Aggregation Need to aggregate impacts across individuals

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Presentation transcript:

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

Individual welfare function for i Ui = Ui(Xi1, Xi2, … Xij) Max L=Ui(Xi1, Xi2, … Xij) – λ(p1*Xi1+p2*Xi2 … - Y) FOC: ∂Uij/∂Xj = λ * Pj ∂Uij/∂Xj = ∂Ui/∂Y * Pj dUi = Σj ∂Ui/∂Xj dXij = Σj ∂Ui/∂Y*Pj dXij

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

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

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).

Gorman Demand form Ui = Ai(P) + B(P) * Yi ∂Ui/∂Y = B (for all i)

Example from Zerbe & Dively 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)

Example 1 Residents Airlines Net Social Value No airport to airport -5000 WTA +3000 WTP -2000 Airport to no airport +3500 WTP -3000 WTA +500 Kaldor Hicks

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

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

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)

Example 1 Residents Airlines Net Social Value No airport to airport -5000 WTA +3000 WTP -2000 Airport to no airport +3500 WTP -3000 WTA +500

Resident airline travelers Example 1A Residents Resident airline travelers Net Social Value No airport to airport -5000 WTA +2000 WTP -3000 Airport to no airport +3500 WTP -3200 WTA +300

Ambiguous Outcomes of Compensation Rules

Resident airline travelers Example 2 Residents Resident airline travelers Net Social Value No airport to airport -5000 WTA +2000 WTP -3000 Airport to no airport +3500 WTP -4000 WTA -500

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.