Implications of the First Welfare Theorem

The two theorems of welfare economics are among the most fundamental results in economics. We have demonstrated the theorems only in the simple Edgeworth box case, but they are true for much more complex models with arbitrary numbers of consumers and goods. The welfare theorems have profound implications for the design of ways to allocate resources.

Let us consider the First Welfare Theorem. This says that any competitive equilibrium is Pareto efficient. There are hardly any explicit assump-

IMPLICATIONS OF THE FIRST WELFARE THEOREM 585

tions in this theorem—it follows almost entirely from the definitions. But there are some implicit assumptions. One major assumption is that agents only care about their own consumption of goods, and not about what other agents consume. If one agent does care about another agent's consumption, we say that there is a consumption externality. We shall see that when consumption externalities are present, a competitive equilibrium need not be Pareto efficient.

To take a simple example, suppose that agent A cares about agent B's consumption of cigars. Then there is no particular reason why each agent choosing his or her own consumption bundle at the market prices will result in a Pareto efficient allocation. After each person has purchased the best bundle he or she can afford, there may still be ways to make both of them better off—such as A paying B to smoke fewer cigars. We will discuss externalities in more detail in Chapter 33.

Another important implicit assumption in the First Welfare Theorem is that agents actually behave competitively. If there really were only two agents, as in the Edge wort h box example, then it is unlikely that they would each take price as given. Instead, the agents would probably recognize their market power and would attempt to use their market power to improve their own positions. The concept of competitive equilibrium only makes sense when there are enough agents to ensure that each behaves competitively.

Finally, the First Welfare Theorem is only of interest if a competitive equilibrium actually exists. As we have argued above, this will be the case if the consumers are sufficiently small relative to the size of the market.

Given these provisos, the First Welfare Theorem is a pretty strong result: a private market, with each agent seeking to maximize his or her own utility, will result in an allocation that achieves Pareto efficiency.

The importance of the First Welfare Theorem is that it gives a general mechanism—the competitive market—that we can use to ensure Pareto efficient outcomes. If there are only two agents involved, this doesn't matter very much; it is easy for two people to get together and examine the possibilities for mutual trades. But if there are thousands, or even millions, of people involved there must be some kind of structure imposed on the trading process. The First Welfare Theorem shows that the particular structure of competitive markets has the desirable property of achieving a Pareto efficient allocation.

If we are dealing with a resource problem involving many people, it is important to note that the use of competitive markets economizes on the information that any one agent needs to possess. The only things that a consumer needs to know to make his consumption decisions are the prices of the goods he is considering consuming. Consumers don't need to know anything about how the goods are produced, or who owns what goods, or where the goods come from in a competitive market. If each consumer knows only the prices of the goods, he can determine his demands, and if the market functions well enough to determine the competitive prices, we are guaranteed an efficient outcome. The fact that competitive markets economize on information in this way is a strong argument in favor of their use as a way to allocate resources.

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Project Management Made Easy

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