Practice Worksheet

Chapter 12 — The Design of the Tax System

Part 1

Short Answer — Marginal and Average Tax Rates

Given Suppose the income tax schedule works as follows:

Income Bracket	Tax Rate
$0 – $20,000	10%
$20,001 – $50,000	20%
$50,001 – $100,000	30%
Above $100,000	40%

These are marginal rates — each rate applies only to income within that bracket.

Question a

Alex earns $40,000 per year. Calculate Alex's total tax owed and average tax rate.

Total Tax Owed ($)

Average Tax Rate (%)

Hint Apply rates bracket by bracket. First $20,000 taxed at 10%. Next $20,000 (from $20,001 to $40,000) taxed at 20%. Add them up. Then divide total tax by total income.

Explanation First bracket: $20,000 × 10% = $2,000.
Second bracket: $20,000 × 20% = $4,000.
Total tax = $2,000 + $4,000 = $6,000.
Average tax rate = $6,000 / $40,000 = 15%.
Note: the marginal rate (rate on the last dollar earned) is 20%, but the average rate is only 15% because the lower rate on the first $20,000 "drags down" the average.

Question b

Jordan earns $80,000 per year. Calculate Jordan's total tax owed and average tax rate.

Total Tax Owed ($)

Average Tax Rate (%)

Hint Three brackets apply: 10% on first $20k, 20% on next $30k, 30% on the remaining income above $50k. Jordan earns $80k, so the third bracket covers $80k − $50k = $30k.

Explanation First bracket: $20,000 × 10% = $2,000.
Second bracket: $30,000 × 20% = $6,000.
Third bracket: $30,000 × 30% = $9,000.
Total tax = $2,000 + $6,000 + $9,000 = $17,000.
Average tax rate = $17,000 / $80,000 = 21.25%.
The marginal rate is 30%, but the average rate is only 21.25%. The average is always lower than the marginal rate in a progressive system.

Question c

Is this tax system progressive, proportional, or regressive? How do you know? Enter the average rate for Alex (at $40k) and Jordan (at $80k) to compare.

Alex's avg rate at $40k (%)

Jordan's avg rate at $80k (%)

Hint Use the answers from parts a and b. If the average rate rises with income, what type of tax is it?

Explanation Alex: average rate = 15%. Jordan: average rate = 21.25%.
Since Jordan (higher income) pays a higher average rate than Alex, the average rate rises with income. This is the definition of a progressive tax. The system is progressive because the marginal rate increases across brackets, which drags the average rate up as income rises.

Part 2

Short Answer — Tax Structure Identification

Given Three taxpayers face a $500 annual road-use fee regardless of income or mileage driven. Their incomes are $25,000, $75,000, and $200,000.

Taxpayer	Income	Fee Paid	Avg Rate
Maya	$25,000	$500	2.0%
Raj	$75,000	$500	0.67%
Chen	$200,000	$500	0.25%

Question d

Is this $500 road-use fee progressive, proportional, or regressive? Which equity principle does it most closely follow?

Progressive; ability-to-pay principle Proportional; vertical equity Regressive; benefits principle Regressive; ability-to-pay principle

Hint Look at the average rates in the table: 2.0%, 0.67%, 0.25%. Is the rate rising or falling as income rises? And does the fee relate to road use (benefits) or financial capacity (ability-to-pay)?

Explanation The average rate falls as income rises (2.0% → 0.67% → 0.25%), making this a regressive tax. The flat fee hits lower-income earners harder as a percentage of their income.

The justification aligns with the benefits principle: all three drivers use the roads equally, so they pay the same flat fee. (It's NOT ability-to-pay, which would require higher earners to pay more.)

Part 3

Multiple Choice

Question 1

The largest source of federal government revenue in the United States is

the corporate income tax payroll taxes (Social Security and Medicare) the individual income tax sales and excise taxes

Hint Think about what the federal government collects the most of. Payroll taxes (for Social Security/Medicare) are large but is there something larger?

Explanation The individual income tax is the largest single source of federal revenue, accounting for roughly 47% of total federal receipts. Payroll taxes are second at ~36%. The corporate income tax and excise taxes are much smaller shares. This is why income tax policy debates are so politically significant.

Question 2

The marginal tax rate is best described as

total tax paid divided by total income the tax rate applied to the next dollar of income earned the lowest tax rate in the tax schedule a tax that is fixed regardless of income level

Hint "Marginal" in economics always refers to the last unit — the extra dollar in this case. Which option relates to that idea?

Explanation The marginal tax rate is the rate applied to the last dollar earned — the rate that determines the tax cost of earning one more dollar. This is the rate that affects incentives to work, save, and invest. Option A describes the average tax rate, not the marginal rate.

Question 3

Which of the following best illustrates the benefits principle of taxation?

A millionaire pays a higher income tax rate than a low-income worker The gasoline tax is used to fund highway construction and maintenance Two people earning the same income pay the same amount of tax A lump-sum tax of $1,000 is levied on every citizen

Hint The benefits principle says: people should pay in proportion to the benefits they receive from government. Which option directly links tax revenue to a specific government service that taxpayers use?

Explanation The gasoline tax is the textbook example of the benefits principle: drivers pay per gallon, and that revenue funds roads. Those who drive more (and benefit more from roads) pay more. Option A illustrates the ability-to-pay principle. Option C illustrates horizontal equity. Option D describes a lump-sum tax (efficient but not linked to benefits).

