付録

People seek the highest level of utility, which means that they wish to be on the highest possible indifference curve. However, people are limited by their budget constraints, which show what tradeoffs are actually possible.

Return to the situation of Lilly’s choice between paperback books and doughnuts. Say that books cost $6, doughnuts are 50 cents each, and that Lilly has $60 to spend. This information provides the basis for the budget line shown in Figure B.2. Along with the budget line are shown the three indifference curves from Figure B.1. What is Lilly’s utility-maximizing choice? Several possibilities are identified in the diagram.

The choice of F with five books and 100 doughnuts is highly desirable, since it is on the highest indifference curve Uh of those shown in the diagram. However, it is not affordable given Lilly’s budget constraint. The choice of H with three books and 70 doughnuts on indifference curve Ul is a wasteful choice, since it is inside Lilly’s budget set, and as a utility-maximizer, Lilly will always prefer a choice on the budget constraint itself. Choices B and G are both on the opportunity set. However, choice G of six books and 48 doughnuts is on lower indifference curve Ul than choice B of three books and 84 doughnuts, which is on the indifference curve Um. If Lilly were to start at choice G, and then thought about whether the marginal utility she was deriving from doughnuts and books, she would decide that some additional doughnuts and fewer books would make her happier—which would cause her to move toward her preferred choice B. Given the combination of Lilly’s personal preferences, as identified by her indifference curves, and Lilly’s opportunity set, which is determined by prices and income, B will be her utility-maximizing choice.

The highest achievable indifference curve touches the opportunity set at a single point of tangency. Since an infinite number of indifference curves exist, even if only a few of them are drawn on any given diagram, there will always exist one indifference curve that touches the budget line at a single point of tangency. All higher indifference curves, like Uh, will be completely above the budget line and, although the choices on that indifference curve would provide higher utility, they are not affordable given the budget set. All lower indifference curves, like Ul, will cross the budget line in two separate places. When one indifference curve crosses the budget line in two places, however, there will be another, higher, attainable indifference curve sitting above it that touches the budget line at only one point of tangency.

A rise in income causes the budget constraint to shift to the right. In graphical terms, the new budget constraint will now be tangent to a higher indifference curve, representing a higher level of utility. A reduction in income will cause the budget constraint to shift to the left, which will cause it to be tangent to a lower indifference curve, representing a reduced level of utility. If income rises by, for example, 50%, exactly how much will a person alter consumption of books and doughnuts? Will consumption of both goods rise by 50%, or will the quantity of one good rise substantially, while the quantity of the other good rises only a little, or even declines?

Since personal preferences and the shape of indifference curves are different for each individual, the response to changes in income will be different, too. For example, consider the preferences of Manuel and Natasha in Figure B.3 (a) and Figure B.3 (b). They each start with an identical income of $40, which they spend on yogurts that cost $1 and rental movies that cost $4. Thus, they face identical budget constraints. However, based on Manuel’s preferences, as revealed by his indifference curves, his utility-maximizing choice on the original budget set occurs where his opportunity set is tangent to the highest possible indifference curve at W, with three movies and 28 yogurts, while Natasha’s utility-maximizing choice on the original budget set at Y will be seven movies and 12 yogurts.

Now, say that income rises to $60 for both Manuel and Natasha, so their budget constraints shift to the right. As shown in Figure B.3 (a), Manuel’s new utility maximizing choice at X will be seven movies and 32 yogurts—that is, Manuel will choose to spend most of the extra income on movies. Natasha’s new utility maximizing choice at Z will be eight movies and 28 yogurts—that is, she will choose to spend most of the extra income on yogurt. In this way, the indifference curve approach allows for a range of possible responses. However, if both goods are normal goods, then the typical response to a higher level of income will be to purchase more of them—although exactly how much more is a matter of personal preference. If one of the goods is an inferior good, the response to a higher level of income will be to purchase less of it.