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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
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
Fairness as an external moral imperative
Fairness as the mirror image of Pareto superiority
Use individuals’ own utility functions
Fairness based on selfishness?
Considered further in the social welfare-function approach
Formulate fairness concept as “absence of envy”
Reason for introducing fairness as a principle
sometimes efficiency criteria alone produce disgusting
results...
example
Fairness in the trading model
Frank Cowell: Microeconomics
x1b
[x°°]
[x′′]
x2a
Ob
The Edgeworth box
Extreme, efficient allocations
Two more efficient allocations
Another, intermediate example
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]
Oa
x2b
x1a
So [x] is not fair
Towards a definition of fairness
Frank Cowell: Microeconomics
Recall the definition of Pareto superiority as:
Use this individualistic approach to formalise fairness
as “no-envy”
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:
Uh(xh) Uh(xk )
given my tastes I weakly prefer my bundle to yours
A result on fairness
Frank Cowell: Microeconomics
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
Fairness result: proof
Frank Cowell: Microeconomics
For every household h let
Ah := {xh: Si pixih yh }
attainable set for h
If [x*] is a CE then
But if all incomes are equal then, for any h and k:
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
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
Oa
[x*] is a CE if
incomes are as
shown
[x*]
x2b
x1a
The fairness result – discussion
Frank Cowell: Microeconomics
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?
Summary
Frank Cowell: Microeconomics
Consider fairness along with other general welfare principles
Efficiency
Potential efficiency
Persuasive but perhaps dangerous economics/politics
Fairness
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