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Suppose we have the following system of equations:

$Q_s=-20+3P$
$Q_d=-220-5P$
$Q_s=Q_d$

Say we want to find the tax burden of the consumer, the tax burden of the firm, and the total revenue generated for the government for some excise tax t.

Do we do this by looking at the elasticity of each the supplier and consumer?

The Elasticity of Q with respect to P can be calculated by:

$\eta_Q,_P = P/Q*dQ/dP$

With this we see that the elasticity of supply is 3 and the elasticity of demand is -5

Can we use these to find the tax burden? And how do we calculate the government tax revenue in terms of t for the government?

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migrated to math.stackexchange.com by Jason B May 1 '12 at 19:55

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is this a homework question, by any chance? –  EnergyNumbers Nov 2 '11 at 7:41
    
Nope, I'm studying for a test tomorow. I missed a lecture and my prof was going over problems such as these. I don't care about the specific solution, I just want to know the method used :) –  Cplayer Nov 2 '11 at 7:57
    
in that case, the approach will be the same - it will be more helpful for you to get hints on how to solve it, than just given the solution - after all, this question with those exact coefficients is unlikely to be coming up on the test! –  EnergyNumbers Nov 2 '11 at 8:04

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