In Section 4.3, we learned how changes in income affect the position of a consumer’s budget constraint. Lower incomes shift the constraint toward the origin; higher incomes shift it out. In this section, we look at how a change in income affects a consumer’s utility-maximizing consumption decisions. This is known as the income effect. To isolate this effect, we hold everything else constant during our analysis. Specifically, we assume that the consumer’s preferences (reflected in the utility function and its associated indifference curves) and the prices of the goods stay the same.

Figure 5.1 shows the effect of an increase in income on consumption for Evan, a consumer who allocates his income between vacations and tickets to basketball games. Initially, Evan’s budget constraint is BC₁ and the utility-maximizing consumption bundle occurs at point A, where indifference curve U₁ is tangent to BC₁. If the prices of vacations and basketball tickets remain unchanged, an increase in Evan’s income means that he can afford more of both goods. As a result, the increase in income induces a parallel, outward shift in the budget constraint from BC₁ to BC₂. Note that, because we hold prices fixed, the slope of the budget constraint (the ratio of the goods’ prices) remains fixed. The new optimal consumption bundle at this higher income level is B, the point where indifference curve U₂ is tangent to BC₂.

Because U₂ shows bundles of goods that offer a higher utility level than those on U₁, the increase in income allows Evan to achieve a higher utility level. Note that when we analyze the effect of changes in income on consumer behavior, we hold preferences (as well as prices) constant. Thus, indifference curve U₂ does not appear because of some income-driven shift in preferences. U₂ was always there even when Evan’s income was lower. At the lower income, however, point B and all other bundles on U₂ (and any other higher indifference curves) were infeasible because Evan could not afford them.

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Notice how the new optimum in Figure 5.1 involves higher levels of consumption for both goods. The number of vacations Evan takes rises from Q_v to Q_v′, and the number of basketball tickets increases from Q_b to Q_b′. This result isn’t that surprising; Evan was spending money on both vacations and basketball tickets before his income went up, so we might expect that he’d spend some of his extra income on both goods. Economists call a good for which consumption rises when income rises—that is, a good for which the income effect is positive—a normal good. Vacations and basketball tickets are normal goods for Evan. As “normal” suggests, most goods have positive income effects.

It is possible that an increase in income can lead to a consumer consuming a smaller quantity of a good. Recall from Chapter 2 that economists call such goods inferior goods. Figure 5.2 presents an example in which one of the goods is inferior. An increase in the consumer’s income from BC₁ to BC₂ leads to more steak being consumed, but less macaroni and cheese. Note that it isn’t just that the quantity of mac and cheese relative to the quantity of steak falls. This change can happen even when both goods are normal (i.e., they both rise, but steak rises more). Instead, it is the absolute quantity of macaroni and cheese consumed that drops in the move from A to B, because Q′_m is less than Q_m. Note also that this drop is optimal from the consumer’s perspective—B is her utility-maximizing bundle given her budget constraint BC₂, and this bundle offers a higher utility level than A because indifference curve U₂ represents a higher utility level than U₁.

What kind of goods tend to be inferior? Usually, they are goods that are perceived to be low-quality or otherwise undesirable. Examples might include generic cereal brands, secondhand clothing, nights spent in youth hostels, and Spam. When we say Spam, we mean the kind you buy in the grocery store, not the kind you get via e-mail. Junk e-mail probably isn’t a good at all, but rather a “bad.”

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We do know that every good can’t be inferior, however. If a consumer were to consume a smaller quantity of everything when his income rises, he wouldn’t be spending all his new, higher income. This outcome would be inconsistent with utility maximization, which states that a consumer always ends up buying a bundle on his budget constraint. (Remember there is no saving in this model.)

Whether the effect of an income change on a good’s consumption is positive (consumption increases) or negative (consumption decreases) can vary with the level of income. (We look at some of these special cases later in the chapter.) For instance, a good such as a used car is likely to be a normal good at low levels of income, and an inferior good at high levels of income. When someone’s income is very low, owning a used car is prohibitively expensive and riding a bike or taking public transportation is necessary. As income increases from such low levels, a used car becomes increasingly likely to be purchased, making it a normal good. But once someone becomes rich enough, used cars are supplanted by new cars and his consumption of used cars falls. Over that higher income range, the used car is an inferior good.

We’ve discussed how the income effect can be positive (as with normal goods) or negative (as with inferior goods). We can make further distinctions between types of goods by looking not just at the sign of the income effect, but at the income elasticity as well, which we discussed in Chapter 2. Remember that the income elasticity measures the percentage change in the quantity consumed of a good in response to a given percentage change in income. Formally, the income elasticity is

where Q is the quantity of the good consumed (ΔQ is the change in quantity), and I is income (ΔI is the change in income). As we noted in our earlier discussion, income elasticity is like the price elasticity of demand, except that we are now considering the responsiveness of consumption to income changes rather than to price changes.

The first ratio in the income elasticity definition is the income effect shown in the equations above: ΔQ/ΔI, the change in quantity consumed in response to a change in income. Therefore, the sign of the income elasticity is the same as the sign of the income effect. For normal goods, ΔQ/ΔI > 0, and the income elasticity is positive. For inferior goods, ΔQ/ΔI < 0, and the income elasticity is negative.

