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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

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  • $\begingroup$ This is not mathematical economics but homework, so please change the tagging. Also, what exactly is "Total Price"? $\endgroup$ – Alecos Papadopoulos Jan 11 '15 at 17:48
  • $\begingroup$ Sorry its Total Profit $\endgroup$ – Luxqs Jan 11 '15 at 17:50
  • $\begingroup$ This question does not meet the standards for homework question as spelled out in the relevant meta posts (see here). $\endgroup$ – jmbejara Jan 12 '15 at 5:02
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    $\begingroup$ Sorry, it was the fastest way to help my girlfriend for tomorrow's exam. Next time I will do my best :) $\endgroup$ – Luxqs Jan 12 '15 at 6:50
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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 $\pi$

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

$\pi = 20$

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  • $\begingroup$ 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? $\endgroup$ – Luxqs Jan 11 '15 at 18:21
  • $\begingroup$ I think you're missing some other information. Did you get those answers from a solutions manual? Is this from a book? $\endgroup$ – Amstell Jan 11 '15 at 18:51
  • $\begingroup$ 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. $\endgroup$ – Luxqs Jan 11 '15 at 18:57
  • $\begingroup$ Ok....it looks good then. Please mark as answered :) $\endgroup$ – Amstell Jan 11 '15 at 19:01
  • $\begingroup$ Sorry but how do they get it? $\endgroup$ – Luxqs Jan 11 '15 at 19:02

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