The Steepness of Indifference Curves

We’ve now established the connection between a consumer’s preferences for two goods and the slope of her indifference curves (the MRSXY). They are the same thing. An indifference curve reveals a consumer’s willingness to trade one good for another, or each good’s relative marginal utility. We can flip this relationship on its head to see what the shapes of indifference curves tell us about consumers’ utility functions. In this section, we discuss two key characteristics of an indifference curve: how steep it is, and how curved it is.

Figure 4.6 presents two sets of indifference curves reflecting two different sets of preferences for concert tickets and MP3s. In panel a, the indifference curves are steep. In panel b, they are flat. (These two sets of indifference curves have the same degree of curvature so we don’t confuse steepness with curvature.)

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Figure 4.6: Figure 4.6 Steepness of Indifference Curves
Figure 4.6: Because the MRS measures the willingness of the consumer to trade one good for another, we can tell a great deal about preferences by examining the shapes of indifference curves. (a) Indifference curves that are relatively steep indicate that the consumer is willing to give up a large quantity of the good on the vertical axis to get another unit of the good on the horizontal axis. Here, the consumer is willing to give up a lot of concert tickets for some additional MP3s. (b) Relatively flat indifference curves imply that the consumer would require a large increase in the good on the horizontal axis to give up a unit of the good on the vertical axis. The consumer with flat indifference curves will give up a lot of MP3s for one additional concert ticket.

When indifference curves are steep, consumers are willing to give up a lot of the good on the vertical axis to get a small additional amount of the good on the horizontal axis. So a consumer with the preferences reflected in the steep indifference curve in panel a would part with many concert tickets for some more MP3s. The opposite is true in panel b, which shows flatter indifference curves. A consumer with such preferences would give up a lot of MP3s for one additional concert ticket. These relationships are just another way of restating the concept of the MRSXY that we introduced earlier.

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figure it out 4.1

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For interactive, step-by-step help in solving the following problem, visit LaunchPad at http://www.macmillanhighered.com/launchpad/gls2e

Ming consumes music downloads (M) and concert tickets (C). His utility function is given by U = 0.5M2 + 2C2, where MUM = M and MUC = 4C.

  1. Write an equation for MRSMC.

  2. Would bundles of (M = 4 and C = 1) and (M = 2 and C = 2) be on the same indifference curve? How do you know?

  3. Calculate MRSMC when M = 4 and C = 1 and when M = 2 and C = 2.

  4. Based on your answers to question b, are Ming’s indifference curves convex? (Hint: Does MRSMC fall as M rises?)

Solution:

  1. We know that the marginal rate of substitution MRSMC equals MUM/MUC.

    We are told that MUM = M and MUC = 4C. Thus, image

  2. For bundles to lie on the same indifference curve, they must provide the same level of utility to the consumer. Therefore, we need to calculate Ming’s level of utility for the bundles of (M = 4 and C = 1) and (M = 2 and C = 2):

    When M = 4 and C = 1, U = 0.5(4)2 + 2(1)2 = 0.5(16) + 2(1) = 8 + 2 = 10

    When M = 2 and C = 2, U = 0.5(2)2 + 2(2)2 = 0.5(4) + 2(4) = 2 + 8 = 10

    Each bundle provides Ming with the same level of utility, so they must lie on the same indifference curve.

  3. and d. To determine if Ming’s indifference curve is convex, we need to calculate MRSMC at both bundles. Then we can see if MRSMC falls as we move down along the indifference curve (i.e., as M increases and C decreases):

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These calculations reveal that, holding utility constant, when music downloads rise from 2 to 4, the MRSMC rises from 0.25 to 1. This means that as Ming consumes more music downloads and fewer concert tickets, he actually becomes more willing to trade concert tickets for additional music downloads! Most consumers would not behave in this way. This means that the indifference curve becomes steeper as M rises, not flatter. In other words, this indifference curve will be concave to the origin rather than convex, violating the fourth characteristic of indifference curves listed above.

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Application: Indifference Curves for Breakfast Cereal

Many people can’t stand to start their mornings without a bowl of their favorite breakfast cereal. Surveys suggest that more than 90% of families in the United States bought breakfast cereal in 2012, the latest year of the data, and total sales are projected to exceed $10 billion by 2016. Hundreds of different kinds of cereals fill grocery store shelves throughout North America.

Some economists study the cereal market and analyze how people decide what cereal to buy. Their findings give us some direct estimates of indifference curves and how they vary across people for the same products.

In one such study, economist Aviv Nevo looked at 25 leading cereal brands in 65 cities.5 He gathered information on the characteristics of the cereals in terms of sugar, calories, fat, fiber, mushiness, and so on, and treated each cereal like a bundle of these characteristics. (An analysis of products using their attributes is called hedonic analysis, and economists have done hedonic analyses of cars, computers, houses, and many other kinds of products.)

5 Aviv Nevo, “Measuring Market Power in the Ready-to-Eat Cereal Industry,” Econometrica 69, no. 2 (2001): 307–342.

Nevo computed the implied marginal rates of substitution for these different product attributes by comparing the demand for different cereals at different prices. Let’s take his results on two of the “goods” people consume when buying cereal—sugar and fiber. Both have a value and both cost money to produce, so consumers must make tradeoffs between them when choosing what cereal to buy.

We can use Nevo’s results to compute a direct estimate of the MRS of fiber for sugar for different kinds of people. Holding everything else equal, Nevo found that a 50-year-old consumer (let’s call him Ricardo) with an income one-third above the national average has an MRS of 1.24. To remain indifferent between his current cereal and a new cereal with 1 less gram of fiber, Ricardo requires 1.24 grams of additional sugar in the new cereal (to sweeten the deal). He clearly likes getting fiber at breakfast.

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The MRS differs for other kinds of people, however. A 20-year-old consumer (let’s call him David) with income about one-third below the national average has a much lower taste for fiber. According to Nevo’s measurements, David’s MRS of fiber for sugar is only 0.57. For David to remain indifferent between his current cereal and a new cereal with 1 less gram of fiber, he requires only 0.57 grams of additional sugar. He likes sugar more and is more willing to give up fiber to get it.

We know that the MRS of fiber for sugar is the ratio of marginal utilities, MUfiber/MUsugar. Ricardo’s ratio is greater than David’s because he is willing to give up more sugar in exchange for fiber. Ricardo’s indifference curves (Figure 4.7a), when drawn with fiber on the horizontal axis and sugar on the vertical axis, are therefore steeper than David’s indifference curves (Figure 4.7b). Because they have different tastes in cereal, the marginal rates of substitution and, in turn, the slopes of the indifference curves look different for older adults and younger adults.

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Figure 4.7: Figure 4.7 Preferences for Breakfast Cereal by Older and Younger Adults
Figure 4.7: Fifty-year-old Ricardo (a) has a greater MRS of fiber for sugar (and steeper indifference curves) than 20-year-old David (b). Accordingly, Ricardo is more likely to want his fiber and less willing to trade fiber content for sugar. Because David has a lower MRS of fiber for sugar, he is more willing to give up fiber for sugar. As a result, his indifference curves are flatter.
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© Kristoffer Tripplaar/Alamy
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Something about 50-year-olds makes them more likely to prefer high-fiber cereals than high-sugar cereals; 20-year-olds prefer just the opposite.
© Jane E. Tufts

This result probably also explains why the people buying Kellogg’s Honey Smacks (with 20 grams of sugar and 1.3 grams of fiber per cup) likely aren’t the same people as those buying Kashi’s Go Lean (with 6 grams of sugar and 10 grams of fiber per cup).

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