Designing a Tax System: Efficiency and Equity

Core Idea

A good tax system raises revenue at a low cost to society and shares the burden fairly. Efficiency concerns two costs beyond the tax paid: the deadweight loss from changed behavior, which depends on the marginal tax rate, and the administrative burden of complying. Equity has two principles: the benefits principle (pay according to benefits received) and the ability-to-pay principle, which splits into vertical equity (people with more ability pay more) and horizontal equity (people in similar situations pay similar amounts). A tax is progressive, proportional, or regressive depending on whether the average tax rate rises, stays constant, or falls as income rises.

How It's Best Learned

Start with a two-bracket income tax and compute average and marginal rates for several incomes, so students see why the two rates differ. Then compare a lump-sum tax with an income tax that raises the same revenue and ask which changes behavior at the margin. Finish by classifying real taxes, such as a flat payroll tax with a cap, by how the average rate moves with income.

Common Misconceptions

• Moving into a higher tax bracket can lower your after-tax income. (In a bracket system, the higher rate applies only to income above the threshold, so earning more always leaves you with more after tax.)
• A tax is progressive if rich people pay more dollars. (Progressivity is defined by the average tax rate rising with income; a proportional tax also takes more dollars from higher earners.)
• The legal taxpayer bears the burden. (Incidence depends on elasticities of supply and demand, so the burden can fall largely on the other side of the market.)

Explainer

Governments need revenue for roads, defense, schools, and transfers. The question is how to raise it. Economists judge a tax system by two standards: efficiency and equity.

Efficiency asks how much a tax costs society beyond the money collected. From your study of deadweight loss, you know that a tax drives a wedge between what buyers pay and what sellers receive, so some trades that would have benefited both sides do not happen. The size of that loss depends on how much behavior changes, which depends on elasticities and on the marginal tax rate, the tax on one more dollar of income or one more unit bought. With linear supply and demand, the deadweight loss grows with the square of the tax rate, so doubling a tax roughly quadruples its deadweight loss. The second efficiency cost is administrative burden: time spent on records and forms, and money spent on tax advice and enforcement.

The most efficient tax in theory is a lump-sum tax, the same fixed amount for everyone. Because it does not depend on anything a person does, its marginal rate is zero, and it creates no deadweight loss. Few governments rely on it, because it takes the same amount from a poor family as from a rich one.

That brings in equity. The benefits principle says people should pay according to the benefits they receive from government, as with a gasoline tax that funds roads. The ability-to-pay principle says people should pay according to how well they can bear the burden. It has two parts. Vertical equity says those with more ability should pay more. Horizontal equity says people with similar ability should pay similar amounts.

Taxes are classified by the average tax rate, total tax divided by income. If the average rate rises with income, the tax is progressive; if it stays the same, proportional; if it falls, regressive. In a bracket system the two rates differ. With 10% on the first $20,000 and 30% above, a person earning $50,000 owes $11,000. The average rate is 22%, but the marginal rate is 30%. Efficiency depends on the marginal rate, while progressivity is about the average rate.

The two goals often conflict. Higher marginal rates on high earners raise vertical equity but increase deadweight loss. Deciding how to balance them involves value judgments as well as economics.