Equivalent variation

Equivalent Variation

Equivalent variation (EV) is a core concept in Welfare Economics, a branch of economics that evaluates the overall well-being of a society based on microeconomic principles. It quantifies the monetary change in an individual's wealth needed to achieve the same level of utility or satisfaction after a change in prices or an economic event⁵⁷, ⁵⁸. In essence, EV measures how much money a consumer would need to be given or taken away from them, at the original prices, to make them just as well off as they would be after a price or policy change⁵⁵, ⁵⁶. This allows economists to assess the impact of such changes on individual welfare in monetary terms⁵⁴.

History and Origin

The concept of equivalent variation, alongside its counterpart compensating variation, is attributed to the British economist John Hicks, who introduced it in his seminal 1939 book, Value and Capital⁵², ⁵³. Hicks' work expanded on earlier consumer demand theory, particularly by distinguishing between the substitution effect and the income effect⁵¹.

Before Hicks, the primary measure of welfare change was consumer surplus, developed by Dupuit and later refined by Marshall⁴⁹, ⁵⁰. However, consumer surplus faced limitations in accurately measuring welfare changes, especially when the marginal utility of money was not constant⁴⁷, ⁴⁸. Hicks' introduction of equivalent variation provided a more theoretically rigorous approach to measuring welfare changes by explicitly accounting for the consumer's utility level before and after a change, even if utility itself is not directly observable⁴⁶. His work laid foundational groundwork for modern microeconomic theory and its application in evaluating the impacts of economic policies⁴⁵.

Key Takeaways

• Equivalent variation (EV) measures the monetary value of a change in welfare, expressed at the initial prices.
• It answers how much money, at current prices, would have the same effect on consumer welfare as the actual price change.
• EV is a crucial tool in economic analysis for evaluating the impact of economic policies and price changes on consumer well-being.
• The concept was introduced by John Hicks in 1939 as a refinement to welfare measurement.
• Unlike compensating variation, EV uses the original prices as the reference point for the hypothetical income adjustment.

Formula and Calculation

The equivalent variation (EV) is calculated using the expenditure function, which represents the minimum expenditure required to achieve a certain level of utility at given prices.

Let:

• $p^0$ be the initial vector of prices
• $p^1$ be the new vector of prices
• $u^0$ be the initial utility level
• $u^1$ be the new utility level
• $e(p, u)$ be the expenditure function

The equivalent variation (EV) is given by:

$EV = e(p^0, u^1) - e(p^0, u^0)$

This formula indicates the amount of income, at the initial prices $p^0$, that would be needed to move the consumer from their initial utility level $u^0$ to the new utility level $u^1$⁴⁴. In simpler terms, it's the difference in the cost of achieving the new utility level at the old prices, compared to the cost of achieving the old utility level at the old prices.

Alternatively, if we consider a price change from $p$ to $p'$ and an income $w$, where utility goes from $u = v(p,w)$ to $u' = v(p',w)$, then the equivalent variation can be expressed as:

$EV = e(p,u') - w$⁴³

Here, $e(p,u')$ represents the expenditure needed to reach the new utility level $u'$ at the initial prices $p$. Subtracting the initial income $w$ reveals the change in wealth equivalent to the price change.

Interpreting the Equivalent Variation

Interpreting the equivalent variation involves understanding its implication for consumer welfare. A positive EV indicates that the consumer is worse off due to the price or policy change, as it represents the amount of money they would need to receive, at the original prices, to be as well off as they were before the change⁴². Conversely, a negative EV suggests that the consumer is better off, as it indicates the amount of money that could be taken away from them, at the original prices, while still leaving them as well off as they are after the change.

EV is particularly useful when policymakers want to assess the impact of a proposed change from the perspective of the initial economic conditions. For instance, when evaluating a new regulation, equivalent variation can show how much better or worse off individuals would be if the regulation were implemented, expressed in terms of a monetary adjustment they would experience under the status quo. This "money-metric" approach allows for a direct comparison of welfare impacts across different scenarios or individuals, even if their underlying preferences or consumption patterns vary⁴¹.

Hypothetical Example

Consider a consumer, Sarah, who frequently buys coffee and pastries. Initially, coffee costs $3 and pastries cost $2. Sarah's utility from her usual consumption bundle is $U_0$.

Now, suppose the price of coffee increases to $4 due to a new supply chain disruption. Sarah adjusts her consumption, and her new utility level is $U_1$, which is lower than $U_0$.

To calculate the equivalent variation, we ask: How much money would Sarah need to be given, at the original prices (coffee $3, pastries $2), to make her as well off as she is now with $U_1$?

If, after calculating, it is determined that Sarah would need an additional $5 at the original prices to reach the utility level $U_1$, then the equivalent variation is +$5. This means the price increase effectively made Sarah $5 poorer in terms of her initial purchasing power and preferences. This measure allows us to quantify the welfare loss in a tangible monetary value, using the prices she was accustomed to.

Practical Applications

Equivalent variation is widely applied in public economics and policy analysis to quantify the welfare effects of various economic interventions and events³⁹, ⁴⁰.

