## 4.34.2 Indifference Curves

indifferent

The special case in which a consumer derives the same utility level from each of two or more consumption bundles.

As we discussed in the previous section, the right way to think about utility is in relative terms; that is, in terms of whether one bundle of goods provides more or less utility to a consumer than another bundle. An especially good way of understanding utility is to take the special case in which a consumer is indifferent between bundles of goods; that is, each bundle provides the consumer with the same level of utility.

Consider a simple case in which there are only two goods to choose between, say, square feet in an apartment and the number of friends living in the same building. Michaela wants a large apartment, but also wants to be able to easily see her friends. First, Michaela looks at a 750-square-foot apartment in a building where 5 of her friends live. Next, she looks at an apartment that has only 500 square feet. For Michaela to be as happy in the smaller apartment as she would be in the larger apartment, there will have to be more friends (say, 10) in the building. Because she gets the same utility from both size/friend combinations, Michaela is indifferent between the two apartments. On the other hand, if her apartment were a more generous 1,000 square feet, Michaela would be willing to make do with (say) only 3 friends living in her building and feel no worse off.

∂ The online appendix explores the mathematics of monotonic transformations of utility functions. (http://glsmicro.com/appendices)

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Figure 4.1a graphs these three bundles. The square footage of the apartment is on the horizontal axis and the number of friends is on the vertical axis. These are not the only three bundles that give Michaela the same level of utility; there are many different bundles that accomplish that goal—an infinite number of bundles, in fact, if we ignore that it might not make sense to have a fraction of a friend (or maybe it does!).

Figure 4.1: Figure 4.1 Building an Indifference Curve
Figure 4.1: (a) Because Michaela receives utility from both the number of friends in her apartment building and the square footage of her apartment, she is equally happy with 10 friends in her building and a 500-square-foot apartment or 5 friends in her building and a 750-square-foot apartment. Likewise, she is willing to trade off 2 more friends in her building (leaving her with 3) to have a 1,000-square-foot apartment. These are three of many combinations of friends in her building and apartment size that make her equally happy.
(b) An indifference curve connects all bundles of goods that provide a consumer with the same level of utility. Bundles A, B, and C provide the same satisfaction for Michaela. Thus, the indifference curve represents Michaela’s willingness to trade off between friends in her apartment building and the square footage of her apartment.

indifference curve

A mathematical representation of the combination of all the different consumption bundles that provide a consumer with the same utility.

The combination of all the different bundles of goods that give a consumer the same utility is called an indifference curve. In Figure 4.1b, we draw Michaela’s indifference curve, which includes the three points shown in Figure 4.1a. Notice that it contains not just the three bundles we discussed, but many other combinations of square footage and friends in the building. Also notice that it always slopes down: Every time we take away a friend from Michaela, she needs more square footage to remain indifferent. (Equivalently, we could say any apartment with less space would require more friends in the building to keep her equally well off.)

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For each level of utility, there is a different indifference curve. Figure 4.2 shows two of Michaela’s indifference curves. Which corresponds to the higher level of utility? The easiest way to figure this out is to think like Michaela. One of the points on the indifference curve U1 represents the utility Michaela would get if she had 5 friends in her building and a 500-square-foot apartment. Curve U2 includes a bundle with the same number of friends and a 1,000-square-foot apartment. By our “more is better” assumption, indifference curve U2 must make Michaela better off. We could have instead held the apartment’s square footage constant and asked which indifference curve had more friends in the building, and we would have found the same answer. Any indifference curve that is closer to the origin (zero units of both goods) than another curve has a lower utility (we learn below that they can’t cross). Michaela’s utility is higher at every point on U2 than at any point on U1.

Figure 4.2: Figure 4.2 A Consumer’s Indifference Curves
Figure 4.2: Each level of utility has a separate indifference curve. Because we assume that more is preferred to less, an indifference curve lying to the right and above another indifference curve reflects a higher level of utility. In this graph, the combinations along curve U2 provide Michaela with a higher level of utility than the combinations along curve U1. Michaela will be happier with a 1,000-square-foot apartment than a 500-square-foot apartment, holding the number of friends living in her building equal at 5.