Australian Government has imposed a tax on Beer. Assume that the tax on Beer is $20 per unit (a unit is a carton of drinks) Assume the demand and supply functions for cartons of Beers per week are: P=200 - 0.5Q and P=0.5Q.

Calculate the amount of tax revenue collected by the government and the distribution of tax payments between buyers and sellers.

Now so far i could do the following

since in equilibrium qty demanded equals qty. supplied. So from the demand and supply functions we get,

0.5Q=200-0.5Q Q=200

So P=0.5*200= 100

Now i get that after tax imposition the supply curve will move leftward, hence the equilibrium price will increase and quantity demanded/supply will decrease. Now please help me to calculate the amount of tax revenue and tax distribution.

  • $\begingroup$ After the tax is imposed, the demanders pay $20 more than the suppliers receive. So instead of two variables, you've got three: Q, Pd, and Ps (the quantity, the price the demanders pay, and the price the suppliers receive). You've also got three equations: The supply curve relates Q to Ps, the demand curve relates Q to Pd, and the third equation is Pd=Ps+20. Now solve the three equations in three unknowns. $\endgroup$ – WillO May 17 '15 at 3:30
  • $\begingroup$ Why does this question have 16k views? $\endgroup$ – user223391 Oct 11 '15 at 4:26

Presumably, your equations for demand and supply are before tax. You have found the volume correctly. We assume the units of $P$ and $Q$ are cartons, though this seems incongruous with the scale of the equations. Now the demand equation doesn't change, but the supply equation should have $P$ replaced by $P-20$ as the producer gets that much less revenue from the selling price.


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