Taxes and Price Ceilings

Put a tax on cigarettes and a cap on rent, then see who actually pays.

A tax drives a wedge between the price buyers pay and the price sellers get. The wedge lands heavier on the side that cannot walk away. A price ceiling freezes the price but makes buyers line up instead. The formula below splits the tax burden.

For example, add a 100-won tax to one 🍬 candy. A 🧑 classmate who cannot live without candy pays almost all of the higher price. A classmate who can take it or leave it just stops buying. Then the 🏪 shop cuts its own price and shoulders the tax.

Pb=Ps+tP_b = P_s + t
buyer share=db+d\text{buyer share} = \frac{d}{b + d}

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Examples & Exercises

A tax of 33 is slapped on cigarettes.

If demand is price-insensitive (Qd=10−0.5PQ_d = 10 - 0.5P), who mostly pays it?

Tax 33, demand responsiveness 0.50.5 — insensitive demand.
Show proof

  1. The tax wedge is Pb=Ps+3P_b = P_s + 3. Solving gives the seller's price Ps≈5.67P_s \approx 5.67 and the buyer's price Pb≈8.67P_b \approx 8.67.

  2. Against the pre-tax price 6.676.67, buyers pay 22 more and sellers receive 11 less — 67%67\% of the tax lands on consumers. The side that cannot walk away pays the tax.

A rent ceiling of 33 is imposed on a market whose equilibrium price is 55.

What happens?

Ceiling 33, no tax — default demand and supply.
Show proof

  1. At the ceiling price 33, buyers want Qd=10−3=7Q_d = 10 - 3 = 7 while sellers offer only Qs=3Q_s = 3.

  2. The gap of 44 is the shortage. A policy meant to make things cheaper creates a queue of people who want to buy but cannot — the red dashed line in the picture is that boundary.

1. Intro to Microeconomics