Concept Architecture
Concept
Theoretically, Equivalent Variation is a welfare economics measure of the monetary value of a change in prices, income, health or policy, expressed as the amount of money that would leave an individual as well off before the change as they would be after the change. It is based on Hicksian welfare theory and measures the willingness to pay for a gain or the willingness to accept compensation for avoiding a loss while referencing the individual's final level of utility. In health economics, equivalent variation provides a monetary measure of the welfare effects of healthcare interventions and policy changes.
Mathematically, equivalent variation is defined using the expenditure function. It is calculated as the difference between the expenditure required to achieve the final level of utility under the original conditions and the expenditure required under the new conditions. The mathematical framework is derived from duality theory and provides a theoretically consistent measure of welfare change that is independent of observed market demand.
In practice, equivalent variation is estimated using expenditure functions derived from demand systems, contingent valuation studies, discrete choice experiments or structural economic models. It is applied in cost-benefit analysis, health policy evaluation and economic appraisal to quantify the monetary value of healthcare interventions while maintaining the post-intervention level of utility.
Purpose
Used to measure the monetary value of welfare changes associated with healthcare interventions or policy reforms while maintaining the individual's final level of utility, thereby supporting welfare analysis and cost-benefit evaluation.
Mathematical Formulae
Primary Formula
EV = e(p?, u?) ? e(p?, u?)
where:
- EV = equivalent variation
- e(�) = expenditure function
- p? = initial prices or conditions
- p? = new prices or conditions
- u? = final utility level
Supporting Formulae
Equivalent relationship:
e(p?, u?) = e(p?, u?) + EV
Related Mathematical Methods
- Hicksian demand analysis
- Expenditure function estimation
- Duality theory
- Welfare economics
- Cost-benefit analysis
- Discrete choice modelling
Example
A new treatment improves patients' health. Under the original healthcare system, a patient would require �19,000 annually to achieve the improved level of wellbeing. Following implementation of the treatment, only �17,200 is required to maintain that same level of utility.
EV = 19,000 ? 17,200 = �1,800
The equivalent variation is �1,800, representing the maximum amount the patient would be willing to pay for the health improvement while remaining at the post-treatment level of welfare.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Subtraction | =B2-B3 | Calculates equivalent variation from estimated expenditure levels. |
| IF | =IF(B2>B3,B2-B3,0) | Restricts calculations to positive welfare gains where appropriate. |
| Data Table | What-If Analysis | Evaluates equivalent variation under alternative policy or pricing scenarios. |
VBA (Optional)
Automate equivalent variation calculations across multiple healthcare policy scenarios using estimated expenditure functions and generate comparative welfare reports.
Sources
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
- Mas-Colell A, Whinston MD, Green JR. Microeconomic Theory. Oxford University Press.
- Varian HR. Microeconomic Analysis. W.W. Norton & Company.
- Hicks JR. ""The Four Consumer's Surpluses."" Review of Economic Studies. 1943.
Related Concepts (2)
Library
Publications
1
The Economics of Health and Health Care — Folland, Goodman, Stano & Danagoulian, 9th Edition ed., 2024 (Routledge)
The market-leading general health economics textbook, giving comprehensive coverage of health economics through core economic themes and balancing theory, empirical evidence and public policy. The ninth edition adds chapters on health disparities and pandemic economics.
BookView source →
Frequently Asked Questions (6)
What is equivalent variation?
A monetary measure of the change in wellbeing from a price or policy change, the sum needed before the change to match post-change welfare.
Source: Hicks 1939
What reference prices does equivalent variation use?
Equivalent variation values a change using the original prices as its reference, rather than the new ones. It asks how much money given to or taken from a person before the change would leave them as well off as the change itself would, so it expresses the change's worth in terms of the world before it happened. This choice of reference is what distinguishes it from compensating variation, which uses the prices after the change. Hicks (1939) defined both measures.
Source: Hicks 1939
How does equivalent variation measure a welfare change?
Equivalent variation measures a welfare change by asking how much money, at the original prices, would be equivalent to the change in its effect on wellbeing. For a beneficial change, it is the sum that would make the person as well off as the change without it occurring; for a harmful change, the sum whose loss would leave them as badly off. It thus expresses the change as a monetary amount using the pre-change situation as the reference.
Source: Hicks 1939
How does equivalent variation differ from compensating variation?
Equivalent and compensating variation both express a welfare change in money but use different reference prices. Compensating variation uses the new prices, measuring the money needed after the change to restore the original utility. Equivalent variation uses the original prices, measuring the money equivalent to the change without it occurring. They differ in whether the post-change or pre-change situation is the baseline, so for the same change they can give different monetary values, particularly when income effects are large.
Source: Hicks 1939
When is equivalent variation used rather than compensating variation?
Equivalent variation is used when the pre-change situation is the natural reference, for instance in comparing several possible changes against the current state, since it values each at the same original prices and so allows them to be ranked consistently. Compensating variation, using each change's own new prices, is less suited to such comparisons. Both are theoretically valid Hicksian measures; the choice depends on the reference point appropriate to the question, with equivalent variation preferred when comparing alternatives from a common baseline.
Source: Hicks 1939
Why is equivalent variation, a Hicksian measure, preferred to consumer surplus?
Hicksian measures such as equivalent variation are preferred to consumer surplus for welfare analysis because they hold utility constant and are defined precisely in terms of the money equivalent of a utility change, whereas consumer surplus, measured along an ordinary demand curve, mixes in income effects and can be an inexact welfare measure. Equivalent and compensating variation give theoretically correct valuations of welfare change, which is why they are the conceptually preferred measures in applied welfare economics, despite being harder to estimate.
Source: Hicks 1939
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 26 Sep 2025
Content version: 1.0.0
Canonical Identity
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