• Policy Evaluation: Governments and organizations use EV to assess the impact of policies such as taxes, subsidies, price controls, and environmental regulations³⁶, ³⁷, ³⁸. For example, the World Bank utilizes equivalent variation to simulate the impact of price changes on welfare, particularly for vulnerable populations³⁴, ³⁵. This helps policymakers understand whether a policy will make individuals better or worse off and to what extent, informing decisions on resource allocation and social programs³², ³³.
• Cost-Benefit Analysis: EV provides a monetary measure of benefits or costs that can be incorporated into cost-benefit analysis of public projects or policy changes³¹. By converting changes in utility into monetary terms, it allows for a more comprehensive assessment of a project's overall societal impact.
• Consumer Welfare Measurement: Beyond direct policy, equivalent variation can be used to measure changes in consumer welfare resulting from non-price changes, such as improvements in product quality or the introduction of new goods²⁹, ³⁰.
• Environmental Economics: In environmental studies, EV helps to estimate individuals' willingness to pay for environmental protection or willingness to accept compensation for environmental degradation, providing a basis for valuing non-market goods and services²⁸.

Limitations and Criticisms

While equivalent variation offers a robust measure of welfare change, it is not without limitations and criticisms.

One key challenge in applying equivalent variation practically is the difficulty in accurately measuring individual utility levels and the precise monetary compensation required²⁷. Utility is subjective and not directly observable, making empirical estimation complex. This often necessitates the use of indirect utility functions or statistical approximations, which can introduce errors²⁵, ²⁶.

Furthermore, equivalent variation, like other welfare measures, can be sensitive to the choice of reference prices. Since EV uses the initial prices, it may not fully capture the welfare implications if the new prices represent a significant shift in market conditions or the introduction of entirely new goods. In situations involving large price changes or substantial shifts in consumption patterns, the assumption of using original prices as a baseline might become less representative²⁴.

Another criticism revolves around the aggregation of equivalent variation across individuals. While EV can quantify welfare changes for a single consumer, aggregating these measures across an entire population can be problematic, especially when individuals have diverse preferences or face different price impacts²³. It does not inherently account for distributional effects, meaning it may not fully reflect how a policy disproportionately affects different income groups²¹, ²². For example, a policy might generate a positive aggregate EV, but if it significantly harms a specific vulnerable group, this nuance might be masked by the overall positive figure.

Finally, while theoretically sound, the practical application of equivalent variation in complex, real-world scenarios can be challenging, as it requires extensive data on consumer preferences, prices, and income, often more detailed than readily available²⁰.

Equivalent Variation vs. Compensating Variation

Equivalent variation (EV) and compensating variation (CV) are both measures of welfare change in consumer theory, but they differ in their reference point for calculating the monetary adjustment¹⁸, ¹⁹. The distinction lies in which set of prices—initial or final—is used to assess the hypothetical income change.

Equivalent Variation (EV): EV asks how much money, at the original prices, would be needed to make the consumer as well off as they are after the price or policy change. It¹⁶, ¹⁷ essentially measures the change in welfare by bringing the consumer's utility back to the new level, but using the initial price structure as a baseline. EV is often seen as a measure of "willingness to pay" for a change.

¹⁵Compensating Variation (CV): CV, on the other hand, asks how much money would be needed to be given to or taken away from the consumer, at the new prices, to restore them to their original utility level. It¹³, ¹⁴ measures the welfare change by adjusting income at the post-change prices to keep the consumer on their initial indifference curve. CV is often associated with the concept of "willingness to accept" compensation for a change.

The choice between EV and CV often depends on the specific policy question being asked and the desired perspective for welfare assessment. Wh¹¹ile they both measure the same utility difference, their numerical values will generally differ unless the consumer's utility function is quasilinear.

#¹⁰# FAQs

What is the primary purpose of equivalent variation?

The primary purpose of equivalent variation is to quantify the monetary value of a change in an individual's economic well-being or utility resulting from a price change or an economic policy. It⁹ allows economists to measure how much income, at original prices, would be equivalent to the welfare impact of the change.

How does equivalent variation differ from consumer surplus?

While both equivalent variation and consumer surplus measure welfare changes, EV is considered a more precise measure because it directly accounts for the consumer's utility function and is based on the concept of compensated demand. Co⁷, ⁸nsumer surplus, typically measured as the area under the demand curve and above the price, is an approximation that assumes the marginal utility of income is constant, which is not always the case.

#⁵, ⁶## Can equivalent variation be negative?
Yes, equivalent variation can be negative. A negative EV indicates that the consumer is better off as a result of the price or policy change, meaning that money could be taken away from them, at the original prices, and they would still achieve the new (higher) level of utility. Co⁴nversely, a positive EV signifies a welfare loss.

Is equivalent variation used in real-world policy decisions?

Yes, equivalent variation is a significant tool in real-world policy analysis, particularly within the field of welfare economics. It helps governments and international organizations, such as the World Bank, evaluate the monetary impact of policies like taxation, subsidies, or price changes on different segments of the population. Ho², ³wever, its practical application can be challenging due to data requirements and the complexity of measuring utility.¹