Question 4

The concept of vertical equity in taxation means that

taxpayers in similar situations should pay similar taxes all citizens should pay the same dollar amount in taxes taxpayers with higher ability to pay should contribute more tax revenue should equal government expenditures

Hint There are two equity concepts: horizontal (similar people, similar treatment) and vertical (different people, different treatment based on capacity). Which does "vertical" describe?

Explanation Vertical equity means that taxpayers with greater ability to pay should bear a greater tax burden. It's the principle behind progressive taxation. Option A describes horizontal equity (similar situations, similar taxes). Option B is a lump-sum approach. Option D is a balanced-budget rule, unrelated to equity.

Question 5

A lump-sum tax is considered the most economically efficient form of taxation because

it raises the most revenue per dollar collected it does not distort economic decisions and creates no deadweight loss it is the most equitable because everyone pays the same amount it reduces government spending automatically

Hint Tax efficiency is about minimizing deadweight loss. A lump-sum tax is fixed — you can't avoid it by working less or earning less. What does that imply about behavior distortion?

Explanation A lump-sum tax (e.g., $1,000 per person regardless of income) creates no deadweight loss because it cannot be avoided by changing behavior. You owe it no matter what you do, so there's no incentive to work less, earn less, or rearrange your activities to escape it. This is why economists consider it efficient. However, it is highly inequitable — $1,000 is a trivial burden for the wealthy but devastating for the poor.

Question 6

The "flypaper theory" of tax incidence suggests that

taxes always stay with whoever legally pays them taxes do not always stick where they land — the economic burden can shift corporate taxes are always passed entirely to consumers as higher prices governments should use sticky taxes to raise revenue without distortion

Hint Think about Ch. 6 tax incidence. Just because the government makes company X write the check doesn't mean X bears the full burden. What happens in markets when a tax is imposed?

Explanation The flypaper theory refers to the naive view that taxes "stick" to whoever legally pays them — like a fly stuck to flypaper. In reality, the burden shifts based on elasticity. Corporate income taxes, for example, may be borne partly by workers (through lower wages), consumers (through higher prices), and shareholders (through lower returns). The economic burden doesn't stay where Congress places the legal liability.

Question 7

If the demand for a taxed good is perfectly inelastic, the burden of the tax falls

entirely on sellers equally on buyers and sellers entirely on buyers on neither buyers nor sellers, since there is no deadweight loss

Hint Perfectly inelastic demand means buyers will buy the same quantity regardless of price. If sellers raise the price by the full tax amount, do buyers reduce their purchases? Connect this to Ch. 6 tax incidence.

Explanation With perfectly inelastic demand, buyers do not respond to price changes — they buy the same quantity no matter what. Sellers can raise the price by the full amount of the tax, and buyers have no alternative but to pay it. Therefore, the entire tax burden falls on buyers. The key Ch. 6 rule: the less elastic side bears more of the tax burden.

Part 4

True or False

Question 8

In a progressive tax system, the average tax rate is always equal to the marginal tax rate.

Hint In a progressive system, not all income is taxed at the top rate. The lower brackets pull the average rate down. Can the average rate equal the marginal rate in that case?

Explanation False. In a progressive system, the marginal rate is the rate on the last dollar earned, but earlier dollars were taxed at lower rates. So the average rate (total tax / total income) is always lower than the marginal rate. Only in a flat-rate (proportional) tax does average = marginal. The confusion between these two rates is one of the most common errors in tax discussions.

Question 9

The administrative costs of a tax system — time spent filing returns, keeping records — are a real economic cost, even though no money changes hands between citizens and the government.

Hint Is time a scarce resource? If a taxpayer spends 10 hours filing taxes instead of working or enjoying leisure, is that 10 hours "free"?

Explanation True. Administrative costs are real economic costs. Time spent on tax compliance has opportunity cost — those hours could be spent producing goods, providing services, or enjoying leisure. Americans collectively spend roughly 6 billion hours per year on tax compliance. This is a deadweight loss in itself, separate from the distortions in behavior caused by the taxes. A simpler tax code could reduce this waste.

Question 10

A sales tax on food is likely to be progressive because food is a necessity that everyone buys.

Hint Food spending as a percentage of income: does a poor household spend a higher or lower fraction of its income on food than a wealthy household? Now apply a flat sales tax rate to that spending.

Explanation False. A sales tax on food is regressive, not progressive. Lower-income households spend a higher fraction of their income on food (a necessity), so a flat sales tax takes a higher percentage of their income. Wealthy households spend more on food in absolute terms, but food is a smaller share of their income, so the tax rate as a percentage of income falls as income rises. This is Engel's Law at work.

Question 11

If the government runs a budget deficit, it means the government is spending more than it collects in taxes and must borrow to cover the gap.

Hint Deficit = spending − revenue > 0. What must the government do when it spends more than it takes in?

Explanation True. A budget deficit occurs when government expenditures exceed tax revenues. The government finances the gap by issuing bonds (borrowing). The accumulated stock of annual deficits becomes the national debt. When revenues exceed expenditures, the government runs a surplus and can pay down debt. The U.S. has run persistent deficits since 2001 (with a brief surplus period in the late 1990s).

Question 12

Horizontal equity in taxation requires that people with different incomes should face different tax rates.

Hint There are two equity concepts: horizontal and vertical. Horizontal is about people in similar situations. Does that require different rates or similar rates?

Explanation False. Horizontal equity says that taxpayers in similar financial situations should face similar tax burdens. A doctor earning $150k and a lawyer earning $150k should owe roughly the same taxes. What the statement describes — different rates for different incomes — is vertical equity (more income, more taxes). Confusing horizontal and vertical equity is a common exam mistake.

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