Prerequisites
Almost essential
Welfare: Basics
WELFARE: FAIRNESS
MICROECONOMICS
Principles and Analysis
Frank Cowell
July 2017
Frank Cowell: Welfare Fairness
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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 2017
Frank Cowell: Welfare Fairness
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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 2017
Frank Cowell: Welfare Fairness
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Fairness in the trading model
x1b
[x°°]
x2a
[x′′]
Ob


 The Edgeworth box
 Extreme, efficient allocations
 Two more efficient allocations
 Another, intermediate example
 Swap a's and b's allocations


[x]
[x°], [x°°] "obviously" unfair?
Perhaps also [x'], [x''] ?
a prefers b's allocation in [x]
O
[x′]

[x°]
a
July 2017
So [x] is not fair
x2b
x1a
Frank Cowell: Welfare Fairness
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Towards a definition of fairness
 Recall the definition of Pareto superiority as:
• allocation [x] is superior to [x′] if:
• for all h: Uh(xh)  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)  Uh(xk )
• given my tastes I weakly prefer my bundle to yours
July 2017
Frank Cowell: Welfare Fairness
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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 2017
Frank Cowell: Welfare Fairness
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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) Uh(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) Uh(x*k ) for any households h and k
• So no one would prefer another person’s bundle
• CE is fair (envy free)
July 2017
Frank Cowell: Welfare Fairness
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The fair allocation
x1b
Ob
x2a
 The Edgeworth box
 An efficient allocation
 Supporting price ratio = MRS
 Incomes in terms of good 1
 Allocation [x*] is CE if

Oa
July 2017
[x*]
incomes are as shown
x2b
x1a
Frank Cowell: Welfare Fairness
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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 2017
Frank Cowell: Welfare Fairness
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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 2017
Frank Cowell: Welfare Fairness
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