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Understanding Aggregation and Kaldor-Hicks Compensation in Social Welfare Analysis

This document explores the principles of aggregation in impact assessments across individuals, emphasizing the aggregation of individual welfare functions into a social welfare function. It discusses key theories, including the Kaldor-Hicks Compensation Tests, which evaluate how benefits and losses from projects, like airport construction, can be compensated among affected parties. The distinctions between willingness to pay (WTP) and willingness to accept (WTA) are highlighted to illustrate the economic implications of social projects. The analysis also addresses the complexities of property rights in determining compensation.

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Understanding Aggregation and Kaldor-Hicks Compensation in Social Welfare Analysis

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  1. Aggregation • Need to aggregate impacts across individuals • Welfare Function: Aggregation of individual welfare functions.

  2. Individual welfare function for i Ui = Ui(Xi1, Xi2, … Xij) Max L=Ui(Xi1, Xi2, … Xij) – λi(p1*Xi1+p2*Xi2 …+pj*Xij - Yi) FOC: ∂Uj/∂Xij = λi * Pj ∂Uj/∂Xij = ∂Ui/∂Yi * Pj dUi = Σj∂Ui/∂Xj dXij = Σj∂Ui/∂Yi*Pj dXij

  3. Social Welfare Function W = W(U1,U2,U3,…Un) dW = Σi∂W/∂Ui dUi = ΣjΣi ∂W/∂Ui *∂Ui/∂Y * Pj dXij = MSUi * MU Incomei * Pj dXij MSUi = Maginal Social Utility of individual i MU Incomei = Marginal utility of income for indivual i.

  4. Kaldor – Hicks Compensation Tests • Kaldor: The winners from a project can in principal compensate the losers • “CV” • Hicks: The losers cannot bribe the potential winners not to undertake the project • “EV” • Scitovsky: Both the Kaldor and Hicks criteria are met.

  5. Kaldor – Hicks Compensation Tests • These compensation tests assume: • MSUi = MSU j for all i, j • MUi Income = MUj Income = k. • A dollar has the same “value” (utility) for all individuals in society, no matter what their income level (or other characteristics).

  6. Example from Zerbe & Dively(pp. 102 -108) • Consider option to build an airport • Impacts: • Costs • If built, neighboring residents will suffer from increased noise • WTP to not have the airport built (EV) • WTA after airport is built (CV) • Benefits • Airlines “gain” from airport (increased profits)

  7. Example 1Plan to build airport Kaldor Hicks

  8. WTP vs WTA • Generally Expect WTP to avoid a negative change will be less than the WTA to accept the change. • Why? • WTP is constrained by limited income • WTA is unconstrained • For normal goods, price reduction will have positive income effect, price increase will have negative income effect

  9. Question? • Why would airlines (firms) have different WTP than WTA? • WTP should be equal to expected future profits • WTA should also be equal to expected future profits • General point – always need to look at final impacts on consumers

  10. Alternative Formulation • Rather than the “benefits” of the airlines, consider the benefits of building the airport to local residents who would be able to use the new airport: • Reduced (total) price of airline travel (including the price of travel to the nearest airport)

  11. Example 1

  12. Example 1A

  13. Ambiguous Outcomes of Compensation Rules

  14. Example 2

  15. Ambiguous Outcomes of Compensation Rules • In this situation: • If airport does not exist, don’t build it • If airport exists, do not get rid of it • “Tyranny of the Status Quo” • Also, depends on property rights. • Do residents have right to quiet. If so they do not have pay the passengers, but passengers must compensate the residents for noise created. • Property rights determines who has “standing” in the analysis, but not necessarily who should have standing

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