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Prerequisites
Almost essential
Welfare: Basics
Frank Cowell: Microeconomics
December 2006
Welfare: Fairness
MICROECONOMICS
Principles and Analysis
Frank Cowell
Fairness: some conceptual problems
Frank Cowell: Microeconomics
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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?
Fairness: Concepts
Frank Cowell: Microeconomics
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Fairness as an external moral imperative
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Fairness as the mirror image of Pareto superiority
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Use individuals’ own utility functions
Fairness based on selfishness?
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Considered further in the social welfare-function approach
Formulate fairness concept as “absence of envy”
Reason for introducing fairness as a principle
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sometimes efficiency criteria alone produce disgusting
results...
example
Fairness in the trading model
Frank Cowell: Microeconomics
x1b
[x°°]
[x′′] 
x2a
Ob
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 The Edgeworth box
 Extreme, efficient allocations
 Two more efficient allocations
 Another, intermediate example
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 Swap a's and b's allocations
[x]
 Are [x°], [x°°]
"obviously" unfair?
 Perhaps also [x'],
[x''] ?
 a prefers to have
[x′]
[x°]
b's allocation in [x]
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Oa
x2b
x1a
 So [x] is not fair
Towards a definition of fairness
Frank Cowell: Microeconomics
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Recall the definition of Pareto superiority as:
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Use this individualistic approach to formalise fairness
as “no-envy”
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allocation [x] is superior to [x′] if…
for all h: Uh(xh)  Uh(x′h)
for some h: Uh(xh) > Uh(x′h)
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:
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Uh(xh)  Uh(xk )
given my tastes I weakly prefer my bundle to yours
A result on fairness
Frank Cowell: Microeconomics
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THEOREM: if all persons have equal incomes then a
competitive equilibrium is a fair allocation.
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An apparently appealing result
Seems to combines two opposing principles:
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individualism – embodied in competitive behaviour
egalitarianism – embodied in equal-incomes requirement
Proof is straightforward
Fairness result: proof
Frank Cowell: Microeconomics
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For every household h let
 Ah := {xh: Si pixih  yh }
 attainable set for h
If [x*] is a CE then
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But if all incomes are equal then, for any h and k:
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x*h  Ah and
Uh(x*h) Uh(xh ) for all xh  Ah
Ah = Ak
so x*k  Ah
Therefore Uh(x*h) Uh(x*k ) for any households h and k
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So no one would prefer another person’s bundle
CE is fair (envy free)
The fair allocation
Frank Cowell: Microeconomics
x1b
 The Edgeworth
box
Ob
 An efficient allocation
 Supporting price ratio = MRS
 Incomes in terms of good 1
x2a
 The allocation
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Oa
[x*] is a CE if
incomes are as
shown
[x*]
x2b
x1a
The fairness result – discussion
Frank Cowell: Microeconomics
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Is the result as appealing as it seems?
What if Alf and Bill have different needs?
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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
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competition?
individualism?
Summary
Frank Cowell: Microeconomics
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Consider fairness along with other general welfare principles
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Efficiency
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Potential efficiency
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Persuasive but perhaps dangerous economics/politics
Fairness
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neat and simple
but perhaps limited
nice idea but doesn't get us far
For these reasons it may be useful to examine an explicit
welfare-function approach