What Can Benefit Cost Analysis Tell Us? Ted Bergstrom UCSB

New Welfare Economics Kaldor and Hicks, 1939.Kaldor and Hicks, Compensation Principle.Compensation Principle. Change is an improvement if gainers could compensate losers.Change is an improvement if gainers could compensate losers.

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

A Sound Chain of reasoning? 1) If a project passes the Compensation test, it is Potentially Pareto improving 2) If a project is potentially Pareto improving, it should be adopted.

Message of this paper Message of this paper Though both links are broken,Though both links are broken, Benefit cost analysis remains a useful tool.

Link 2 of the chain: Hicks on Compensation “Every simple economic reform inflicts a loss on some people. Yet when such reforms have been carried through…compensation has not been given, and economic progress has accumulated a roll of victims, sufficient to give all sound policy a bad name. “

Link 1 of the chain Link 1 of the chain A reallocation in a pure exchange private goods economy need not be potentially Pareto improving even if the sum of compensating variations over all individuals is positive. A reallocation in a pure exchange private goods economy need not be potentially Pareto improving even if the sum of compensating variations over all individuals is positive. Money values are a rubbery measuring rod—Samuelson (1950) Money values are a rubbery measuring rod—Samuelson (1950) Boadway paradox. Boadway paradox.

A public goods economy Consider an economy with 1 private good, and n public goods. Consider an economy with 1 private good, and n public goods. Each consumer has utility U i (x i,y)Each consumer has utility U i (x i,y) Cost of private goods vector y is given by a function C(y).Cost of private goods vector y is given by a function C(y). Sum of individual private consumptions plus C(y) is a constant. Sum of individual private consumptions plus C(y) is a constant.

Salvaging Link 1: In public goods economy there is only 1 private good. In public goods economy there is only 1 private good. This can be used as measuring rod, avoiding index number problems, Boadway paradox, etc.This can be used as measuring rod, avoiding index number problems, Boadway paradox, etc. Reasonable if policy change does not substantially affect relative prices of private goods. (Ng-Mishan defense)Reasonable if policy change does not substantially affect relative prices of private goods. (Ng-Mishan defense)

Compensation test in a public goods economy Define consumer j’s willingness to pay for a change in public goods from y to y’ as w j where:Define consumer j’s willingness to pay for a change in public goods from y to y’ as w j where: U i (x j - w j,y) = U i (x j,y’) U i (x j - w j,y) = U i (x j,y’) Compensation test: Compare. Compensation test: Compare. Sum of wj’s to C(y’)-C(y).

Repairs on Link 1 Theorem: For a public goods economy, a project passes the compensation test if and only if it is potentially Pareto improving.Theorem: For a public goods economy, a project passes the compensation test if and only if it is potentially Pareto improving. Trivial proof.Trivial proof.

What to choose? Disadvantage of compensation test: It doesn’t order alternatives relative to each other, only a single alternative relative to status quo.Disadvantage of compensation test: It doesn’t order alternatives relative to each other, only a single alternative relative to status quo. You could proceed sequentially, but you would need a separate study for each conceivable alternative. You could proceed sequentially, but you would need a separate study for each conceivable alternative.

Samuelson condition Samuelson condition brings calculus to aid in search.Samuelson condition brings calculus to aid in search. With smoothness, a necessary condition for an increase in y to be potentially Pareto improving is With smoothness, a necessary condition for an increase in y to be potentially Pareto improving is (sum of mrs)> mc (sum of mrs)> mc Also sufficient for small changes. Also sufficient for small changes.

Potential Pareto Improvement in a public goods model

Scitovsky-style paradoxes remain An “ordering” on allocations that respects the compensation principle will have still have cycles, even with a single public good.An “ordering” on allocations that respects the compensation principle will have still have cycles, even with a single public good.

Got Paradoxes?

Orderly Nesting

Three 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 Defense Income distribution is controlled by forces beyond control of benefit cost analysts. Income distribution is controlled by forces beyond control of benefit cost analysts. A project that passes the benefit cost test will ultimately result in a better outcome for (almost) everybody A project that passes the benefit cost test will ultimately result in a better outcome for (almost) everybody Therefore the dollar-is-a-dollar rule is a good one for benefit cost. Therefore the dollar-is-a-dollar rule is a good one for benefit cost.

Probing the Rotten Kid Defense? Like Becker’s family example, this argument has some appeal if utility possibility frontiers are nested and “parallel.” Like Becker’s family example, this argument has some appeal if utility possibility frontiers are nested and “parallel.” Supported by bargaining theory only if “threat points” are not altered. (Pollack and Lundberg examples) Supported by bargaining theory only if “threat points” are not altered. (Pollack and Lundberg examples) Projects may change shape of UPF. If so, potential Pareto improvement need not result in actual Pareto improvement. Projects may change shape of UPF. If so, potential Pareto improvement need not result in actual Pareto improvement.

The Fair Gamble Defense Government should have a policy of accepting projects if and only if they the benefit-cost test, while paying for them using the existing tax structure. Government should have a policy of accepting projects if and only if they the benefit-cost test, while paying for them using the existing tax structure. Although individuals win some and lose some, they will on average be best off with this policy. Although individuals win some and lose some, they will on average be best off with this policy.

Weakness of the Fair Gamble Defense It does not offer a complete ordering among multiple projects It does not offer a complete ordering among multiple projects Some projects, though passing the fair gamble test have clearly identifiable winners and losers. Some projects, though passing the fair gamble test have clearly identifiable winners and losers.

When Fair Gamble Defense Applies. Incomplete information about individual preference types, but good statistical information about distribution. Incomplete information about individual preference types, but good statistical information about distribution. Projects (though possibly large) have small enough impacts on individual wealth so that risk neutrality is a good assumption. Projects (though possibly large) have small enough impacts on individual wealth so that risk neutrality is a good assumption.

The Search Tool Defense Benefit Cost can tell Where to look and Where not to look for Pareto improvements

Two-Stage Procedure. 1)If policy fails the BC test, drop it. If policy passes, look for Pareto improving ways to apply it. 2)If policy passes and benefits are unevenly distributed in known ways, allocate costs accordingly. If specific beneficiaries unidentifiable, consider whether fair gamble argument justifies.