Frank Cowell: Welfare Fairness

WELFARE: FAIRNESSMICROECONOMICSPrinciples and Analysis Frank Cowell

Almost essential Welfare: Basics

Prerequisites

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Frank Cowell: Welfare Fairness

Fairness: some conceptual problems Can fairness be reconciled with an individualistic approach to

welfare? How can fairness be incorporated into a model?

• on what can we base it?• what relation to other welfare concepts?

Why introduce a concept of fairness?

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Frank Cowell: Welfare Fairness

Fairness: Concepts Fairness as an external moral imperative

• Considered further in the social welfare-function approach Fairness as the mirror image of Pareto superiority

• Use individuals’ own utility functions Fairness based on selfishness?

• Formulate fairness concept as “absence of envy” Reason for introducing fairness as a principle

• sometimes efficiency criteria alone produce disgusting results...

example

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Frank Cowell: Welfare Fairness

Oa

x1b

x1a

x2a

x2b

Fairness in the trading model

[x°], [x°°] "obviously" unfair?

Ob

The Edgeworth box Extreme, efficient allocations Two more efficient allocations Another, intermediate example

[x°]

[x°°]

[x′]

[x′′]

[x]Perhaps also [x'], [x''] ?

Swap a's and b's allocations

a prefers b's allocation in [x]

So [x] is not fair

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Frank Cowell: Welfare Fairness

Towards a definition of fairness Recall the definition of Pareto superiority as:

• allocation [x] is superior to [x′] if:• for all h: Uh(xh) ³ Uh(x′h)• for some h: Uh(xh) > Uh(x′h)

Use this individualistic approach to formalise fairness as “no-envy”• compare, not with an alternative, hypothetical bundle…• ..but with the bundles enjoyed by other people

An allocation is fair if, for every pair of individuals h and k:• Uh(xh) ³ Uh(xk )• given my tastes I weakly prefer my bundle to yours

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Frank Cowell: Welfare Fairness

A result on fairness THEOREM: if all persons have equal incomes then a

competitive equilibrium is a fair allocation An apparently appealing result Seems to combines two opposing principles:

• individualism – embodied in competitive behaviour• egalitarianism – embodied in equal-incomes requirement

Proof is straightforward

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Frank Cowell: Welfare Fairness

Fairness result: proof For every household h let

• Ah := {xh: Si pixih yh }

• attainable set for h If [x*] is a CE then

• x*h Ah and • Uh(x*h) ³Uh(xh ) for all xh Ah

But if all incomes are equal then, for any h and k:• Ah = Ak

• so x*k Ah

Therefore Uh(x*h) ³Uh(x*k ) for any households h and k• So no one would prefer another person’s bundle• CE is fair (envy free)

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Frank Cowell: Welfare Fairness

Oa

x1b

x1a

x2a

x2b

The fair allocation

Allocation [x*] is CE if incomes are as shown [x*]

Ob

The Edgeworth box An efficient allocation Supporting price ratio = MRS Incomes in terms of good 1

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Frank Cowell: Welfare Fairness

The fairness result – discussion Is the result as appealing as it seems? What if Alf and Bill have different needs?

• Age,• disability, • family...?

Should not this be reflected in money incomes? Would not the equal-income solution be regarded as “unfair” Does the problem come from

• competition? • individualism?

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Frank Cowell: Welfare Fairness

Summary Consider fairness along with other general welfare principles Efficiency

• neat and simple• but perhaps limited

Potential efficiency • Persuasive but perhaps dangerous economics/politics

Fairness• nice idea but doesn't get us far

For these reasons it may be useful to examine an explicit welfare-function approach

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