Quantitative Analysis of Taxes: Videos & Practice Problems

To calculate the new equilibrium price and quantity after a tax on suppliers, you first adjust the supply equation by replacing the price variable $p$ with $p-\mathrm{tax}$. For example, if the original supply equation is $\mathrm{Q\_s}=2p-6$ and the tax is \$1, the new supply equation becomes $\mathrm{Q\_s}=2(p-1)-6=2p-8$. Next, set this new supply equal to the demand equation, for example, $\mathrm{Q\_d}=10-p$, 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's effect on supply, shifting the supply curve and changing the market equilibrium.

When a tax is imposed on suppliers, the price buyers pay and the price sellers receive differ by the amount of the tax. The buyers pay the new equilibrium price $\mathrm{P\_B}$, which is found by solving the market equilibrium with the shifted supply curve. Sellers receive the price after the tax is deducted, calculated as $\mathrm{P\_S}=\mathrm{P\_B}-\mathrm{tax}$. For example, if the equilibrium price buyers pay is \$6 and the tax is \$1, sellers receive \$5. This difference reflects the tax burden shared between buyers and sellers, with sellers effectively receiving less per unit sold due to the tax.

We replace price $p$ with $p-\mathrm{tax}$ in the supply equation because the tax reduces the amount suppliers effectively receive per unit sold. The suppliers must pay the tax to the government, so their net revenue per unit is the market price minus the tax. This substitution shifts the supply curve upward (or leftward), reflecting the higher cost of supplying each unit. It allows us to accurately calculate the new equilibrium price and quantity by incorporating the tax's impact on suppliers' incentives.

Imposing a tax on suppliers generally decreases the market equilibrium quantity. The tax increases suppliers' costs, shifting the supply curve upward or leftward, which leads to a higher price for buyers and a lower quantity supplied. When the new supply curve is set equal to the demand curve, the resulting equilibrium quantity is lower than before the tax. For example, if the original equilibrium quantity was higher, after a \$1 tax on suppliers, the equilibrium quantity might decrease to 4 units, reflecting reduced market activity due to the tax.

Interestingly, it does not matter whether the tax is imposed on buyers or sellers when calculating the new equilibrium price and quantity. The economic incidence of the tax—the division of the tax burden between buyers and sellers—remains the same. The difference lies in which curve shifts: a tax on sellers shifts the supply curve, while a tax on buyers shifts the demand curve. However, both approaches lead to the same equilibrium price paid by buyers and quantity traded. This is because the market adjusts to the tax regardless of who is legally responsible for paying it.