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What are the advantages of leaving the allocation of a country's resources to the price mechanism?

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If relatively weak conditions are satisfied, then whatever allocation of resources results from the use of the price mechanism cannot be improved upon for any person in the country without harming someone else.

The main conditions required are:

1. Either a finite number of agents or goods.

2. No externalities. That is, the consumption of one person should not harm or benefit anyone else.

3. No matter how much a person is consuming, they must be able to be made slightly happier by consuming a bit more of something.

This result is the First Fundamental Theorem of Welfare Economics.

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