Questions: Compensating and Equivalent Variation: Welfare Measurement

Question 1

A government raises the price of electricity and wants to calculate how much cash to give low-income households to make them exactly as well off as before the price increase. Which welfare measure should it use?

• A. Equivalent variation, because EV measures the income change at original prices that achieves the same utility as the price change
• B. Consumer surplus change, because it is the simplest measure and is always accurate for policy analysis
• C. Compensating variation, because CV measures the income change at new prices needed to restore the consumer to original utility
• D. Equivalent variation, because EV is always larger than CV for a price increase, giving a more generous estimate

Answer: (C)

Compensating variation (CV) is defined precisely as the income adjustment needed after the price change to restore the consumer to their original utility level — evaluated at the new prices. This is exactly what the government wants: how much to pay at the new higher electricity price to make consumers whole. EV asks a different question (what would consumers pay at old prices to prevent the change?) and uses new utility as its reference point — not useful for computing actual compensation after the fact.

Question 2

Why do compensating variation and equivalent variation typically give different numerical values for the same price change?

• A. CV and EV use different discount rates to convert future utility into present income equivalents
• B. CV uses the Hicksian demand curve at the original utility level while EV uses the Hicksian demand curve at the new utility level, and these curves differ whenever there are income effects
• C. CV measures gains while EV measures losses, so they differ in sign but not in magnitude
• D. CV is computed at original prices while EV is computed at new prices, so they capture different segments of the Marshallian demand curve

Answer: (B)

Both CV and EV are areas under Hicksian (compensated) demand curves — but different ones. CV uses the Hicksian demand curve holding utility at u₀ (original utility); EV uses the curve holding utility at u₁ (new utility). These two curves are separated by the income effect: when income effects are non-zero (normal or inferior goods), the two Hicksian curves differ, and so do CV and EV. Only when income effects are zero (quasilinear preferences) do the two Hicksian curves coincide and CV = EV = consumer surplus change.

Question 3

For a price increase on a normal good, the ordering EV < consumer surplus loss < CV holds.

• T. True
• F. False

Answer: True

This is a standard result in welfare economics. For a normal good facing a price increase, the Hicksian demand curve at the original (higher) utility lies to the right of the Marshallian demand curve, which lies to the right of the Hicksian curve at the new (lower) utility. The area under each curve between old and new prices gives CV > CS change > EV. CV must compensate at the new higher prices (the consumer needs more income to restore lost utility), while EV is evaluated at old prices where the consumer had greater purchasing power.

Question 4

CV and EV equal the change in consumer surplus when income effects are large, making most three measures equivalent in practice for most goods.

• T. True
• F. False

Answer: False

This is exactly backward. CV, EV, and consumer surplus converge when income effects are *zero* — specifically, when preferences are quasilinear (utility linear in income). In that case, the Marshallian and both Hicksian demand curves coincide. When income effects are large (goods that constitute a significant share of the consumer's budget), CV, EV, and CS diverge substantially — and it is precisely in those cases that using consumer surplus instead of CV or EV leads to seriously misleading welfare conclusions.

Question 5

Explain why CV, EV, and consumer surplus all give the same answer when consumer preferences are quasilinear, but diverge for other preference structures.

Model answer: With quasilinear preferences, utility is linear in income (e.g., u = v(x) + m), meaning the marginal utility of income is constant — there is no income effect. The Marshallian demand for the good depends only on price, not income. Both Hicksian demand curves (at u₀ and u₁) coincide with the Marshallian demand curve because holding utility constant is identical to holding income constant when there are no income effects. Since all three curves are identical, the area under any of them between old and new prices is the same, so CV = EV = consumer surplus change.

For goods with income effects, the Marshallian demand curve shifts as income changes, causing it to diverge from the Hicksian curves. CV, computed at original (higher) utility, uses a Hicksian curve further from the origin; EV uses a Hicksian curve closer to the origin. The Marshallian curve lies between them. The divergence grows with the size of the income effect — large for necessities that dominate the budget, negligible for goods with small expenditure shares.