Market -Welfare The Invisible hand What are the implications of this theorem? In a general equilibrium everyone maximises utility selfishly" given prices. Firms" selfishly" maximise profits. However, as a result of this selfish behaviour(given the assumptions discussed earlier) a socially desirable outcome arises. An allocation is achieved where no-one can be made better off without making someone else worse off. This is a formalisation of the invisible hand argument of Adam Smith. What role is there for government intervention in such an efficient world? There are two possibilities 1. Market failure: If one of the assumptions fail, the allocation may no longer be efficient. 2. Distributive Goals: Pareto efficiency says nothing about distributional fairness Market- welfare The Second Welfare Theorem An equilibrium is efficient, are efficient allocations always part of an equilibrium? Theorem: The second welfare theorem states that every Pareto efficient allocation can be supported by a general equilibrium set of prices given a suitable reallocation of the endowment Equilibrium Prices The demonstration proceeds constructively. Which set of prices port the above Pareto efficient allocation (r)as a general equilibrium? The answer is the given by the budget line that separates the two indifference curves. In order to support r the endowment would need to reallocated from w to wMarket — Welfare 3 The Invisible Hand • What are the implications of this theorem? • In a general equilibrium everyone maximises utility “selfishly” given prices. Firms “selfishly” maximise profits. • However, as a result of this selfish behaviour (given the assumptions discussed earlier) a socially desirable outcome arises. An allocation is achieved where no-one can be made better off without making someone else worse off. • This is a formalisation of the invisible hand argument of Adam Smith. • What role is there for government intervention in such an efficient world? There are two possibilities: 1. Market failure: If one of the assumptions fail, the allocation may no longer be efficient. 2. Distributive Goals: Pareto efficiency says nothing about distributional fairness. Market — Welfare 4 The Second Welfare Theorem • An equilibrium is efficient, are efficient allocations always part of an equilibrium? • Theorem: The second welfare theorem states that every Pareto efficient allocation can be supported by a general equilibrium set of prices given a suitable reallocation of the endowment. ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... ....................................................................................................................................................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................................................................................................................................................... . . .......................................................... ...... ...... ... ...... ...... ...... ... ........................ . . . . . . . . . . . . . . .. .. .. ...... ...... . ........................................................................................................ ........................................................................................................ A B • x Equilibrium Prices • ω 0 ω • • The demonstration proceeds constructively. Which set of prices can support the above Pareto efficient allocation (x) as a general equilibrium? The answer is the given by the budget line that separates the two indifference curves. • In order to support x the endowment would need to reallocated from ω to ω 0