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Given some unspecified demand and supply functions.

I need to calculate quantity and price after taxation, but what is the difference between having a tax of 20% of total revenue and 20% of profits ($\pi$)? I mean how to calculate this tax in those two cases? And what precisely should be changed when calculating Q and P after tax of those two types is imposed on.

Whether tax of 20% of total revenue creates simply consumer price on a level of $1.2(\text{producerprice})$ or is it something different? In case of profits is it $0.8(\text{supplyfunction})$? **hope this question now satisfies required format **

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    $\begingroup$ It remains always a homework question even after your edit. You can ask your homework questions but you should show what you have tried and tell us where you stuck. Unless, nobody will give an answer once they understand that it is a homework question without effort made. $\endgroup$ – optimal control Feb 1 '16 at 14:30
  • $\begingroup$ I was trying to follow sites policy on homework questions i.e. to make it more general. What if some questions are short thus you cannot be stuck at any point as the question is obviously too short? $\endgroup$ – mkropkowski Feb 2 '16 at 10:40
  • $\begingroup$ No better? I do not understand this strange attitude towards question of this kind, frankly you have no idea whether it's a homework question or not. It may be simply a question from a book i am reading right know. Am i right? $\endgroup$ – mkropkowski Feb 2 '16 at 10:44
  • $\begingroup$ @mkopkowski It is not strange at all. For this kind of short questions, If you don't show where you stuck in terms of reasoning or calculation, we assume that you did not make any effort. Do edit your question in this way, with words or calculations to tell us where you stuck. If you are not giving any effort, nobody will make any effort. $\endgroup$ – optimal control Feb 2 '16 at 13:31
  • $\begingroup$ I think i have added the point where i am stuck $\endgroup$ – mkropkowski Feb 2 '16 at 13:38
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Deriving those functions, you can find $p^*$ and $Q^*$, which, multiplying both, should give you equilibrium profits. Now, if you take that tax rate (20%, I reckon?), you can calculate taxes over profits and the tax-free price.

To find the equilibrium price $p^*$, you need to have those two functions in a system and solve for $p$. Then, just replace it on both functions and you should have equilibrium quantities.

Now, I'm assuming demand absorves all quantities produced by companies, no production restrictions and that this market is one in perfect competition. If this last paragraph changes, then my solution will not be correct. To answer your question - what is the difference -, well, in this case, it is none because we are not considering production costs. If we did, you can see that both values would change.

Nevertheless, to calculate taxes, you need to work around with the system. That will give you total revenues, cost and tax free. Applying 20% leads to net earnings, because you do not have any production costs associated with the problem - something commonly done in Economics. That or consider a variable $c$ of costs.

This kind of exercises are also good to understand what are the effects of costs on revenues/profits. There's actually a financial term for that but I cannot recall :)

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