First theorem of welfare economics

There are two fundamental theorems of welfare economics.

The First Theorem states that a market will tend toward a competitive equilibrium that is weaklyPareto optimal when the market maintains the following three attributes:

1. complete markets - No transaction costs and because of this each actor also has perfect information, and

2. price-taking behavior - No monopolists and easy entry and exit from a market.

Furthermore, the First Theorem states that the equilibrium will be fully Pareto optimal with the additional condition of:

3. local nonsatiation of preferences - For any original bundle of goods, there is another bundle of goods arbitrarily close to the original bundle, but that is preferred.

The Second Theorem states that, out of all possible Pareto optimal outcomes, one can achieve any particular one by enacting a lump-sum wealth redistribution and then letting the market take over.

The First Theorem is often taken to be an analytical confirmation of Adam Smith's "invisible hand" hypothesis, namely that competitive markets tend toward an efficient allocation of resources. The theorem supports a case for non-intervention in ideal conditions: let the markets do the work and the outcome will be Pareto efficient. However, Pareto efficiency is not necessarily the same thing as desirability; it merely indicates that no one can be made better off without someone being made worse off. There can be many possible Pareto efficient allocations of resources and not all of them may be equally desirable by society.

This appears to make the case that intervention has a legitimate place in policy – redistributions can allow us to select from all efficient outcomes for one that has other desired features, such as distributional equity. The shortcoming is that for the theorem to hold, the transfers have to be lump-sum and the government needs to have perfect information on individual consumers' tastes as well as the production possibilities of firms. An additional mathematical condition is that preferences and production technologies have to be convex.

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