Within the class of normal goods, economists occasionally make a further distinction. The quantities of goods with an income elasticity between zero and 1 (sometimes called necessity goods) rise with income, but at a slower rate. Because prices are held constant when measuring income elasticities, the slower-than-income quantity growth implies the share of a consumer’s budget devoted to the good falls as income grows. Many normal goods fit into this category, especially items that just about everyone uses or needs, like toothpaste, salt, socks, and electricity. Someone who earns $1 million a year may well consume more of these goods (or more expensive varieties) than an aspiring artist who earns $10,000 annually, but the millionaire, whose income is 100 times greater than the artist’s, is unlikely to spend 100 times more on toothpaste (or salt, or socks . . .) than the artist spends.

Luxury goods have an income elasticity greater than 1. Because their quantities consumed grow faster than income does, these goods account for an increasing fraction of the consumer’s expenditure as income rises. First-class airline tickets, jewelry, and beach homes are all likely to be luxury goods.

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Imagine repeating the analysis in the previous section for every possible income level, starting with 0. That is, for a given set of prices and a particular set of preferences, find the utility-maximizing bundle for every possible budget constraint, where each constraint corresponds to a different income level. Those optimal bundles will be located wherever an indifference curve is tangent to a budget line. In the examples above, bundles A and B were optimal at the two income levels.

Figure 5.3 shows how Meredith allocates her income between bus rides and bottled water. Points A, B, C, D, and E are the optimal consumption bundles at five different income levels that correspond to the budget constraints shown. Point A is Meredith’s utility-maximizing bundle for the lowest of the five income levels, point B is the bundle for the second-lowest income, and so on. Note that the indifference curves themselves come from Meredith’s utility function. We have chosen various shapes here just to illustrate that these points can move around in different ways.

If we draw a line connecting all the optimal bundles (the five here plus all the others for budget constraints we don’t show in the figure), it would trace out a curve known as the income expansion path. This curve always starts at the origin because when income is zero, the consumption of both goods must also be zero. Figure 5.3 shows Meredith’s income expansion path for bus rides and bottled water.

When both goods are normal goods, the income expansion path will be positively sloped because consumption of both goods rises when income does. If the slope of the income expansion path is negative, then the quantity consumed of one of the goods falls with income while the other rises. The one whose quantity falls is an inferior good. Remember that whether a given good is normal or inferior can depend on the consumer’s income level. In Figure 5.3, for example, both bus rides and bottled water are normal goods at incomes up to the level corresponding to the budget constraint containing bundle D. As income rises above that and the budget constraint continues to shift out, the income expansion path begins to curve downward. This outcome means that bus rides become an inferior good as Meredith’s income rises beyond that level. We can also see from the income expansion path that bottled water is never inferior, because the path never curves back to the left. When there are only two goods, it’s impossible for both goods to be inferior at any income level. If they were both inferior, an increase in income would actually lead to lower expenditure on both goods, and the consumer wouldn’t be spending all of her income.

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The income expansion path is a useful tool for examining how consumer behavior changes in response to changes in income, but it has two important weaknesses. First, because we have only two axes, we can only look at two goods at a time. Second, although we can easily see the consumption quantities of each good, we can’t see directly the income level that a particular point on the curve corresponds to. The income level equals the sum of the quantities consumed of each good (which are easily seen in the figure) multiplied by their respective prices (which aren’t easily seen). The basic problem is that when we talk about consumption and income, we care about three numbers—the quantities of each of the two goods and income—but we have only two dimensions on the graph in which to see them.

A better way to see how the quantity consumed of one good varies with income (as opposed to how the relative quantities of the two goods vary) is to take the information conveyed by the income expansion path and plot it on a graph with income on the vertical axis and the quantity of the good in question on the horizontal axis. Panel a of Figure 5.4 shows the relationship between income and the quantity of bus rides from our example. The five points mapped in panel a of Figure 5.4 are the same five consumption bundles represented by points A, B, C, D, and E in Figure 5.3; the only difference between the figures is in the variables measured by the axes.

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The lines traced out in Figure 5.4 are known as Engel curves, named for the nineteenth-century German economist Ernst Engel who first presented the data in this way. Engel curves tell you the quantities of goods—bus rides and bottled water, in this case—that are consumed at each income level. If the Engel curve has a positive slope, the good is a normal good at that income level. If the Engel curve has a negative slope, the good is an inferior good at that income. In Figure 5.4a, bus rides are initially a normal good, but become inferior after bundle D, just as we saw in Figure 5.3. In panel b, bottled water is a normal good at all income levels and the Engel curve is always positively sloped.

Whether the income expansion path or Engel curves are more useful for understanding the effect of income on consumption choices depends on the question. If we care about how the relative quantities of the two goods change with income, the income expansion path is more useful because it shows both quantities at the same time. On the other hand, if we want to investigate the impact of income changes on the consumption of each particular good, the Engel curve is best because it isolates this relationship more clearly. The two curves contain the same information but display it in different ways due to the limitations imposed by having only two axes.

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