The excise tax in Per-Unit Taxes raised the buyers' price by part of the tax and lowered the sellers' price by the rest. How the burden splits depends on elasticity (Price Elasticity of Supply, Elastic, Inelastic and What Decides It), not on who writes the check.
Key idea
Tax incidence is who really bears a tax. Buyers bear $P_b - P^*$ per unit and sellers bear $P^* - P_s$; the two add up to the tax. The less elastic side of the market bears more of the tax, whoever is legally required to pay it.
Why it works
A tax pushes buyers and sellers apart. Whichever side can more easily walk away (buy a substitute, or sell something else) does, and so avoids most of the tax; the side with few alternatives is stuck absorbing it. If demand is very inelastic, like demand for gasoline in the short run, buyers keep buying, and the price they pay rises by nearly the whole tax. If supply is very inelastic, like the supply of land, sellers can't reduce what they offer, and their price falls by nearly the whole tax.
Worked example: Splitting a \$3 tax
$Q_d = 24 - P$ and $Q_s = -6 + 2P$. A \$3 tax is collected from sellers. How much of it do buyers bear?
- Before the tax: $24 - P = -6 + 2P$, so $P^* = 10$ and $Q^* = 14$.
- With the tax: $24 - P_b = -6 + 2(P_b - 3)$, so $36 = 3P_b$, $P_b = 12$ and $P_s = 9$.
- Buyers bear $\$12 - \$10 = \$2$ per unit ($\tfrac{2}{3}$); sellers bear $\$10 - \$9 = \$1$ ($\tfrac{1}{3}$).
- At $P^* = 10$, $Q^* = 14$: demand's elasticity is $1 \times \tfrac{10}{14} \approx 0.71$ and supply's is $2 \times \tfrac{10}{14} \approx 1.43$. Buyers, the less elastic side, bear more.
Answer: \$2 of the \$3, two thirds.
Worked example: Reasoning without numbers
A city taxes each pack of cigarettes, collected from stores. Smokers' demand is very inelastic, while stores can easily sell other products. Who bears most of the tax?
- Demand is the less elastic side.
- So the price smokers pay rises by most of the tax, and stores' price falls only a little.
Answer: Mostly the smokers, although the stores send in the money.
Common mistake
Thinking whoever is legally required to pay the tax also bears its burden. The law decides who sends the check; the elasticities decide who ends up poorer. A payroll tax split "half and half" on paper falls mostly on workers if labor supply is less elastic than labor demand. Check: compare the price each side ends up with to the old equilibrium price.