## Characteristics of Indifference Curves

Generally speaking, the positions and shapes of indifference curves can tell us a lot about a consumer’s behavior and decisions. However, our four assumptions about utility functions put some restrictions on the shapes that indifference curves can take.

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.

Draw some indifference curves to really understand the concept

Indifference curves, like many abstract economic concepts, are often confusing to students when they are first introduced. But one nice thing about indifference curves is that preferences are the only thing necessary to draw your own indifference curves, and everybody has preferences! If you take just the few minutes of introspection necessary to draw your own indifference curves, the concept starts to make sense.

Start by selecting two goods that you like to consume—maybe your favorite candy bar, pizza, hours on Facebook, or trips to the movies. It doesn’t matter much what goods you choose (this is one of the nice things about economic models—they are designed to be very general). Next, draw a graph that has one good on the vertical axis and the other good on the horizontal axis (again, it doesn’t matter which one goes where). The distance along the axis from the origin will measure the units of the good consumed (candy bars, slices of pizza, hours on Facebook, etc.).

The next step is to pick some bundle of these two goods that has a moderate amount of both goods, for instance, 12 pieces of candy and 3 slices of pizza. Put a dot at that point in your graph. Now carry out the following thought experiment. First, imagine taking a few pieces of candy out of the bundle and ask yourself how many additional slices of pizza you would need to leave you as well off as you are with 12 pieces of candy and 3 slices of pizza. Put a dot at that bundle. Then, suppose a couple of more candy pieces are taken away, and figure out how much more pizza you would need to be “made whole.” Put another dot there. Next, imagine taking away some pizza from the original 12-piece, 3-slice bundle, and determine how many extra candy pieces you would have to be given to be as well off as with the original bundle. That new bundle is another point. All those points are on the same indifference curve. Connect the dots, and you’ve drawn an indifference curve.

Now try starting with a different initial bundle, say, one with twice as many of both goods as the first bundle you chose. Redo the same thought experiment of figuring out the tradeoffs of some of one good for a certain number of units of the other good, and you will have traced out a second indifference curve. You can start with still other bundles, either with more or less of both goods, figure out the same types of tradeoffs, and draw additional indifference curves.

There is no “right” answer as to exactly what your indifference curves will look like. It depends on your preferences. However, their shapes should have the basic properties that we have discussed: downward-sloping, never crossing, and convex to the origin.

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