VisualizingNeoclassical economics has concentrated much of its attention on efficient allocation of resources, as we have seen and will see in other chapters of this book. However, many social philosophers, economists and other people believe that equity is just as important as efficiency. Since the 1970's, there has been a neoclassical economic analysis of equity, and this analysis of equity is based on the preference approach. The general idea is that the allocation of resources is equitable if no one person would prefer the bundle of goods and services enjoyed by another person to the bundle she herself consumes. This page will illustrate the concept with some numerical examples.
1) We consider a very small economy consisting of two persons, Grasshopper and Ant, two jobs, a hard job and an easy job, and an income that can come in two sizes: large and small. The institutions of the society (the "rules of the game") link the large income to the hard job and the small income to the easy job. We suppose that Grasshopper is a bit of a lazybones. Grasshopper's preferences among jobs and incomes is shown by Table 9:
| income | |||
| large | small | ||
| job | easy | 1 | 2 |
| hard | 3 | 4 | |
That is, an easy job with a large income is Grasshopper's first preference (naturally enough) and the easy job with a small income comes next, the hard job with a large income next yet, and (again naturally enough) a hard job with a small income ranks lowest. Ant's preferences are different and are shown by Table 10:
| income | |||
| large | small | ||
| job | easy | 1 | 3 |
| hard | 2 | 4 | |
At the extremes, Ant ranks the alternatives in the same natural way as Grasshopper does, an easy job with a large income first and a hard job with a low income last. In between, however, Ant ranks the other two choices in the opposite way, choosing a hard job and a large income over the reverse.
Now suppose that Ant is allocated the hard job, and the large income that comes with it, and Grasshopper is allocated the easy job with its low income. Then Ant has his second preference, while Grasshopper's allocation is Ant's third preference. Ant would not choose Grasshopper's portion over his own. Conversely, what Ant has is Grasshopper's third preference, and Grasshopper has his own second preference, so Grasshopper would not, either, choose Ant's portion if he could. Since each insect has a job-and-income package he positively prefers over the package the other insect has, the allocation between the two insects is said to besuperfair. In general, if each insect were indifferent between her own package and the package the other insect enjoys, then, in superfairness theory, the allocation would be described as "fair;""when each positively prefers her own package, then the allocation is "superfair."
Suppose instead that by accident Ant had been assigned the easy job and Grasshopper the hard job. Now Grasshopper has his own third choice, but Ant has Grasshopper's second choice: Grasshopper "envies" Ant. Conversely, Ant has his own third choice, but Grasshopper has Ant's second choice: Ant "envies" Grasshopper. There is inequity all around. But the inequity is easily remedied by a market transaction: given the opportunity, Ant and Grasshopper will voluntarily exchange jobs. Then both superfairness and efficiency are established. In this simple economy, a free market equilibrium is superfair.
2) Now we consider the same small economy except for one change: the rules will be different, and a hard job will be associated with a small income, while an easy job has a large income. Perhaps that is because the easy job is highly assisted by technology, while the hard job is not. Anyway, in this small economy there is no fair or superfair assignment of jobs. No matter who gets the easy, high-pay job, he has the other insect's first choice, and the other insect has his own fourth choice. There is no free-market switch that will eliminate the inequity -- switching jobs just changes the victim. We could say that it is the economic system itself -- the rule for assigning jobs and incomes -- that is inequitable, since, with a system like that, there can never be a fair assignment of jobs.
3) Now consider one more variation on the same small economy. This time we will again associate the large income with the hard job, but there are two Ants in the population and no Grasshopper. Let's call the two Ants Adam and Hillary. One of the Ants will have to be assigned the easy job/small income bundle. Let us suppose it is Adam. Adam finds that he is stuck with his own third preference, while Hillary has Adam's second preference. Adam "envies" Hillary and the allocation between them is inequitable. Switching the Ants will not help -- one or the other of them will "envy" the other. Inequity is unavoidable in this example also.
4) In the second and third example inequity cannot be avoided in part because we have assumed that incomes come on only two indivisible sizes and are rigidly associated with effort supplies. To make the example a little less rigid, we might allow income to be divisible, while retaining the simple assumption that each job requires a fixed, larger or smaller, amount of effort. Generalizing the first example above, we suppose that a Grasshopper will accept a hard job rather than an easy job on the condition that the hard job pays $5 more, and an Ant will accept a hard job rather than an easy job on the condition that the hard job pays $3 more. Let the "rules of the game" assign (by productivity?) an income of $4 for an easy job and $8 to a hard job. Otherwise, each of the two prefers more income to less. We have example 1 over again -- the market assignment of jobs will be superfair.
5) Continuing with the preference valuations in paragraph 4, we generalize example 2, supposing that the "rules of the game" assign income of $4 to a hard job and $8 to an easy job. Once again, here is no fair or superfair assignment of jobs and incomes, since each insect must be assigned to his first or last preference. Suppose, however, that a benevolent economic planner assigns Grasshopper to the easy job and Ant to the hard job, then redistributes $4 of the productivity-based income of Grasshopper to Ant. Ant now has a hard job and $8 of income, while Grasshopper has an easy job and $4. Ant does not prefer what Grasshopper has, net of the tax and transfer, since Grasshopper has $4 less income now; and Grasshopper does not prefer what Ant has, since Ant has a hard job and only $4 more income. Redistribution of income from the more productive to the less productive (but harder working) insect has restored equity in a case in which equity would otherwise be impossible.
6) Now generalizing example 3, we again suppose that the "rules of the game" assign income of $8 to a hard job and $4 to an easy job, but we have to allocate jobs between two Ants. Since only one can have the high-income job, one Ant will prefer the bundle the other has to her own bundle -- inequity. Now, however, our planner assigns Hillary to the easy job and Adam to the hard job, the redistributes $0.50 of Adam's income to Hillary. Now Hillary has the easy job and $4.50 while Adam has the hard job and $7.50. The difference in pay is just $3.00, which makes both Ants indifferent between the hard job and the easy job with their associated incomes. The result is a fair (not superfair) allocation.
What examples 5) and 6) illustrate is that income redistribution may restore equity in a situation in which equity would be impossible without income redistribution. In some cases, market competition can lead to an equitable outcome, as example 1) shows. In some cases, market outcomes can be very far off from the neoclassical concept of equity, as example 5 illustrates -- it was necessary in that case to redistribute half of Grasshopper's income to Ant to make the distribution of jobs and income equitable. In the real world, that much redistribution would distort the incentives to work and produce inefficiency. One economist who has studied these issues, Dr. William Baumol, believes that the loss of production involved would be very great indeed. In any case, it is clear that our real economy does not come very close to an equitable allocation of resources, and perhaps only limited progress in that direction is possible.
Once again, though, we can approach the study of economic equity without any numerical measures of "utility" -- strictly through preference theory. That illustrates some of the wide applicability of preference theory in modern economics.
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