1. Frank Cowell: Microeconomics Welfare: Fairness MICROECONOMICS Principles and Analysis Frank Cowell Almost essential Welfare: Basics Almost essential Welfare: Basics Prerequisites December 2006

2. Frank Cowell: Microeconomics Fairness: some conceptual problems Can fairness be reconciled with an individualistic approach to welfare? Can fairness be reconciled with an individualistic approach to welfare? How can fairness be incorporated into a model? 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? Why introduce a concept of fairness?

3. Frank Cowell: Microeconomics Fairness: Concepts Fairness as an external moral imperative Fairness as an external moral imperative  Considered further in the social welfare-function approach social welfare-functionsocial welfare-function Fairness as the mirror image of Pareto superiority Fairness as the mirror image of Pareto superiority  Use individuals’ own utility functions Fairness based on selfishness? Fairness based on selfishness?  Formulate fairness concept as “absence of envy” Reason for introducing fairness as a principle Reason for introducing fairness as a principle  sometimes efficiency criteria alone produce disgusting results... example

4. Frank Cowell: Microeconomics OaOa x1x1 b x1x1 a x2x2 a x2x2 b Fairness in the trading model   Are [x°], [x°°] "obviously" unfair? ObOb   The Edgeworth box   Extreme, efficient allocations   Two more efficient allocations   Another, intermediate example ll ll [x°] ll ll [x°°] ll ll [x′] ll ll [x′′] ll ll [x]   Perhaps also [x'], [x''] ?   Swap a's and b's allocations ll ll   a prefers to have b's allocation in [x]   So [x] is not fair

5. Frank Cowell: Microeconomics Towards a definition of fairness Recall the definition of Pareto superiority as:   allocation [x] is superior to [x′] if…   for all h: U h (x h )  U h (x′ h )   for some h: U h (x h )  U h (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:   U h (x h )  U h (x k )   given my tastes I weakly prefer my bundle to yours

6. Frank Cowell: Microeconomics A result on fairness THEOREM: if all persons have equal incomes then a competitive equilibrium is a fair allocation. THEOREM: if all persons have equal incomes then a competitive equilibrium is a fair allocation. An apparently appealing result An apparently appealing result Seems to combines two opposing principles: Seems to combines two opposing principles:  individualism – embodied in competitive behaviour  egalitarianism – embodied in equal-incomes requirement Proof is straightforward Proof is straightforward

7. Frank Cowell: Microeconomics Fairness result: proof For every household h l For every household h let   A h := {x h :  i p i x i h  y h  }   attainable set for h If [x * ] is a CE then   x *h  A h and   U h (x *h )  U h (x h ) for all x h  A h hk But if all incomes are equal then, for any h and k:   A h = A k   so x *k  A h hk Therefore U h (x *h )  U h (x *k ) for any households h and k   So no one would prefer another person’s bundle   CE is fair (envy free)

8. Frank Cowell: Microeconomics OaOa x1x1 b x1x1 a x2x2 a x2x2 b The fair allocation   The allocation [x*] is a CE if incomes are as shown l l [x * ] ObOb   The Edgeworth box   An efficient allocation   Supporting price ratio = MRS   Incomes in terms of good 1

9. Frank Cowell: Microeconomics The fairness result – discussion Is the result as appealing as it seems? Is the result as appealing as it seems? What if Alf and Bill have different needs? What if Alf and Bill have different needs?  Age,  disability,  family...? Should not this be reflected in money incomes? Should not this be reflected in money incomes? Would not the equal-income solution be regarded as “unfair” Would not the equal-income solution be regarded as “unfair” Does the problem come from Does the problem come from  competition?  individualism?

10. Frank Cowell: Microeconomics Summary Consider fairness along with other general welfare principles Consider fairness along with other general welfare principles Efficiency Efficiency  neat and simple  but perhaps limited Potential efficiency Potential efficiency  Persuasive but perhaps dangerous economics/politics Fairness Fairness  nice idea but doesn't get us far For these reasons it may be useful to examine an explicit welfare-function approach For these reasons it may be useful to examine an explicit welfare-function approachexplicit welfare-functionexplicit welfare-function