The Uses of Indifference Contours

What to Read For Do economists actually have precise measurements of the shapes of indifference curves? If not, why bother with the idea? Is it possible to answer interesting social questions using indifference curves, even though we don't precisely know their shapes? Is it better to give small towns cheap mail or direct cash subsidies? Can an offer of free, public education sometimes lower the amount of education consumed? How do indifference curves answer such questions?

Like crossword puzzles and mathematical games, the study of the shapes of indifference curves has a certain arid charm. The next chapter will continue the fun and games. But it is as well to show immediately here that indifference curves are not mere toys. On the contrary, they show real behavior.

This would be obvious if economists had actually measured indifference curves. If they could look up in a "Handbook of Hills of Utility" the shapes of curves between food and all other goods, as engineers can look up the breaking point of steel under stress, then they would have no trouble predicting exactly how consumers would react to a rise in the price of food or to a fall in income. There is no such handbook. Economics, like most other social sciences and unlike physics and chemistry, cannot very easily fill in the blanks in its theories with laboratory experiments. Like astronomy or meteorology, it must take its experiments as the world gives them. And it has the additional handicap that, unlike astronomy and meteorology, which are applied physics and chemistry, it cannot draw on a rich array of results from the laboratory. Statistical methods in economics—econometrics—have since the 1930s filled in some of the blanks. Yet a tendency to apply these methods only to recent experience has limited our understanding of economic behavior. The next chapter offers some further, theoretical, reasons why the handbook of facts does not exist.

Subsidies of Income Still, economists can go a long way with a crude notion of the shapes of indiffer-and of Price ence curves. The crude notion is that they are convex. For example, it is the mere convexity of indifference curves which makes a subsidy in cash more valuable than a subsidy in kind (see Problem 1 at the end of this section, and the discussion on p. 14).

A similar point applies to subsidies that reduce prices. For instance, customers of the U.S. Postal Service in Baroda, Michigan, or Solon, Iowa, get rates lower than the cost of mail there. These are paid for by rates above costs in New York City, or by government subsidies. The heavy budget line in Figure 2.7 is the budget line representing the full cost of sending and receiving letters in Solon, the ordinary line is the budget line after the subsidy. The price of letters falls.

The subsidy is in the amount marked Subsidy if the citizens of Solon buy the mail they want at the low price and achieve the indifference curve Good. They would be even better off, however, if the Subsidy extracted from New Yorkers was simply given to the Solonians directly as Additional Income (in the form of all other goods) without the artificial reduction in the relative

All Other Goods

Additional

Figure 2.7

A Subsidy to Income Is Always Better Than a Subsidy to a Price

A subsidized postal rate that results in the government's spending Subsidy is inferior to a direct transfer in the same amount given as Additional Income, because the Subsidy leads only to a Good Equilibrium while the transfer leads to a Better Equilibrium.

Better Equilibrium

All Other Goods

Figure 2.7

Better Equilibrium

Good Equilibrium

Additional

Good Equilibrium

Better Indifference Curve Good Indifference Curve

Subsidized Cost

Letters Mailed in Solon price of mail. The Solonians could move out the dashed line to the point Better Equilibrium, tangent to the Better indifference curve. The dashed line constructed in this way (parallel to the unsubsidized price line since the relative price of mail is now kept unchanged) intersects the Good indifference curve at the Good Equilibrium, which means that there is always a Better Equilibrium. In short, for the same hurt to New Yorkers, Solonians would be made better off by paying the full cost of mails and receiving the subsidy as additional income. It is better to give people additional income than to fool with the prices they face.3

Gifts That Foreclose It is not always true that subsidies to a price or gifts of goods increase the Other Opportunities amounts consumed. This also can be demonstrated with indifference curves.

Consider a good provided free that makes it impossible to buy still more of the good, such as education. If Joseph Reid goes full time to a free public school or college, he cannot simultaneously go full time to an expensive private school or college.

Q: 1. Draw the budget line between education and all other goods facing Reid. (Hint: It is not a line alone, but a line and a point outside the line. How much of all other goods could he consume if he accepted the free public education?) Assume that public education is a Standardized Amount and that the alternative, private education, can be purchased in varying amounts.

2. Draw an indifference curve that would imply that

Reid would not accept the offer of free public education in the Standardized Amount. In other words, draw an indifference curve such that a point on the ordinary, market budget line is on a higher indifference curve than is the point Standardized Amount.

3. Draw an indifference curve implying that Reid would accept free public education and would consume more education than he would without the offer.

