$

$\Rightarrow$ $ \pi = 20Q - 2Q^2 - C$ $\hspace{8mm} (3)$

Additional Information :

$AC = 3Q$ and $MC = MR$

Know : $AC = \frac{C}{Q}$

Therefore :

$C = 3Q^2$

Max $\pi$

$ \pi = 20Q - 2Q^2 - 3Q^2$

$\frac{\partial \pi}{\partial Q} = 20 - 4Q - 6Q = 0$

Solve for Q then plug into (1) to find P:

$Q = 2$ and $P = 16$

Plug P and Q into $\pi$

$\pi = 20(2) - 2(2^2) - 3(2^2)$

$\pi = 20$

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

> **Comments:**
> **username_0**: And in case there are extra conditions: **AC=3Q** and **MC=MR** I get results Q=2, P=16, TP=20. Dont ask me how I get it :D Are the results OK?  
> **username_3**: I think you're missing some other information.  Did you get those answers from a solutions manual?  Is this from a book?  
> **username_0**: Consider that the company maximizes profit. That is only extra information. Someone else calculated it. If you got some other results, let me know. Thanks.  
> **username_3**: Ok....it looks good then.  Please mark as answered :)  
> **username_0**: Sorry but how do they get it?  
> **username_3**: I've updated the answer....let me know if you have questions....i think I got all the equations formatted correctly  

---

