In welfare economics, the First Welfare Theorem is that a system of free markets will lead to a Pareto efficient equilibrium. This was first demonstrated mathematically by economists Kenneth Arrow and Gerard Debreu, although the restrictive assumptions necessary for the proof mean that the result may not necessarily reflect the workings of real economies. Welfare economics is a branch of economics that uses microeconomic techniques to simultaneously determine the allocational efficiency of a macroeconomy and the income distribution consequences associated with it. ... Pareto efficiency, or Pareto optimality, is a central concept in game theory with broad applications in economics, engineering and the social sciences. ... Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. ... Gerard Debreu (July 4, 1921–December 31, 2004) was a French-born American economist who won the 1983 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel. ...

A fuller statement of this theorem is available here. The Two Fundamental Theorems of Welfare Economics are two well-known axiomatic propositions in welfare economics. ...

Conditions for the theorem

• Markets exist for all possible goods.
• Markets are perfectly competive.
• Transaction costs are negligible.
• There are no externalities.

A market is a mechanism which allows people to trade, normally governed by the theory of supply and demand, so allocating resources through a price mechanism and bid and ask matching so that those willing to pay a price for something meet those willing to sell for it. ... A good in economics is any physical object (natural or man-made) or service that, upon consumption, increases utility, and therefore can be sold at a price in a market. ... Perfect competition is a model in economic theory. ... In economics and related disciplines, a transaction cost is a cost incurred in making an economic exchange. ... An externality occurs in economics when a decision (for example, to pollute the atmosphere) causes costs or benefits to stakeholders other than the person making the decision. ...

Implications of the theorem

Under idealized conditions, the first welfare theorem implies that Pareto efficiency can be obtained with very little government action - the function of government can be restricted that of protecting property rights and allowing trade. Solely by changing the initial distribution of resources, any pareto-efficient outcome can be attained. It should be clear however, that Pareto efficiency is not the only possible goal to attain. Some people could tolerate eventual inefficiencies, if the income distributions had some desirable characteristics. The real meaning of the theorem is that the result of free markets, under the conditions mentioned, will be efficient. Thus there is nothing we can do to change this result without hurting some participants. The question if we want to accept this result, believing in the value of individual rights, or if we think the state should change it to attain some other goal, is rather philosophical. The answer should be found in the works of Robert Nozick or John Rawls.