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Suppose the supply of a good is given by the equation $Q_S = 360*P_S - 720$. And the demand for a good is given by $Q_D = 960 - 120*P_D$. The government decides to levy a tax of \$2 per unit on the good, to be paid by the seller.

And I must find the equilibrium quantity of the curves, after the \$2 tax has been taken into account for. I know the equilibrium quantity is 540 before the tax based on the following calculations:

  1. $Q_S=Q_D$
  2. $360P-720 = 960-120P$
  3. $480P = 1680$
  4. $P = 3.5$
  5. If we sub in 3.5 into both equations ($Q_S$ and $Q_D$) then we get 540.

Therefore, the equilibrium quantity is 540 before taxes have been taken into account. However, I am unsure how to figure out the equilibrium quantity after the tax.

Does anyone know how to go about solving this issue?

All help is appreciated.

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    $\begingroup$ Hi! We prefer you type in the information from the pictures. There are several reasons for this. meta.economics.stackexchange.com/questions/1365/ Additionally, you should show what you've tried so far, otherwise this will be closed as a homework question with no effort shown. $\endgroup$ – dismalscience Oct 13 '15 at 23:41
  • $\begingroup$ So how would you represent the tax in this system of equations? A \$2 per-unit tax is equivalent to the seller receiving 2 fewer dollars per unit, right? First, which equation should change? Second, how should that equation change? $\endgroup$ – dismalscience Oct 14 '15 at 0:06
  • $\begingroup$ The supply equation (Qs) should change, I think. I have tried (360(1.5) - 720 = -180), since 3.5-2 = 1.5. But, I don't think that the new equilibrium quantity is a negative. $\endgroup$ – Kelsey Oct 14 '15 at 0:11
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    $\begingroup$ Ah! I see your problem. You've written it as though the price will decrease by 2. Why should the price decrease by two? Perhaps instead the supplier will ask for a higher price to offset the tax, and the buyers will pay some of the increased price, resulting in a new price and quantity? Remember that the consequence of a tax is that the supplier is now receiving $2 less than the demander is paying. Consider inserting a new equation to reflect this: Ps=Pd-2, and rearrange the equations for the supply and demand curves so that you you're solving for price, rather than quantity. $\endgroup$ – dismalscience Oct 14 '15 at 0:19
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Implementing @dismalscience comment suggestion, the unit tax burdens the suppliers. So the demand schedule is not affected, only supply. How? Since the tax is fixed per unit sold (and not a percentage charge), then the slope of the supply curve should not change. Therefore what remains is an upwards shift, that will lead to increased equilibrium price-decreased equilibrium quantity. The algebra should lead one to

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One could see this as a fixed shift in overall (not just production) marginal cost: the quantity has the same production marginal cost as before -but now "$2" is added as an obligation per unit, to cover the tax.

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