3 But see the Warning at the end of the section. It applies here.

4. Draw an indifference curve implying that Reid would accept free public education but would consume less education than he would without the offer.

5. When would you expect an offer of a Standardized Amount of public education to reduce rather than raise the educational attainment of the population?

A: Reid can either accept the offer of free public education, getting the Standardized Amount of education and devoting all his income to all other goods, or he can refuse the offer, giving up some all other goods to get some private education. In other words, his budget line—the collection of attainable points—is the line Private Education or (not and) the point Public Education in Figure 2.8. At the point Public Education he can devote all his income to all other goods, since the government has spared him any expense of education.

If the indifference curve tangent to private education resembles U2, then the offer of the alternative public education would have no effect, since the point Public Education is on a lower indifference curve. This is the case of education-loving students, for whom the Standardized Amount of public education is too low to be tempting. If the indifference curve resembles Ua, then the offer increases the amount of education consumed, since Public Education is now on a higher indifference curve, and in accepting the offer the students consume more (the Standardized Amount is more than £0). This is the case of all-other-goods-loving students, for whom the Standardized Amount of public education exceeds the amount they would consume privately.

If the indifference curve resembles Ui, however, the offer decreases the amount of education consumed. The point Public Education is on a higher indifference curve, but in accepting the offer students consume less than they would without the offer (the Standardized Amount is less than E^. This is the case of education-liking-but-not-loving students for whom the Standardized Amount of public education is literally acceptable, but less than they would consume privately. Evidently, if much of the population consumes larger amounts of private education per student than is to be provided free, then the offer can reduce the educational attainment of the population. The population is happier with the offer, but happily ignorant. The government may in this way fail if it is attempting to increase the amount of education consumed.4

comment The key to the problem is to set up the diagram correctly. Once the details of the diagram are correct—a budget line between the two goods and a point mutually exclusive to the budget line—the problem solves itself. The diagram is a machine for thinking. You can make mistakes and still get the essential argument correct. For instance, you might not realize that the point Public Education will be exactly horizontal to the maximum attainable of all other goods. But if you recognize that the deal being offered is a choice between the point (wherever located exactly) and the budget line, you have most of it.

A warning is in order. The arguments about how a subsidy of one or another sort affects consumers are fine if one is interested only in how the particular group of consumers is affected and if the group is not a large one in society as a whole. The cross subsidies from New Yorkers to Fairfieldians fit the mold; the subsidy to all public education does not. To provide the Public Education in the diagram shown in Figure 2.8, the economy must tax itself. That is, the

4 The logic of the argument is not controversial, but the facts are. Two people who believe the facts warrant taking the argument seriously are Sam Peltzman, "The Effect of Subsidies-in-Kind on Private Expenditures: The Case of Higher Education," Journal of Political Economy 81 (January 1973): 1-27, who applies it to college education in the United States; and E. G. West, "Educational Slowdown and Public Intervention in 19th-century England," Explorations in Economic History 12 (January 1975): 61-87, who applies it to primary schooling in England after the introduction of state education in the 1870s.

Warning: The Society Must Stay on Its Budget Line

All Other Goods

Public Education

Figure 2.8

Free Education Can Reduce the Amount Consumed

A consumer initially at E0, with preferences given by indifference curve U0, accepts the offer of Standardized Amount of free Public Education and thereby increases his consumption of Education. A consumer at Elr with preferences given by (A, accepts the offer and thereby consumes less Education. A consumer at f2 rejects the offer. If there are enough consumers at Ei, and if fx is far enough to the right of the Standardized Amount, the amount of Education consumed will fall.

Public Education

Figure 2.8

Free Education Can Reduce the Amount Consumed

Private Education

Standardized Amount

Private Education

Standardized Amount

Education (amount)

society as a whole cannot in reality provide itself with a point such as Public Education outside its original budget line. The budget line typical of the society as a whole must be the budget line in the diagram. Unless a tiny group is being subsidized disproportionately by the rest of society (as is the case, for example, with state-supported higher education), an analysis that simply assumes that the point Public Education is available is incomplete and may be radically misleading.5

Summary Economists have usually only a vague idea of the shape of indifference curves between bread and meat or education and all other goods. Vague though it is, the idea of convexity is enough to cast light on many social questions. The key to answering such questions is close thinking about the budget lines involved. A nonordinary budget line dropped onto ordinary indifference curves may yield definite results. Definite though they are, however, the results must not violate the true budget line for the whole society.

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