Indifference Curves

We can show a consumer's preferences graphically with the use of indifference curves. An indifference curve represents all combinations of market baskets that provide the same level of satisfaction to a person. That person is therefore indifferent among the market baskets represented by the points on the curve.

Given the three assumptions about preferences discussed above, we know that a consumer can always indicate a preference for one market basket over another or indifference between the two. This information can then be used to rank all possible consumption choices. To see this in graphic form, we assume there are only two goods, food F and clothing C, available for consumption. In this case, market baskets describe combinations of food and clothing that a person might wish to consume. Table 3.1 provides some examples of market baskets containing various amounts of food and clothing.

Figure 3.1 shows the same market baskets that are in Table 3.1. The horizontal axis measures the number of units of food purchased each week, and the vertical axis measures the number of units of clothing. Market basket A, with 20 units of food and 30 units of clothing, is preferred to market basket G because A contains more food and more clothing (recall our third assumption that more is better than less). Similarly, market basket E, which contains still more food and more clothing, is preferred to A. In fact, we can easily compare all market baskets in the shaded areas (such as E and G) to A because they

Clothing (units per week)

10 20 30 40 (units per week)

FIGURE 3.1 Describing Individual Preferences. Because more of each good is preferred to less, we can compare market baskets in the shaded areas. Market basket A is clearly preferred to market basket G, while E is clearly preferred to A. However, A cannot be compared with B, D, or H without additional information.

contain either more or less of both food and clothing. However, comparisons of market basket A with market baskets B, D, and H are not possible without more information about the consumer's ranking because B contains more clothing but less food, and D contains more food but less clothing than A.

This additional information is provided in Figure 3.2, which shows an indifference curve, labeled U i, that passes through points A, B, and D. This curve indicates that the consumer is indifferent among these three market baskets. It tells us that the consumer feels neither better nor worse off in giving up 10 units of food to obtain 20 additional units of clothing in moving from market basket A to B. Likewise, the consumer is indifferent between points A and D (i.e., will give up 10 units of clothing to obtain 20 units of food). On the other hand, the consumer prefers A to H, which lies below U\.

The indifference curve in Figure 3.2 slopes downward from left to right. To understand why this must be the case, suppose instead that the indifference curve sloped upward from A to E. This would violate the assumption that

(units per week)

figure 3.2 An Indifference Curve. A person's indifference curve li, shows all market baskets that generate the same level of satisfaction as does market basket A. The person prefers market basket E, which lies above Uv to A, but prefers A to H or G, which lie below Ui.

more of any commodity is preferred to less. Since market basket E has more of both food and clothing than market basket A, it must be preferred to A and therefore cannot be on the same indifference curve as A. In fact, any market basket lying above and to the right of indifference curve Ui in Figure 3.2 is preferred to any market basket on U\.

To describe a person's preferences for all combinations of food and clothing, we can graph a set of indifference curves. This is called an indifference map. Each indifference curve in the map shows the market baskets among which the person is indifferent. Figure 3.3 shows three indifference curves that form part of an indifference map. Indifference curve t/3 generates the highest level of satisfaction, followed by indifference curves Ui and Ui.

Indifference curves cannot intersect. To see why, we will assume the contrary and see how it violates the assumptions about consumer behavior. Figure 3.4 shows two indifference curves, ^ and Ui that intersect at A. Since A and B are both on indifference curve Ui, the consumer must be indifferent between the two market baskets. Both A and D lie on indifference curve Ui so the consumer must be indifferent between both these market baskets. As a result, the consumer must also be indifferent between B and D. But this can't be true because market basket B must be preferred to D since it contains more of both food and clothing than D. Hence indifference curves that intersect would contradict our assumption that more is preferred to less.

Of course, there are an infinite number of nonintersecting indifference curves, one for every possible level of satisfaction. In fact, every possible mar-

(units per week)

figure 3.3 An Indifference Map. An indifference map is a set of indifference curves that describes a person's preferences. Any market basket on indifference curve U3, such as market basket A, is preferred to any market basket on curve U2 (e.g., basket B), which in turn is preferred to any market basket on Uu such as D.

figure 3.4 Indifference Curves Cannot Cross. If indifference curves !ii and U2 intersected, one of the assumptions of consumer theory would be violated. According to this diagram, the consumer should be indifferent among market baskets A, B, and D. Yet B is preferred to D because B has more of both goods.

ket basket (corresponding to a point on the graph) has an indifference curve passing through it.

Ordinal Versus Cardinal Rankings

For simplicity, we have shown only three indifference curves in Figure 3.3. The three curves provide an ordinal ranking of market baskets. An ordinal ranking places market baskets in the order of most preferred to least preferred, but it does not indicate by how much one market basket is preferred to another. For example, we know that consumption of any basket on Us, such as A, is preferred to consumption of any basket on Ui such as B. However, the amount by which A is preferred to B (and B to D) is not revealed by the indifference map.

By contrast, when economists first studied utility, they hoped that individuals' preferences could be easily quantified or measured in terms of basic units and could therefore provide a cardinal ranking of alternatives. Today, however, we know that the particular unit of measurement of utility is unimportant. For example, although we cannot say that consumers on Ui are twice as happy as they might be on Ui, an ordinal ranking is sufficient to help us explain how most individual decisions are made. In the few instances where it is not, we will discuss an alternative approach to describing preferences.

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