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There are two fundamental theorems of welfare economics. The first states that in economic equilibrium , a set of complete markets , with complete information , and in perfect competition , will be Pareto optimal (in the sense that no further exchange would make one person better off without making another worse off).
The second fundamental theorem states that given further restrictions, any Pareto efficient outcome can be supported as a competitive market equilibrium. [3] These restrictions are stronger than for the first fundamental theorem, with convexity of preferences and production functions a sufficient but not necessary condition.
Fundamental theorems of welfare economics [ edit ] In 1951, Arrow presented the first and second fundamental theorems of welfare economics and their proofs without requiring differentiability of utility, consumption, or technology, and including corner solutions.
Second fundamental theorem of welfare economics — For any total endowment , and any Pareto-efficient state achievable using that endowment, there exists a distribution of endowments {} and private ownerships {,}, of the producers, such that the given state is a market equilibrium state for some price vector + +.
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In a pure exchange economy, a sufficient condition for the first welfare theorem to hold is that preferences be locally nonsatiated. The first welfare theorem also holds for economies with production regardless of the properties of the production function. Implicitly, the theorem assumes complete markets and perfect information.
With equilibrium defined as 'competitive equilibrium', the first fundamental theorem can be proved even if indifference curves need not be convex: any competitive equilibrium is (globally) Pareto optimal. However the proof is no longer obvious, and the reader is referred to the article on Fundamental theorems of welfare economics.
The second welfare theorem is essentially the reverse of the first welfare theorem. It states that under similar, ideal assumptions, any Pareto optimum can be obtained by some competitive equilibrium , or free market system, although it may also require a lump-sum transfer of wealth.