How Do I Calculate the After-Tax Equilibrium Quantity of a Supply and Demand Graph? 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:


$Q_S=Q_D$
$360P-720 = 960-120P$
$480P = 1680$
$P = 3.5$
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.
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



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.