Questions: Welfare Analysis: Deadweight Loss and Policy Evaluation

Question 1

A government raises a tax from $2 to $4 per unit. Approximately what happens to the deadweight loss?

• A. It doubles — DWL is proportional to the tax rate
• B. It quadruples — DWL grows with the square of the distortion
• C. It stays the same — the tax just redistributes income
• D. It decreases — a higher tax raises more revenue, reducing the need for other distortionary taxes

Answer: (B)

The key result of welfare analysis is that deadweight loss is approximately proportional to the square of the distortion. Doubling the tax from $2 to $4 quadruples (2² = 4 times) the DWL, not merely doubles it. This squared relationship explains why economists prefer many small taxes over a few large ones — and why incremental increases to already-high taxes are especially costly. Option A is the intuitive but incorrect answer; options C and D describe other real phenomena (revenue, tax interaction effects) but don't capture the DWL relationship.

Question 2

A policy eliminates a market distortion and increases total surplus by $500 million, but concentrates most gains among the top quintile while imposing costs on the lowest quintile. Advanced welfare analysis says this policy is unambiguously welfare-improving.

• T. True
• F. False

Answer: False

Advanced welfare analysis recognizes that efficiency and distribution are inseparable. A policy that increases total surplus but worsens the position of the worst-off may reduce social welfare under any reasonable welfare criterion that places higher weight on gains to lower-income individuals. The $500 million gain to the wealthy does not 'compensate' the poor who lose unless actual transfers are made. Treating the surplus increase as decisive while ignoring distributional consequences is a failure of advanced welfare analysis, not its conclusion.

Question 3

Compensating variation measures the change in consumer surplus after a price change.

• T. True
• F. False

Answer: False

Compensating variation (CV) is a more precise welfare measure than consumer surplus change. CV asks: how much money must we give (or take from) a consumer after the price change to restore their original utility level? It differs from the consumer surplus change because it accounts for income effects — as prices change, the marginal utility of money changes, making simple surplus calculations inaccurate when income effects are large. Consumer surplus uses the ordinary (Marshallian) demand curve; CV uses the compensated (Hicksian) demand curve.

Question 4

Why does the squared relationship between distortion size and deadweight loss matter for real-world tax policy design?

Model answer: Because DWL scales with the square of the tax rate, doubling a tax more than doubles the efficiency cost — it roughly quadruples DWL. This means it is far less costly to impose small taxes on many goods than large taxes on a few goods, even if total revenue is the same. It also means that existing high tax rates should be scrutinized carefully, because incremental increases carry disproportionately large DWL. The squared relationship is the mathematical foundation for the 'broad base, low rate' principle in tax policy.

Intuitively, the first dollar of tax disrupts only the most marginal transactions (those barely worth doing at the current price). The second dollar disrupts more transactions plus the now-distorted response to the first dollar. Each additional unit of tax causes a growing wedge, pushing out a larger triangle of lost trades. A policy designer who treats DWL as linear in the tax rate will systematically underestimate the cost of high taxes and overestimate the revenue-raising ability of tax increases.

Question 5

Which welfare measure is most appropriate when evaluating a policy that significantly raises the price of a basic necessity consumed heavily by low-income households?

• A. Consumer surplus change, because it correctly captures the area under the demand curve
• B. Compensating or equivalent variation, because income effects are large for necessities and low-income consumers
• C. Producer surplus change, because the policy affects firm profitability most directly
• D. Deadweight loss alone, because it captures the full social cost of the distortion

Answer: (B)

For goods that represent a large share of household budgets — especially for low-income consumers — income effects are significant. When the price of a necessity rises substantially, the marginal utility of income changes, making Marshallian consumer surplus an inaccurate welfare measure. Compensating or equivalent variation, which use Hicksian demand curves that hold utility constant, give the correct welfare measure. DWL (option D) captures only the efficiency cost and ignores distributional impacts entirely; producer surplus (option C) is not the primary concern for a consumer-side price increase.