Characteristics of Indifference Curves

1. We can always draw indifference curves. The first assumption, completeness and rankability, means that we can always draw indifference curves: All bundles have a utility level, and we can rank them.

2. We can figure out which indifference curves have higher utility levels and why they slope downward. The “more is better” assumption implies that we can look at a set of indifference curves and figure out which ones represent higher utility levels. This can be done by holding the quantity of one good fixed and seeing which curves have larger quantities of the other good. This is exactly what we did when we looked at Figure 4.2. The assumption also implies that indifference curves never slope up. If they did slope up, this would mean that a consumer would be indifferent between a particular bundle and another bundle with more of both goods. There’s no way this can be true if more is always better.

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3. Indifference curves never cross. The transitivity property implies that indifference curves for a given consumer can never cross. To see why, suppose our apartment-hunter Michaela’s hypothetical indifference curves intersect with each other, as shown in Figure 4.3. The “more is better” assumption implies she prefers bundle E to bundle D, because E offers both more square footage and more friends in her building than does D. Now, because E and F are on the same indifference curve U₂, Michaela’s utility from consuming either bundle must be the same by definition. And because bundles F and D are on the same indifference curve U₁, she must also be indifferent between those two bundles. But here’s the problem: Putting this all together means she’s indifferent between E and D because each makes her just as well off as F. We know that can’t be true. After all, she must like E more than D because it has more of both goods. Something has gone wrong. What went wrong is that we violated the transitivity property by allowing the indifference curves to cross. Intersecting indifference curves imply that the same bundle (the one located at the intersection) offers two different utility levels, which can’t be the case.

   

   Figure 4.3: Figure 4.3 Consumer’s Indifference Curves Cannot Cross

   Figure 4.3: Indifference curves cannot intersect. Here, Michaela would be indifferent between bundles D and F and also indifferent between bundles E and F. The transitivity property would therefore imply that she must also be indifferent between bundles D and E. But this can’t be true, because more is preferred to less, and bundle E contains more of both goods (more friends in her building and a larger apartment) than D.

4. Indifference curves are convex to the origin (i.e., they bend toward the origin in the middle). The fourth assumption of utility—the more you have of a particular good, the less you are willing to give up of something else to get even more of that good—implies something about the way indifference curves are curved. Specifically, it implies they will be convex to the origin; that is, they will bend in toward the origin as if it is tugging on the indifference curve, trying to pull it in.

   To see what this curvature means in terms of a consumer’s behavior, let’s think about what the slope of an indifference curve means. Again, we’ll use Michaela as an example. If the indifference curve is steep, as it is at point A in Figure 4.4, Michaela is willing to give up a lot of friends to get just a few more square feet of apartment space. It isn’t just coincidence that she’s willing to make this tradeoff at a point where she already has a lot of friends in the building but a very small apartment. Because she already has a lot of one good (friends in the building), she is willing to give up quite a lot of it in order to gain more of the other good (apartment size) she doesn’t have much of. On the other hand, where the indifference curve is relatively flat, as it is at point B of Figure 4.4, the tradeoff between friends and apartment size is reversed. At B, the apartment is already big, but Michaela has few friends around, so she now needs to receive a great deal of extra space in return for a small reduction in friends to be left as well off.

   

   Figure 4.4: Figure 4.4 Tradeoffs along an Indifference Curve

   Figure 4.4: At point A, Michaela is willing to give up a lot of friends to get just a few more square feet, because she already has a lot of friends in the building but little space. At point B, Michaela has a large apartment but few friends around, so she now would require a large amount of space in return for a small reduction in friends to be left equally satisfied.

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   Because tradeoffs between goods generally depend on how much of each good a consumer would have in a bundle, indifference curves are convex to the origin. Except for some extreme cases where the indifference curves become completely flat lines or bend all the way into right angles (which we will discuss later in the chapter), all the indifference curves we draw will have this shape.