Indifference Curve vs Compensating Variation
Indifference Curve and Compensating Variation are two Microeconomic Theory concepts in AP Economics that students often mix up. An indifference curve shows all combinations of two goods that give a consumer the same total satisfaction (utility). Compensating variation is the amount of money that, after a price change, would return a consumer to exactly the utility they had before it. Here is how they compare side by side.
Consumers are indifferent among points on the same curve. Curves farther from the origin represent higher utility. They slope downward and are bowed inward (convex) because of the diminishing marginal rate of substitution; the optimal bundle is where the budget line is tangent to the highest reachable curve.
Compensating variation measures the welfare effect of a price change in dollars, using the new prices as the reference point. After a price rise, it is the payment a consumer would need to be as well off as before; after a price fall, it is the amount you could take away and still leave the consumer as well off as before. It answers a practical question: how much does this change actually cost this household in money terms? Equivalent variation is the mirror image, asking instead how much money at the OLD prices would do the same damage or good as the price change; because the two use different reference prices, they usually differ in size. Both are more precise than the change in consumer surplus, which only approximates them.
Indifference Curve vs Compensating Variation: The Curve and the Cash That Gets You Back to It
| Indifference Curve | Compensating Variation | |
|---|---|---|
| What it is | A curve joining every bundle the consumer ranks equally | One sum of money attached to one specific price change |
| Do prices enter it | No; the map is drawn before any price is mentioned | Always; it is defined by an old price and a new one |
| Reference utility level | Every level has its own curve somewhere on the map | Fixed at the level the buyer enjoyed before the change |
| What is actually measured | Nothing; the curve records a ranking, not a quantity | The gap between two parallel budget lines, one grazing the old curve |
| Units of the answer | An arbitrary index, where relabeling changes nothing | Money, comparable across people and across policies |
| Typical use | Deriving the tangency condition and the demand curve | Putting a dollar figure on a tax, a tariff or a price shock |
Compensating variation is a distance measured on the indifference curve diagram, not a rival to it
Take a shopper with 60 to spend on food and everything else, where everything else is priced at 1 and she always splits her budget evenly between the two. Food starts at 1 a unit, so she buys thirty food and thirty of everything else, and her utility index, the square root of the product, is 30. Food then jumps to 4 a unit. She now buys seven and a half food and thirty of everything else, and the index falls to 15. Compensating variation asks how much extra money would put her back on the curve labeled 30 while she still faces the higher food price. Hand her more income at those prices and she keeps splitting it evenly, so her index works out to a quarter of her income, and reaching 30 takes 120. She began with 60, so the compensating variation is 60, and she would spend it on fifteen food and sixty of everything else, whose product is 900 and whose square root is 30 once more. On the diagram this is a distance you can point at. Because everything else costs 1, the vertical intercept of any budget line reads off her income directly, so the compensation is the vertical gap between her actual new budget line and a parallel copy pushed outward until it just grazes the original curve. Notice she does not return to her original bundle, only to her original curve. See /glossary/budget-line.
Compensating and equivalent variation answer different questions, and agree only when income effects vanish
Turn the question around and the number changes, which is the part that feels unfair the first time. Equivalent variation asks how much income you could take away at the old prices to hurt her exactly as much as the price rise did. At the original food price her index equals half her income, so landing her at 15 means leaving her with 30, making the equivalent variation 30. Same shopper, same price change, one measure says 60 and the other says 30. Neither is wrong. Compensating variation prices the change after the fact and is the right number for designing a rebate; equivalent variation prices it beforehand and is the right number for asking what she would accept to let the change go through. The change in consumer surplus, the area to the left of her demand curve between the two prices, comes to about 41.6 here and sits between the other two, exactly where theory puts it for a normal good facing a price rise. All three collapse onto one number in a single special case: preferences quasilinear in the numeraire, where demand for the good ignores income entirely. No income effect means no gap between the before and after reference points. That assumption is what licenses the casual use of consumer surplus as an exact welfare measure. See /calculate/consumer-surplus and /blog/utility-maximization-and-consumer-choice.
Frequently asked questions
How do you read compensating variation off an indifference curve diagram?
Draw the new budget line with its new slope, then slide a parallel copy outward until it just touches the original indifference curve. The gap between the two lines is the compensation, and when the good on the vertical axis is priced at 1, that gap can be read straight off the vertical intercepts as income. The touching point is the bundle the buyer would choose with the compensation in hand, which is not the bundle she started with, because she substitutes toward whatever became relatively cheaper.
What is the difference between compensating variation and equivalent variation?
Both convert a price change into money, and they differ in which prices and which utility level serve as the reference. Compensating variation uses the new prices and the old utility level: the payment that would restore the buyer after the change. Equivalent variation uses the old prices and the new utility level: the income loss that would hurt just as much without the change happening. The two coincide only when the good carries no income effect, and can differ by a factor of two in ordinary textbook examples.
Is compensating variation the same as the change in consumer surplus?
Only under quasilinear preferences, where demand for the good does not depend on income. In general the change in consumer surplus is an approximation that lands between compensating and equivalent variation, and all three sit close together when the good takes a small share of spending. For a big-ticket item, or a price change large enough to move real income noticeably, the numbers separate widely and picking the right one starts to matter. See /glossary/consumer-surplus.
Related comparisons
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