Equity and Efficiency

We have shown that different efficient allocations of goods are possible, and we have seen how a perfectly competitive economy generates an efficient allocation. But are efficient allocations equitable? Unfortunately, economists and others disagree both about how to define equity and how to quantify it. Any such view would involve subjective comparisons of utility, and reasonable

5 The second theorem of welfare economics states that if individual preferences are convex, then every efficient allocation (every point on the contract curve) is a competitive equilibrium for some initial allocation of goods.

people could disagree about how to make these comparisons. In this section we discuss this general point and then illustrate it in a particular case by showing that there is no reason to believe that the allocation associated with a competitive equilibrium will be equitable.

The Utility Possibilities Frontier

Recall that every point on the contract curve in our two-person exchange economy shows the levels of utility that James and Karen can achieve. In Figure 16.7 we put the information from the Edgeworth box in a different form. James's utility is measured on the horizontal axis and Karen's on the vertical axis. Any point in the Edgeworth box corresponds to a point in Figure 16.7 because every allocation generates utility for both people. Every movement to the right in Figure 16.7 represents an increase in James's utility, and every upward movement an increase in Karen's.

The utility possibilities frontier represents all allocations that are efficient. Point 0; is one extreme in which James has no goods and therefore zero utility, while point Ok is the opposite extreme where Karen has no goods. All other points on the frontier, such as E, F, and G, correspond to points on the contract curve, so that one person cannot be made better off without making the other worse off. Point H, however, represents an inefficient allocation because any trade within the tan-shaded area makes one or both parties better off. At L both people

FIGURE 16.7 Utility Possibilities Frontier. The utility possibilities frontier shows the levels of satisfaction that each of two people achieve when they have traded to an efficient outcome on the contract curve. Points E, and G correspond to points on the contract curve and are efficient. Point //is inefficientbecause any trade within the tan-shaded area will make one or both people better off.

would be better off, but L is not attainable because there is not enough of both goods to generate the levels of utility that the point represents.

It might seem reasonable to conclude that an allocation must be efficient to be equitable. Compare point H with F and £. Both F and E are efficient, and (relative to H) each makes one person better off without making the other worse off. We might agree, therefore, that it is inequitable to James or Karen or both for an economy to yield allocation H, as opposed to F or E.

But suppose H and G are the only possible allocations. Is G more equitable than W Not necessarily Compared with H, G yields more utility for James and less for Karen. Some people may feel that H is more equitable than G; others may feel the opposite. We can conclude, therefore, that one inefficient allocation of resources may be more equitable than another efficient allocation.

The problem is how to define an equitable allocation. Even if we restrict ourselves to all points on the utility possibilities frontier, which point is the most equitable? The answer depends on what one thinks equity entails, and, therefore, on the interpersonal comparisons of utility that one is willing to make.

In economics, we often use a social welfare function to describe the particular weights that are applied to each individual's utility in determining what is socially desirable. One social welfare function, the utilitarian, weights everyone's utility equally and consequently maximizes the total utility of all members of society. Each social welfare function can be associated with a particular view about equity. But some views do not explicitly weight individual utilities and cannot therefore be represented by a social welfare function. For example, a market-oriented view argues that the outcome of the competitive market process is equitable because it rewards those who are most able and who work the hardest.7 If E is the competitive equilibrium allocation, for example, E would be deemed to be more equitable than F, even though the goods are less equally allocated.

When more than two people are involved, the meaning of the word equity becomes even more complex. The Rawlsian view8 emphasizes that an equal distribution of resources may remove the incentive that most productive people have to work hard (because the wealth they achieve will be taxed away). This view allows inequalities, if these inequalities make the least-well-off person in society better off. According to Rawls, the most equitable allocation maximizes the utility of the least-well-off person in society. The Rawlsian perspective could be egalitarian, involving an equal allocation of goods among all members of society, but it need not be. Suppose that by rewarding more productive people more highly than less productive people, we can get the most productive people to work harder. This could produce more goods and services, some of which could then be reallocated to make the poorest members of society better off.

The four views of equity in Table 16.2 move roughly from most to least egalitarian. The egalitarian view explicitly requires equal allocations, while the

6 One of the important developers of utilitarian thought was Jeremy Bentham (1748-1832). See An Introduction to the Principle of Morals and Legislation (London: Oxford University Press, 1907). See Robert Nozick, Anarchy, State, and Utopia (New York: Basic Books, 1974). See John Rawls, A Theory of Justice (New York: Oxford University Press, 1971).

TABLE 16.2 Four Views of Equity

1. Egalitarian-all members of society receive equal amounts of goods

2. Rawlsian-maximize the utility of the least-well-off person

3. Utilitarian-maximize the total utility of all members of society

4. Market-oriented-the market outcome is the most equitable

Rawlsian puts a heavy weight on equality (otherwise some would be much worse off than others). The utilitarian is likely to require some difference between the best- and worst-off members of society. Finally, the market-oriented view may lead to substantial inequality in the allocations of goods and services.

Equity and Perfect Competition

A competitive equilibrium leads to a Pareto efficient outcome that may or may not be equitable. In fact, a competitive equilibrium could occur at any point on the contract curve, depending on the initial allocation. Imagine, for example, that the initial allocation gave all food and clothing to Karen. This would be at Oj in Figure 16.7, and Karen would have no reason to trade. Point 0/ would then be a competitive equilibrium, as would point Ok and all intermediate points on the contract curve.

Because efficient allocations are not necessarily equitable, society must rely to some extent on government to redistribute income or goods among households to achieve equity goals. These goals can be reached through the tax sys-tem-a progressive income tax redistributes income from the wealthy to the poor, for example. The government can also provide public services, such as medical aid to the poor (Medicare), or it can transfer funds through programs such as Food Stamps.

Unfortunately, all programs that redistribute income in our society are costly. Taxes may encourage individuals to work less or cause firms to devote resources to avoiding taxes rather than to producing output. So as a practical matter, there is a trade-off between the goals of equity and efficiency.9

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