1. Frank Cowell: Welfare Fairness WELFARE: FAIRNESS MICROECONOMICS Principles and Analysis Frank Cowell Almost essential Welfare: Basics Almost essential Welfare: Basics Prerequisites July 2015 1

2. 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

3. 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

4. Frank Cowell: Welfare Fairness OaOa x1x1 b x1x1 a x2x2 a x2x2 b Fairness in the trading model  [ x°], [x°°] "obviously" unfair? ObOb  The Edgeworth box  Extreme, efficient allocations  Two more efficient allocations  Another, intermediate example l [x°] l [x°°] l [x′] l [x′′] l [x]  Perhaps also [x'], [x''] ?  Swap a's and b's allocations l  a prefers b 's allocation in [x]  So [x ] is not fair July 2015 4

5. 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: 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 July 2015 5

6. 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

7. Frank Cowell: Welfare Fairness Fairness result: proof  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  But if all incomes are equal then, for any h and k: A h = A k so x *k  A h  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) July 2015 7

8. Frank Cowell: Welfare Fairness OaOa x1x1 b x1x1 a x2x2 a x2x2 b The fair allocation  Allocation [ x * ] is CE if incomes are as shown l [x * ] ObOb  The Edgeworth box  An efficient allocation  Supporting price ratio = MRS  Incomes in terms of good 1 July 2015 8

9. 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

10. 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