Quantitative Analysis of Taxes: Videos & Practice Problems

To calculate the new equilibrium price and quantity when a tax is imposed on suppliers, you first adjust the supply equation by substituting the price variable $P$ with $P-\mathrm{tax}$. For example, if the original supply equation is $Q=\; 2P-\; 6$ and the tax is \$1, the new supply equation becomes $Q=\; 2(P-\; 1)\; -\; 6\; =\; 2P-\; 8$. Next, set this new supply equal to the demand equation, such as $Q=\; 10\; -P$, and solve for $P$. This gives the new equilibrium price. Substitute this price back into either equation to find the equilibrium quantity. This method accounts for the tax shifting the supply curve and helps determine the market's new balance.

After a tax is applied, the price buyers pay is higher than the price sellers receive by the amount of the tax. The tax creates a wedge between these two prices. For example, if the tax is \$1 and the new equilibrium price (the price buyers pay) is \$6, then sellers receive $P$_s = 6 - 1 = 5. Buyers pay the full market price, while sellers receive the market price minus the tax. This difference reflects the tax incidence, showing how the tax burden is shared between buyers and sellers.

We replace $P$ with $P-\mathrm{tax}$ in the supply equation because the suppliers effectively receive less money per unit sold after paying the tax. The tax reduces the amount suppliers keep, so the price they receive is the market price minus the tax. This substitution shifts the supply curve upward (or leftward), reflecting the higher cost of supplying each unit due to the tax. It allows us to calculate the new equilibrium considering the tax burden on suppliers.

Imposing a tax on suppliers generally decreases the market equilibrium quantity. The tax increases the cost of supplying goods, shifting the supply curve upward or leftward. This results in a higher price for buyers and a lower effective price for sellers. Because the price buyers pay rises and sellers receive less, the quantity demanded and supplied at the new equilibrium decreases. For example, if the original equilibrium quantity was higher, after a \$1 tax on suppliers, the equilibrium quantity might fall to 4 units, reflecting reduced market activity due to the tax.

Interestingly, it does not matter who is legally responsible for paying the tax; the final prices buyers pay and sellers receive will be the same. Whether the tax is imposed on suppliers or buyers, the market adjusts so that the economic burden is shared according to the relative elasticities of supply and demand. The tax shifts either the supply or demand curve, but the equilibrium price difference between buyers and sellers equals the tax amount. This concept is known as tax incidence, showing that legal responsibility does not determine who ultimately bears the tax burden.