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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.
The first fundamental theorem of welfare economics [ edit ] We have seen that the points of tangency of indifference curves are the Pareto optima, but we also saw previously that the economic equilibria are those points at which indifference curves are tangential to a common price line.
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 + +.
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.
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. In an economy with externalities , for example, it is possible for equilibria to arise that are not efficient.
When Kenneth Arrow proved his theorem in 1950, it inaugurated the modern field of social choice theory, a branch of welfare economics studying mechanisms to aggregate preferences and beliefs across a society. [14] Such a mechanism of study can be a market, voting system, constitution, or even a moral or ethical framework. [1]