On measuring welfare: Marshall versus Hicks

This article presents arguments by Willig (1976) and Hausman (1981) who compared Marshall’s and Hicks’s methods for measuring welfare changes due to price shifts. While both considered Hicks’s method to be superior, Willig argued that the two approaches result in very similar estimates of consumer surplus for goods that both i) account for a small share of total expenditure, and ii) have a small income elasticity of demand. Hausman challenged Willig’s conclusion by showing that small differences in consumer surplus can still translate into large percentage disparities in deadweight loss. In other words, even under Willig’s conditions, Marshall’s approach can still lead to large errors when measuring economic efficiency.

Picture of Sir John Richard Hicks

Marshall’s and Hicks’s welfare metrics

Measuring welfare can be a contentious topic among economists since it is often 1) what economic policy aims to improve, and 2) hard to measure. This article discusses two classic tools used for measuring welfare changes for consumers: Marshall’s consumer surplus and Hicks’s compensating variation.

Marshall’s consumer surplus measures welfare changes through the notional savings that consumers gain when the market price is below their maximum willingness to pay. For example, if a consumer spends $10 on a t-shirt but is willing to pay up to $15, then, according to Marshall, they would earn a consumer surplus of $5 ($15-$10). And if the price rose to $12, then the consumer surplus would fall to $3 ($15-$12). The issue with Marshall’s approach is its implicit assumption that people’s wealth doesn’t affect how much they value money (or, in formal terms, that the marginal utility of money is constant). This assumption was severely criticised at its time, which inspired Hicks’s later formulation (for more on Marshall’s approach, you can read our previous blog).

Hicks’s compensating variation, which doesn’t require Marshall’s utility assumption, defines welfare changes as the amount of money that needs to be given to a consumer before a price change to keep them as well-off as before. For example, if the electricity price rises from 25p to 0.50p per kWh, increasing the bill by £10 under initial consumption, Hicks’s compensating variation would capture the funds required to return the consumer to their initial utility level. This amount is often less than the £10 bill rise, since consumers could shift part of their electricity consumption towards cheaper alternatives.

Willig’s case for using Marshall’s consumer surplus

Despite Hicks’s approach being theoretically more sound, its practical complexity has meant that Marshall’s consumer surplus has remained widely used in economic research. Willig’s 1976 paper, ‘Consumer’s Surplus Without Apology’, attempted to defend this approach by showing that, under certain common conditions, the two measures yield very similar welfare change estimates for consumers.

In particular, Willig showed that the percentage difference between compensating variation and changes in consumer surplus could be quite small for normal goods that account for a small share of total spending. For example, assuming an income elasticity of 0.8 and a consumer surplus change equal to 5% of income, Willig’s formula estimates that Marshall’s metric would differ from Hicks’s by less than 2% (see formula below – η signifies the lowest and highest values for income elasticity of demand).

Willig’s (1976) formula for estimating percentage errors in Marshallian surplus:

Hausman’s response - an important clarification

Hausman’s 1981 paper, ‘Exact Consumers’ Surplus and Deadweight Loss’, challenged Willig’s claim that Marshall’s approach can often be used interchangeably with Hicks’s. He illustrated that, even when measurements of consumer welfare are closely aligned, the implied estimates of deadweight loss can dramatically differ. Consequently, he argued that economists should avoid using Marshall’s approach when assessing economic efficiency.

Hausman illustrated his point through an example in which he assumed that the gasoline price rose from $0.75 to $1.50 per gallon, that the income elasticity was 1.1, and that the average monthly income was $720. He first confirmed Willig’s result that Marshall’s consumer surplus was very close to Hicks’s compensating variation, with the difference being just 3.2% ($35.99 vs. $37.17). And he then showed that the approaches yielded strikingly different estimates for deadweight loss – at $3.96, the Marshallian measure was almost 32% higher.

Conclusion

Overall, Willig’s paper illustrates that, under certain conditions, Marshall’s approach can closely approximate Hicks’s metric of consumer welfare. However, as shown by Hausman, this doesn’t mean that it would also lead to an accurate measurement of economic efficiency.