Market -Welfare Welfare maximisation The government wishes to choose the best allocation according to the Swf- it wishes to maximise welfare Not all allocations are possible. The utility possibilities set is the set of feasible allocations. U U The feasible allocations lie within the sets U in the graph above. The boundary of this set is called the Pareto frontier. The isowelfare lines- lines of equal social welfare are illustrated for two exam The first example is for a Rawlsian SWF-it results in equality, ui ug. The second example is for a Utilitarian SWF-"the greatest good to the greatest number-it does not result in equality, ui>us Notice that every Pareto efficient point(a point on the Pareto frontier)is the maximum of some SWF. Market- welfare Fairness, Envy and Equity Another approach might be to propose a particular type of allocation-a fair one for example. What is a fair allocation? An envy free or equitable allocation is one where consumer A does not prefer the bundle consumer B gets and vice-versa. In the Edgeworth box the other consumers bundle is the"mirror image"bundle. would prefer to be at y- that is, neither nsumer wants to swap bundles with the other. Notice that w lies on this budget line also- equal endowments. In fact if bot ers start with an equal amount of the two goods each they will trade to a fair allocation. A appetitive equilibrium from equal division must be a fair allocation.Market — Welfare 11 Welfare Maximisation • The government wishes to choose the best allocation according to the SWF — it wishes to maximise welfare. • Not all allocations are possible. The utility possibilities set is the set of feasible allocations. ............. ............. ............. ............. ............. ........... . . . . . . ............. ............. ............. ............. ............. ............. ............. . . . . . ............................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................... . . ............................................................................................................. . ........................................................................................................................................ . . ......... ........ .... . ......... ........ .... . .. .. ... ... ... ... ... ... ... ..... ....... ........ ......... .......... ............. ....................... .............................. . .. .. ... ... ... ... ... ... ... ..... ....... ........ ......... .......... ............. ....................... .............................. U U • • u1 u1 u2 u2 u ∗ 1 u ∗ 2 u ∗ 1 u ∗ 2 0 0 • The feasible allocations lie within the sets U in the graph above. The boundary of this set is called the Pareto frontier. The isowelfare lines — lines of equal social welfare are illustrated for two examples. • The first example is for a Rawlsian SWF — it results in equality, u ∗ 1 = u ∗ 2 . The second example is for a Utilitarian SWF — “the greatest good to the greatest number” — it does not result in equality, u ∗ 1 > u ∗ 2 . • Notice that every Pareto efficient point (a point on the Pareto frontier) is the maximum of some SWF. Market — Welfare 12 Fairness, Envy and Equity • Another approach might be to propose a particular type of allocation — a fair one for example. • What is a fair allocation? An envy-free or equitable allocation is one where consumer A does not prefer the bundle consumer B gets and vice-versa. In the Edgeworth box the other consumer’s bundle is the “mirror image” bundle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....................................................................................................................................................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................................................................................................................................................... . . ....................................... . . . . . . . . . . . . . . .. .. .. ...... ...... . .......................................................................................................................................... .......................................................................................................................................... A B • x • • y ω • x is a fair allocation, (if) it is equitable and efficient. Neither consumer would prefer to be at y — that is, neither consumer wants to swap bundles with the other. Notice that ω lies on this budget line also — equal endowments. • In fact if both consumers start with an equal amount of the two goods each they will trade to a fair allocation. A competitive equilibrium from equal division must be a fair allocation