Prerequisites Almost essential Welfare Basics WELFARE FAIRNESS MICROECONOMICS

Prerequisites Almost essential Welfare: Basics WELFARE: FAIRNESS MICROECONOMICS Principles and Analysis Frank Cowell April 2018 Frank Cowell: Welfare Fairness 1

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? April 2018 Frank Cowell: Welfare Fairness 2

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 April 2018 Frank Cowell: Welfare Fairness 3

Fairness in the trading model b x 1 [x°°] a x 2 [x′′] b O • • § 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] • [x′] Oa • [x°] April 2018 §So [x] is not fair b x 2 a x 1 Frank Cowell: Welfare Fairness 4

Towards a definition of fairness § Recall the definition of Pareto superiority as: • allocation [x] is superior to [x′] if: • for all h: Uh(xh) ³ 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) ³ Uh(xk ) • given my tastes I weakly prefer my bundle to yours April 2018 Frank Cowell: Welfare Fairness 5

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 April 2018 Frank Cowell: Welfare Fairness 6

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) ³Uh(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) ³Uh(x*k ) for any households h and k • So no one would prefer another person’s bundle • CE is fair (envy free) April 2018 Frank Cowell: Welfare Fairness 7

The fair allocation b x 1 Ob a x 2 § The Edgeworth box § An efficient allocation § Supporting price ratio = MRS § Incomes in terms of good 1 § Allocation [x*] is CE if • [x*] Oa April 2018 incomes are as shown b x 2 a x 1 Frank Cowell: Welfare Fairness 8

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? April 2018 Frank Cowell: Welfare Fairness 9

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 April 2018 Frank Cowell: Welfare Fairness 10