Implications of the Second Welfare Theorem

The Second Theorem of Welfare Economics asserts that under certain conditions, every Pareto efficient allocation can be achieved as a competitive equilibrium.

What is the meaning of this result? The Second Welfare Theorem implies that the problems of distribution and efficiency can be separated. Whatever Pareto efficient allocation you want can be supported by the market mechanism. The market mechanism is distributionally neutral; whatever your criteria for a good or a just distribution of welfare, you can use competitive markets to achieve it.

Prices play two roles in the market system: an allocative role and a distributive role. The allocative role of prices is to indicate relative scarcity; the distributive role is to determine how much of different goods different agents can purchase. The Second Welfare Theorem says that these two roles can be separated: we can redistribute endowments of goods to determine how much wealth agents have, and then use prices to indicate relative scarcity.

Policy discussions often become confused on this point. One often hears arguments for intervening in pricing decisions on grounds of distributional equity. However, such intervention is typically misguided. As we have seen above, a convenient way to achieve efficient allocations is for each agent to face the true social costs of his or her actions and to make choices that reflect those costs. Thus in a perfectly competitive market the marginal decision of whether to consume more or less of some good will depend on the price—which measures how everyone else values this good on the margin. The considerations of efficiency are inherently marginal decisions— each person should face the correct marginal tradeoff in making his or her consumption decisions.

The decision about how much different agents should consume is a totally different issue. In a competitive market this is determined by the value of the resources that a person has to sell. From the viewpoint of the pure theory, there is no reason why the state can't transfer purchasing power— endowments—among consumers in any way that is seen fit.

In fact the state doesn't need to transfer the physical endowments themselves. All that is necessary is to transfer the purchasing power of the endowment. The state could tax one consumer on the basis of the value of his endowment and transfer this money to another. As long as the taxes are based on the value of the consumer's endowment of goods there will


be no loss of efficiency. It is only when taxes depend on the choices that a consumer makes that inefficiencies result, since in this case, the taxes will affect the consumer's marginal choices.

It is true that a tax on endowments will generally change people's behavior. But, according to the First Welfare Theorem, trade from any initial endowments will result in a Pareto efficient allocation. Thus no matter how one redistributes endowments, the equilibrium allocation as determined by market forces will still be Pareto efficient.

However, there are practical matters involved. It would be easy to have a lump-sum tax 011 consumers. We could tax all consumers with blue eyes, and redistribute the proceeds to consumers with brown eyes. As long as eye color can't be changed, there would be no loss in efficiency. Or we could tax consumers with high IQs and redistribute the funds to consumers with low IQs. Again, as long as IQ can be measured, there is no efficiency loss in this kind of tax.

But there's the problem. How do we measure people's endowment of goods? For most people, the bulk of their endowment consists of their own labor power. People's endowments of labor consist of the labor that they could consider selling, not the amount of labor that they actually end up selling. Taxing labor that people decide to sell to the market is a distortionary tax. If the sale of labor is taxed, the labor supply decision of consumers will be distorted—they will likely supply less labor than they would have supplied in the absence of a tax. Taxing the potential value of labor—the endowment of labor—is not distort ionary. The potential value of labor is, by definition, something that is not changed by taxation. Taxing the value of the endowment sounds easy until we realize that it involves identifying and taxing something that might be sold, rather than taxing something that is sold.

We could imagine a mechanism for levying this kind of tax. Suppose that we considered a society where each consumer was required to give the money earned in 10 hours of his labor time to the state each week. This kind of tax would be independent of how much the person actually worked—it would only depend on the endowment of labor, not on how much was actually sold. Such a tax is basically transferring some part of each consumer's endowment of labor time to the state. The state could then use these funds to provide various goods, or it could simply transfer these funds to other agents.

According to the Second Welfare Theorem, this kind of lump-sum taxation would be nondistortionary. Essentially any Pareto efficient allocation could be achieved by such lump-sum redistribution.

However, no one is advocating such a radical restructuring of the tax system. Most people's labor supply decisions are relatively insensitive to variations in the wage rate, so the efficiency loss from taxing labor may not be too large anyway. But the message of the Second Welfare Theorem is important. Prices should be used to reflect scarcity. Lump-sum transfers of wealth should be used to adjust for distributional goals. To a large degree, these two policy decisions can be separated.

People's concern about the distribution of welfare can lead them to advocate various forms of manipulation of prices. It has been argued, for example, that senior citizens should have access to less expensive telephone service, or that small users of electricity should pay lower rates than large users. These are basically attempts to redistribute income through the price system by offering some people lower prices than others.

When you think about it this is a terribly inefficient way to redistribute income. If you want to redistribute income, why don't you simply redistribute income? If you give a person an extra dollar to spend, then he can choose to consume more of any of the goods that he wants to consume—not necessarily just the good being subsidized.

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