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Module 02 of 855 min readAdvanced

Welfare foundations

Compensating and equivalent variation, Kaldor-Hicks, consumer and producer surplus, and the question of whose welfare counts (standing).

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Learning objectives

By the end of this module, you should be able to:

  • 01Derive benefits from consumer and producer surplus and willingness to pay
  • 02Distinguish compensating and equivalent variation from Marshallian surplus
  • 03State the Kaldor-Hicks compensation test and its hypothetical-compensation critique
  • 04Explain why aggregating willingness to pay embeds a distributional judgement

CBA's numbers are not arbitrary; they rest on welfare economics. To value a benefit credibly — and to know what a CBA result does and does not mean — you need the micro foundations: surplus, willingness to pay, the exact welfare measures, and the compensation test that licenses adding everyone's gains and losses together. This module supplies them.

Surplus and willingness to pay

The benefit of a project to a person is what it is worth to them, measured by their willingness to pay (WTP) for the gain (or willingness to accept, WTA, compensation for a loss). For a price reduction or quantity increase, the benefit shows up as a change in consumer surplus (the area between the demand curve and the price — the excess of what people would have paid over what they did pay); for producers, as a change in producer surplus (the area between price and the supply/marginal-cost curve). The total benefit of a project is the sum of the changes in consumer and producer surplus it causes — the building blocks every CBA aggregates.

The exact welfare measures

Compensating and equivalent variation

Marshallian (ordinary) consumer surplus is an approximation, because it ignores the income effect of a price change. The exact welfare measures, due to Hicks, are: • Compensating variation (CV) — the amount of money that, taken from the person after a beneficial change, would return them to their original welfare. (How much would you pay to keep the gain?) • Equivalent variation (EV) — the amount that, given to the person instead of the change, would make them as well off as the change would. (How much would you need to forgo the gain?) CV and EV differ from each other, and from Marshallian surplus, by the size of the income effect; for small changes in goods that are a small share of income, the three roughly coincide, which is why ordinary surplus is usually a fine approximation. The distinction matters for large changes and for the choice of reference point — and it underlies the often-large gap between WTP and WTA for the same item.

The Kaldor-Hicks test

CBA adds up the WTP of winners and the WTA of losers and asks whether the net is positive. The justification is the Kaldor-Hicks (potential Pareto) criterion: a change is an improvement if the winners gain enough that they could fully compensate the losers and still be better off — whether or not they actually do. This is what licenses aggregation across people: it converts many individual welfare changes into one net figure. It is also where CBA's deepest controversy lives.

Compensation is hypothetical

Kaldor-Hicks requires only that compensation COULD be paid, not that it IS. So a project with a positive NPV can make a society 'better off' in the Kaldor-Hicks sense while actually leaving identifiable people worse off, because the compensation never happens. A dam with NPV > 0 may genuinely improve aggregate efficiency while the displaced villagers, uncompensated, bear a real loss. Critics (Scitovsky showed the test can even be inconsistent — both a move and its reverse can pass) argue this makes CBA a tool that sanctions uncompensated harm in the name of efficiency. The defence is that efficiency and distribution are separate questions, and that compensation, where warranted, should be arranged separately. But the appraiser must never forget that a positive NPV is a statement about potential, not actual, improvement — which is exactly why distribution (module 7) cannot be ignored.

The ability-to-pay problem

WTP is weighted by income

The foundation of CBA hides a distributional judgement. Willingness to pay is constrained by ability to pay: a rich person can and will pay more for the same benefit (an hour saved, a risk reduced) than a poor person, simply because they have more money. So when CBA aggregates unweighted WTP, it implicitly counts a shilling of benefit to the rich the same as a shilling to the poor — and therefore counts the rich person's underlying gain as larger, because they expressed it in more shillings. Standard CBA thus has a built-in bias toward projects that serve those with money. This is not a bug to be patched casually; it is intrinsic to valuing benefits by WTP, and it is the analytical reason the distribution question (weights, the MVPF) cannot be left out — a theme this course returns to in module 7.

Exercise

A government can build one of two clean-water projects with equal cost. Project A serves a wealthy suburb where residents have high willingness to pay for reliable piped water; Project B serves a poor informal settlement where residents desperately need clean water but can pay very little. A standard CBA finds Project A has the higher NPV. (1) Explain, using WTP and ability to pay, why A scores higher even though B may address greater need. (2) Relate this to the Kaldor-Hicks basis of CBA and the hypothetical-compensation critique. (3) Is the CBA 'wrong'? Explain what it is and isn't telling you. (4) Preview how the appraisal could be adjusted to reflect that a shilling of benefit means more to the poor.

Key takeaways

  • A project's benefit to a person is their willingness to pay (or willingness to accept for a loss); total benefit is the change in consumer plus producer surplus
  • Compensating and equivalent variation are the exact (Hicksian) welfare measures; Marshallian surplus approximates them well for small changes in small budget shares
  • Kaldor-Hicks (potential Pareto) licenses aggregating gains and losses — a change is an 'improvement' if winners COULD compensate losers — which is what lets CBA produce one net figure
  • But compensation is hypothetical: a positive NPV can leave real, identifiable people worse off (the dam-and-displaced-villagers problem); positive NPV means potential, not actual, improvement
  • Aggregating unweighted WTP embeds a distributional judgement — WTP is capped by ability to pay, so standard CBA tilts toward serving those with money; the analytical reason distribution can't be ignored

Further reading

  1. 01

    The Welfare Economics of Public Policy

    Richard Just, Darrell Hueth & Andrew Schmitz · Edward Elgar · 2004The rigorous welfare-economics foundations of applied CBA — surplus, CV/EV, and aggregation. The deep reference.

  2. 02

    The Theory of Cost-Benefit Analysis

    Jean Drèze & Nicholas Stern · Handbook of Public Economics Vol. 2 · 1987The authoritative theoretical statement, including shadow prices and distributional weights as one framework. Demanding but definitive.

  3. 03

    A Note on Welfare Propositions in Economics

    Nicholas Kaldor · Economic Journal 49 · 1939The original compensation criterion. Two pages; read it alongside Hicks (1939) and Scitovsky (1941) for the foundational debate.

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