Ch2. Tax Principles and Tax Incidence

The Three Principles of a Good Tax System

A well-designed tax system should satisfy three principles.

1. Efficiency

A tax should not distort the behavior of economic actors more than necessary.

Excess burden (deadweight loss): The social cost of a tax that exceeds the revenue raised — the welfare loss imposed on the private sector beyond what the government collects.

Excess burden increases with the square of the tax rate
Taxing inelastic goods minimizes excess burden

Neutral tax: A tax that does not change relative prices and therefore creates no behavioral distortion. In theory, a lump-sum tax is perfectly neutral but fails on equity grounds.

2. Equity

The tax burden should be distributed fairly. There are two dimensions:

Principle	Content	Example
Horizontal equity	Similarly situated people should pay similar taxes	Two taxpayers with identical income pay the same tax
Vertical equity	Those with greater ability to pay should bear a larger burden	Higher-income earners face higher marginal rates

Ability-to-pay principle: The theoretical basis for vertical equity — those with higher income or wealth have greater capacity to contribute.

Benefit principle: Taxpayers should pay in proportion to the benefits they receive from government services. The federal gas tax (Highway Trust Fund) is a classic application.

3. Simplicity

The tax system should be easy to understand and inexpensive to administer.

Taxpayers must be able to comply without prohibitive costs
Administrative costs for the IRS and state agencies should be minimized
In practice, efficiency, equity, and simplicity often conflict

Tax Incidence: Who Actually Bears the Burden?

Statutory incidence: The party legally required to remit the tax.

Economic incidence: The party whose real income falls as a result of the tax.

Key principle: Statutory and economic incidence can differ. The party that remits the tax can shift the burden to others through market price changes.

Elasticity and Tax Burden Distribution

The distribution of a tax between buyers and sellers is determined by elasticity.

Basic rule: The less elastic (more inelastic) side bears a greater share of the tax burden.

Demand Elasticity and Burden

Demand elasticity	Consumer’s share	Producer’s share
Perfectly inelastic (= 0)	100%	0%
Unit elastic (= 1)	50%	50%
Perfectly elastic (= ∞)	0%	100%

Example — cigarette excise tax: Demand for cigarettes is inelastic. Therefore, most of the cigarette tax is borne by smokers. Tobacco companies can pass the tax increase to consumers through higher prices.

Supply Elasticity and Burden

Supply elasticity	Consumer’s share	Producer’s share
Perfectly inelastic (= 0)	0%	100%
Perfectly elastic (= ∞)	100%	0%

Example — land value tax: The supply of land is perfectly inelastic (fixed in quantity). Therefore, a land value tax falls entirely on landowners. Raising the land tax does not raise rents paid by tenants.

Tax Burden Formula

Producer’s share:

Producer's share = Ed / (Ed + Es)

Consumer’s share:

Consumer's share = Es / (Ed + Es)

Calculation example:

Ed = 1, Es = 3
Producer’s share = 1/(1+3) = 25%
Consumer’s share = 3/(1+3) = 75%

Capital Tax Incidence: Open vs. Closed Economy

Small Open Economy

In a small open economy, capital is perfectly mobile internationally.

When a capital tax is imposed:

Capital flows to lower-tax countries
To maintain the after-tax return at the international rate, the burden shifts from capital owners to workers through lower wages

Therefore, in a small open economy, a capital tax may be borne effectively by labor.

Closed Economy

In a closed economy where capital cannot move, the capital tax burden falls on capital owners.

Excess Burden Calculation

Deadweight loss (excess burden) of a tax:

Excess burden = (1/2) × t² × Ed × Qs

Where:

t = tax rate (as a decimal)
Ed = price elasticity of demand (absolute value)
Qs = pre-tax equilibrium quantity supplied

Key insight: Excess burden is proportional to the square of the tax rate. Doubling the tax rate quadruples the excess burden. This is why economists warn against high marginal tax rates.

Optimal Tax Theory

Economists have developed optimal taxation theory to balance efficiency and equity.

Inverse Elasticity Rule (Ramsey Rule)

To minimize excess burden: impose higher tax rates on goods with lower price elasticity of demand.

However, the inverse elasticity rule ignores equity. Necessities (food, medicine) have low elasticity but taxing them heavily is regressive — a serious equity concern.

Optimal Income Tax Design

Set an exemption threshold (to ensure progressivity)
The optimal marginal rate is inversely proportional to the labor supply elasticity

Progressive, Proportional, and Regressive Taxes

Type	Definition	Example
Progressive	Tax rate rises with income	Federal income tax (graduated brackets)
Proportional	Flat rate regardless of income	Flat income tax proposals
Regressive	Tax rate falls as income rises	Sales tax (higher burden on lower incomes as a share of income)

The US federal sales tax equivalent (general sales taxes are state-level) is nominally proportional, but because lower-income households spend a larger share of their income, the effective burden is regressive.

Frequently Tested Concepts

Tax incidence:

The less elastic side bears more — memorize this rule
Perfectly inelastic demand → consumer bears 100%
Perfectly inelastic supply → producer bears 100%

Excess burden:

Proportional to the square of the tax rate → danger of high rates
Taxing inelastic goods minimizes excess burden

Inverse elasticity rule:

Efficiency only: high rates on inelastic goods
Creates regressive burden — conflicts with equity

Study Checklist

Explain the three principles of taxation (efficiency, equity, simplicity)
Distinguish statutory incidence from economic incidence
Calculate tax burden shares using the elasticity formula
Understand why excess burden is proportional to the square of the tax rate
Explain the inverse elasticity rule and its equity limitation

Key Concept Cards

Excess Burden vs. Tax Revenue ★★★★★ : Excess burden (DWL) is the social cost of the tax over and above the revenue collected. It arises because the tax reduces transactions that would have been mutually beneficial.

Benefit Principle vs. Ability-to-Pay ★★★★ : Benefit principle: pay in proportion to benefits received (gas tax → highway funding). Ability-to-pay: pay in proportion to capacity (progressive income tax).

Ramsey Rule (Inverse Elasticity) ★★★★ : To minimize DWL, tax inelastic goods at higher rates. In practice, this conflicts with equity because inelastic goods are often necessities consumed disproportionately by lower-income households.

Practice Quiz

Q. Who bears more of a payroll tax — employers or employees — and why?

The burden depends on the relative elasticity of labor supply and demand. Labor supply tends to be relatively inelastic; labor demand is more elastic. Therefore, workers typically bear the larger share of a payroll tax, regardless of whether it is nominally assessed on the employer or employee.

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