Compensating Variation
What is Compensating Variation?
Compensating variation is the amount of money that, after a price change, would return a consumer to exactly the utility they had before it.
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.
Compensating Variation: a worked example
A commuter uses exactly 40 gallons of gasoline a month and cannot cut back, since her route is fixed. Suppose the price rises from $3.00 to $4.00 a gallon, so buying the same 40 gallons now costs 40 × $1.00 = $40 more each month. Because she has no way to substitute, $40 is her compensating variation: hand her $40 and she is exactly as well off as before the price rose. If she could switch to transit for some trips, she would need less than $40, because part of the loss can be dodged by changing her bundle.
The mistake students make with compensating variation
The frequent error is calculating compensation as the old quantity times the price increase and calling that the exact loss. That product is an upper bound: a consumer who can substitute toward cheaper goods needs less money to get back to the old utility level. Students also swap compensating and equivalent variation. Compensating variation is measured at the NEW prices, equivalent variation at the OLD ones.
Compensating Variation questions
What is the difference between compensating variation and equivalent variation?
Compensating variation asks how much money at the NEW prices restores the old utility, while equivalent variation asks how much money at the OLD prices would have produced the new utility. They use different reference prices, so they generally give different dollar amounts for the same price change. They coincide only when the good has no income effect.
Is compensating variation positive or negative for a price increase?
For a price increase, compensating variation is a positive amount the consumer must receive to be as well off as before. For a price cut it flips: it is the amount you could take away and still leave the consumer at the original utility. Reading the sign as gain or loss to the consumer, rather than memorizing it, avoids most errors.
How does compensating variation relate to consumer surplus?
The change in consumer surplus is an approximation that sits between compensating variation and equivalent variation for a normal good. All three measure the money value of a price change, but consumer surplus uses ordinary demand while the two variations hold utility constant. When income effects are small the three are close enough that economists use consumer surplus for convenience.
Formula / Example
Related terms
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated