What Can Benefit Cost What Can Benefit Cost Analysis Tell Us? Analysis Tell Us?

Ted BergstromUCSB

New Welfare Economics New Welfare Economics

• Kaldor and Hicks, 1939. Kaldor and Hicks, 1939. • Compensation Principle.Compensation Principle.• Change is an improvement if Change is an improvement if

gainers gainers could could compensate losers.compensate losers.

A Dollar is a Dollar?A Dollar is a Dollar?

““When evaluating net benefits and When evaluating net benefits and costs of a given action the costs costs of a given action the costs and benefits accruing to each and benefits accruing to each individual should normally be individual should normally be added without regard to the added without regard to the individual(s) to whom they individual(s) to whom they accrue.”---Harbergeraccrue.”---Harberger

A Sound Chain of A Sound Chain of reasoning? reasoning?

1) If a project passes the 1) If a project passes the

Compensation test, it isCompensation test, it is

Potentially Pareto improvingPotentially Pareto improving

2) If a project is potentially Pareto 2) If a project is potentially Pareto improving, it should be adopted.improving, it should be adopted.

Message of this paperMessage of this paper

• Though both links are broken,Though both links are broken,

Benefit cost analysis remains a Benefit cost analysis remains a useful tool.useful tool.

Link 2 of the chain: Link 2 of the chain: Hicks on CompensationHicks on Compensation

““Every simple economic reform inflicts a Every simple economic reform inflicts a loss on some people. Yet when such loss on some people. Yet when such reforms have been carried through…reforms have been carried through…compensation has not been given, and compensation has not been given, and economic progress has accumulated a economic progress has accumulated a roll of victims, sufficient to give all roll of victims, sufficient to give all sound policy a bad name. “sound policy a bad name. “

Link 1 of the chainLink 1 of the chain • A reallocation in a pure exchange A reallocation in a pure exchange

private goods economy need not private goods economy need not be potentially Pareto improving be potentially Pareto improving even if the sum of compensating even if the sum of compensating variations over all individuals is variations over all individuals is positive. positive.

• Money values are a rubbery Money values are a rubbery measuring rod—Samuelson (1950)measuring rod—Samuelson (1950)

• Boadway paradox.Boadway paradox.

A public goods economyA public goods economy

• Consider an economy with 1 Consider an economy with 1 private good, and n public goods. private good, and n public goods.

• Each consumer has utility UEach consumer has utility U ii(x(xii,y) ,y)

• Cost of private goods vector y is Cost of private goods vector y is given by a function C(y). given by a function C(y).

• Sum of individual private Sum of individual private consumptions plus C(y) is a consumptions plus C(y) is a constant. constant.

Salvaging Link 1:Salvaging Link 1:

• In public goods economy there is only 1 In public goods economy there is only 1 private good. private good.

• This can be used as measuring rod, This can be used as measuring rod, avoiding index number problems, avoiding index number problems, Boadway paradox, etc. Boadway paradox, etc.

• Reasonable if policy change does not Reasonable if policy change does not substantially affect relative prices of substantially affect relative prices of private goods. (Ng-Mishan defense)private goods. (Ng-Mishan defense)

Compensation test in a Compensation test in a public goods economypublic goods economy

• Define consumer j’s willingness to Define consumer j’s willingness to

pay for a change in public goods pay for a change in public goods from y to y’ as wfrom y to y’ as wj j where:where:

• UUii(x(xjj- w- wjj,y) = U,y) = Uii(x(xjj,y’) ,y’)

• Compensation test: Compare . Compensation test: Compare .

Sum of wj’s to C(y’)-C(y).Sum of wj’s to C(y’)-C(y).

Repairs on Link 1Repairs on Link 1

• TheoremTheorem: For a public goods : For a public goods

economy, a project passes the economy, a project passes the compensation test if and only if it compensation test if and only if it is potentially Pareto improving. is potentially Pareto improving.

• Trivial proof. Trivial proof.

What to choose?What to choose? • Disadvantage of compensation test: It Disadvantage of compensation test: It

doesn’t order alternatives relative to doesn’t order alternatives relative to each other, only a single alternative each other, only a single alternative relative to status quo.relative to status quo.

• You could proceed sequentially, but You could proceed sequentially, but you would need a separate study for you would need a separate study for each conceivable alternative. each conceivable alternative.

Samuelson conditionSamuelson condition • Samuelson condition brings Samuelson condition brings

calculus to aid in search.calculus to aid in search.

• With smoothness, a necessary With smoothness, a necessary condition for an increase in y to be condition for an increase in y to be potentially Pareto improving ispotentially Pareto improving is

(sum of mrs)> mc (sum of mrs)> mc • Also sufficient for small changes. Also sufficient for small changes.

Potential Pareto Improvement Potential Pareto Improvement in a public goods modelin a public goods model

Scitovsky-style paradoxes Scitovsky-style paradoxes remain remain

• An “ordering” on allocations that An “ordering” on allocations that

respects the compensation respects the compensation principle will have still have principle will have still have cycles, even with a single public cycles, even with a single public good.good.

Got Paradoxes? Got Paradoxes?

Orderly Nesting Orderly Nesting

Three Repair CrewsThree Repair Crews • Rotten-Kid Defense –Becker, Parish, NgRotten-Kid Defense –Becker, Parish, Ng

• Fair Gamble Defense Fair Gamble Defense

• Search Tool Defense Hicks, et alSearch Tool Defense Hicks, et al

Rotten-Kid DefenseRotten-Kid Defense • Income distribution is controlled by Income distribution is controlled by

forces beyond control of benefit cost forces beyond control of benefit cost analysts.analysts.

• A project that passes the benefit cost A project that passes the benefit cost test will ultimately result in a better test will ultimately result in a better outcome for (almost) everybodyoutcome for (almost) everybody

• Therefore the dollar-is-a-dollar rule is a Therefore the dollar-is-a-dollar rule is a good one for benefit cost.good one for benefit cost.

Probing the Rotten Kid Probing the Rotten Kid Defense?Defense?

• Like Becker’s family example, this Like Becker’s family example, this

argument has some appeal if utility argument has some appeal if utility possibility frontiers are nested and possibility frontiers are nested and “parallel.”“parallel.”

• Supported by bargaining theory only if Supported by bargaining theory only if “threat points” are not altered. (Pollack “threat points” are not altered. (Pollack and Lundberg examples)and Lundberg examples)

• Projects may change shape of UPF. If so, Projects may change shape of UPF. If so, potential Pareto improvement need not potential Pareto improvement need not result in actual Pareto improvement.result in actual Pareto improvement.

The Fair Gamble DefenseThe Fair Gamble Defense • Government should have a policy of Government should have a policy of

accepting projects if and only if they accepting projects if and only if they the benefit-cost test, while paying for the benefit-cost test, while paying for them using the existing tax structure.them using the existing tax structure.

• Although individuals win some and lose Although individuals win some and lose some, they will on average be best off some, they will on average be best off with this policy.with this policy.

Weakness of the Fair Weakness of the Fair Gamble DefenseGamble Defense

• It does not offer a complete It does not offer a complete

ordering among multiple projectsordering among multiple projects• Some projects, though passing Some projects, though passing

the fair gamble test have clearly the fair gamble test have clearly identifiable winners and losers. identifiable winners and losers.

When Fair Gamble When Fair Gamble Defense Applies. Defense Applies.

• Incomplete information about Incomplete information about

individual preference types, but good individual preference types, but good statistical information about statistical information about distribution. distribution.

• Projects (though possibly large) have Projects (though possibly large) have small enough impacts on individual small enough impacts on individual wealth so that risk neutrality is a good wealth so that risk neutrality is a good assumption. assumption.

The Search Tool Defense The Search Tool Defense Benefit Cost can tell Benefit Cost can tell Where to look and Where to look and Where not to look forWhere not to look forPareto improvementsPareto improvements

Two-Stage ProcedureTwo-Stage Procedure ..1)1) If policy fails the BC test, drop it. If If policy fails the BC test, drop it. If

policy passes, look for Pareto improving policy passes, look for Pareto improving ways to apply it. ways to apply it.

2)2) If policy passes and benefits are If policy passes and benefits are unevenly distributed in known ways, unevenly distributed in known ways, allocate costs accordingly. If specific allocate costs accordingly. If specific beneficiaries unidentifiable, consider beneficiaries unidentifiable, consider whether fair gamble argument justifies. whether fair gamble argument justifies.