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  Equilibrium-Efficiency-Theorems of Welfare

Equilibrium and Efficiency-The First and Second Fundamental Theorems of Welfare Economics:

A general equilibrium in a competitive market economy has been proven to exists, given some quite weak assumptions about consumers’ preferences. The allocation that a general equilibrium in a competitive market economy results in is furthermore, Pareto efficient. In such equilibrium:

1. All consumers maximize their utility subject to budget restrictions, determined by their initial allocations and the relative prices;

2. The aggregate excess demands are non-positive on all markets at the same time (if all goods are desirable the aggregate excess demand for all goods is equal to zero).

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Since all consumers maximize their utility, and there are no goods left over, it must be the case that the final allocation cannot be changed so that someone is better off, without anyone else being worse off. This result is called the first fundamental theorem of welfare economics, or the “invisible hand theorem” after Adam Smith’s metaphor of how competition works for the general (public) good, without that being the intent (or even in the interest) of each individual.

The first fundamental theorem is only concerned with efficiency, i.e., whether the market allocation is such that resources are used in an efficient way. This is certainly important: Why waste resources, if they can be employed to someone’s benefit? However, a Pareto efficient allocation can be extremely unequal then it comes to the final distribution of utility (or consumption). Under certain circumstances a government can intervene to “Fix” this inequality, but without interfering in the market system, and the trading that goes on between individual consumers. The second fundamental theorem of welfare economics claims that:

Any Pareto-optimal allocation can be implemented as general competitive market equilibrium by a redistribution of the initial allocation, through a system of lump-sum taxes and transfers. The second welfare theorem is illustrated in figure below, where we assume that the initial allocation is at point A. If the government does not intervene, the equilibrium will be at Point B, where consumer 1 gets almost all utility. A lump-sum tax on consumer 1′s endowment of good 2, will shift the initial allocation to point C. The new equilibrium will be at point D, with a much more equal distribution of utility than at point B. The catch with the second theorem is that lump-sum taxes are almost impossible to implement. In practice the most important endowment of anything is our own labor ability, and different abilities are notoriously difficult to observe, and therefore to tax. (Note that we do observe labor supply choices, which will normally depend on abilities, but if the government tries to tax labor actually supplied, it will distort this decision, and the tax is not lump-sum in nature. The same goes for taxing capital; such a tax will influence the savings decision.) In general, the government must resort to distortionary taxation, which we’ve seen have associated dead weight losses. The question of redistribution therefore becomes a question of trading off efficiency against equality.

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