Market -Welfare Convexity and the Theorem The crucial assumption here is that of conuerify. Preferences need elk-behaved for the theorem to work What would happen if they were not? Consider the following case. A has well-behaved preferences. B does not Can a point like r be supported neral equilibrium? The budget line is a set of prices, separating th maximisIng rB maximises utility given these prices for consumer B. r maximises utility for consumer A. This is not a general equilibrium since the market for good 2 is not clearing Market- welfare Implications of the Theorem Notice that convexity is only required for the second theorem. The first theorem holds for any preferences What are the implications of the second theorem Distributional issues can be separated from efficiency issues. A government, operating in such a world can simply transfer endowments to achieve any distributional goals they might have and leave the market to attain efficiency Prices play two roles in the market, (i) allocative- relative scarcity of the two goods and(ii)distributive-how much agents can afford. These can be separated. Do not use prices to attain distributive goals, use endowments. Note: Although only pure exchange economies have been considered so far, everything goes through analogous way for a production economy. The assumptions need to apply both to consumers and firms.Market — Welfare 5 Convexity and the Theorem • The crucial assumption here is that of convexity. Preferences need to be well-behaved for the theorem to work. • What would happen if they were not? Consider the following case. A has well-behaved preferences. B does not. ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....................................................................................................................................................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................................................................................................................................................... . . . ........................................................................................................ .............................................................................................. ...... ...... ...... ...... ............................................................................................................ ................. ............................. A B • x xB • • Can a point like x be supported as a general equilibrium? The budget line is a set of prices, separating the two indifference curves. A is maximising. B is not — they could do better, by choosing xB. • xB maximises utility given these prices for consumer B, x maximises utility for consumer A. This is not a general equilibrium since the market for good 2 is not clearing. Market — Welfare 6 Implications of the Theorem • Notice that convexity is only required for the second theorem. The first theorem holds for any preferences. • What are the implications of the second theorem? • Distributional issues can be separated from efficiency issues. A government, operating in such a world can “simply” transfer endowments to achieve any distributional goals they might have and leave the market to attain efficiency. • Prices play two roles in the market, (i) allocative — relative scarcity of the two goods and (ii) distributive — how much agents can afford. These can be separated. Do not use prices to attain distributive goals, use endowments. • Of course, such a transfer of endowments is not so simple — it may be impossible. • Note: Although only pure exchange economies have been considered so far, everything goes through in an analogous way for a production economy. The assumptions need to apply both to consumers and firms