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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 July
Citation preview
Frank Cowell: Welfare Fairness
WELFARE: FAIRNESSMICROECONOMICSPrinciples and Analysis Frank Cowell
Almost essential Welfare: Basics
Prerequisites
July 2015 1
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?
July 2015 2
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
July 2015 3
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
July 2015 4
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
July 2015 5
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
July 2015 6
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)
July 2015 7
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
July 2015 8
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?
July 2015 9
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
July 2015 10