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First Welfare Theorem
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For a fuller statement of this theorem, see The Two Fundamental Theorems Of Welfare Economics .


CONDITIONS FOR THE THEOREM


Draw an Edgeworth Box for two goods.

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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.