Tax Incidence Calculator
Learn who really bears a tax using a student-friendly Tax Incidence Calculator. Enter a linear demand curve and supply curve, add a per-unit tax, and instantly see the before-tax equilibrium, after-tax equilibrium, buyer price, seller price, consumer burden, producer burden, tax revenue, and deadweight loss.
Background
Tax incidence asks how the burden of a tax is split between buyers and sellers. Even if the government legally collects the tax from only one side, the economic burden is usually shared. The more inelastic side of the market generally bears more of the tax burden.
How to use this calculator
- Enter a linear demand curve in the form P = a − bQ.
- Enter a linear supply curve in the form P = c + dQ.
- Enter the per-unit tax, choose whether it is legally placed on buyers or sellers, then click Calculate.
How this calculator works
- Before tax, equilibrium is where a − bQ = c + dQ.
- With a tax on sellers, the effective supply becomes P = c + dQ + t.
- With a tax on buyers, the effective demand becomes P = a − bQ − t.
- The calculator then shows the price paid by buyers, the price received by sellers, and how the tax burden is split.
Formulas & Equations Used
Demand: P = a − bQ
Supply: P = c + dQ
Before-tax equilibrium quantity: Q* = (a − c)/(b + d)
After-tax quantity: Q_t = (a − c − t)/(b + d)
Tax revenue: TR = t · Q_t
Deadweight loss: DWL = 0.5 · t · (Q* − Q_t)
Example Problem & Step-by-Step Solution
Example 1 — Finding tax incidence in equation form
Suppose demand is P = 100 − 2Q, supply is P = 20 + Q, and the government imposes a tax of t = 12 per unit.
- Before tax, solve 100 − 2Q = 20 + Q to get Q* = 26.67.
- Substitute back to find the original equilibrium price: P* = 46.67.
- With the tax on sellers, solve 100 − 2Q = 20 + Q + 12 to get Q_t = 22.67.
- Buyer price becomes P_b = 54.67.
- Seller price becomes P_s = 42.67.
- Buyers bear 8 per unit of the tax, while sellers bear 4 per unit.
Example 2 — Sellers bear more of the tax burden
Suppose demand is P = 100 − 0.5Q, supply is P = 10 + 2Q, and the tax is t = 12 per unit.
- Before tax, solve 100 − 0.5Q = 10 + 2Q to get Q* = 36.
- Original equilibrium price is P* = 82.
- With the tax, solve 100 − 0.5Q = 10 + 2Q + 12 to get Q_t = 31.2.
- Buyer price becomes P_b = 84.4.
- Seller price becomes P_s = 72.4.
- Buyers bear 2.4 per unit, while sellers bear 9.6 per unit.
- This shows sellers bear more of the tax burden in this market.
Example 3 — Buyers bear more of the tax burden
Suppose demand is P = 120 − 3Q, supply is P = 20 + 0.5Q, and the tax is t = 12 per unit.
- Before tax, solve 120 − 3Q = 20 + 0.5Q to get Q* ≈ 28.57.
- Original equilibrium price is P* ≈ 34.29.
- With the tax, solve 120 − 3Q = 20 + 0.5Q + 12 to get Q_t ≈ 25.14.
- Buyer price becomes P_b ≈ 44.57.
- Seller price becomes P_s ≈ 32.57.
- Buyers bear about 10.28 per unit, while sellers bear about 1.72 per unit.
- This shows buyers bear more of the tax burden in this market.
Frequently Asked Questions
Q: What is tax incidence?
Tax incidence is the actual split of the tax burden between buyers and sellers, regardless of which side legally sends the payment to the government.
Q: Does it matter whether the tax is placed on buyers or sellers?
In the standard linear competitive-market model, the final economic burden is the same either way. The legal assignment changes the shifted curve, but not the final incidence split.
Q: Who bears more of the tax burden?
Usually the side that is less price-responsive, or more inelastic, bears more of the tax burden.
Q: Why does quantity fall after a tax?
The tax drives a wedge between the buyer price and seller price, so fewer mutually beneficial trades take place.