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Taxes & Subsidies

A tax of 6 per unit: do buyers pay it, or sellers? Usually both, in proportions set by the slopes of the curves. See the new prices, the tax revenue, and the trade that no longer happens — or what a subsidy costs.

EconomicsTaxesWelfare
Inputs
Input examples
Straight lines: demand Qd = A − B·P, supply Qs = C + D·P. A tax per unit drives a wedge between the price buyers pay and the price sellers keep; it does not matter who hands it to the government. A subsidy does the opposite.

Who Really Pays a Tax?

A tax raises the price buyers pay and lowers the price sellers keep; the difference is the tax. How it is split — the tax incidence — depends only on how strongly each side reacts to the price. The side that cannot easily walk away, the less elastic one, carries more of the burden.

Because the price goes up, some trades that would have been worth it no longer happen. The value they would have created is simply lost: the deadweight loss, the triangle in the chart. A subsidy creates the opposite situation, but costs the government more than buyers and sellers gain.

buyers’ share= D / (B + D)
inelastic sidepays more
DWLgrows with t²
who pays it indoes not matter

The Tax Wedge

tax
demand
supply (dashed: shifted by the tax)
tax revenue
deadweight loss
Result
Enter the values above

Bigger Taxes

your curves
Tax per unitQuantityRevenueDeadweight loss

Worked Techniques

Price with a Tax

Demand at the buyers’ price must equal supply at the sellers’ price.

Example: tax 6: buyers pay 24 (was 20), sellers keep 18.
Tax Revenue

The tax per unit times the units still traded. Raise the tax far enough and revenue falls again, because trade dries up.

Example: 6 × 520 = 3 120.
Deadweight Loss

The triangle between the curves for the units that are no longer traded. Doubling the tax makes it four times as large.

Example: ½ × 6 × (600 − 520) = 240.

Sources & Verification

References
  1. N. G. Mankiw, Principles of Economics, 9th ed., Cengage, 2021 — Ch. 6 (Supply, Demand, and Government Policies) and Ch. 8 (Application: The Costs of Taxation).