## The Marginal Rate of Substitution

People face trade-offs when choosing among two or more goods, and indifference curves can help to clarify those trade-offs. The indifference curve in Figure 3.5 illustrates this. Starting at market basket A and moving to market basket B, we see that the consumer is willing to give up six units of clothing to obtain one extra unit of food. However, moving from B to D, he is willing to give up only four units of clothing to obtain an additional unit of food, and in moving from D to E, he will give up two units of clothing for one unit of food. The more clothing and the less food a person consumes, the more clothing he will give up to obtain more food. Similarly, the more food that a person possesses, the less clothing he will give up for more food.

Clothing (units per week) 14

FIGURE 3.5 The Marginal Rate of Substitution. The slope of an indifference curve measures the consumer's,marginal rate of substitution between two goods. In the figure/ the marginal rate of substitution between clothing (C) and food (F), -AC/AF, falls from 6 to 4 to 2 to 1. When the marginal rate of substitution diminishes along an indifference curve, the indifference curve is convex.

Food

(units per week)

To quantify the amount of one good a consumer will give up to obtain more of another good, we use a measure called the marginal rate of substitution (MRS). The MRS of food F for clothing C is the maximum amount of clothing that a person is willing to give up to obtain one additional unit of food. If the MRS is 3, the consumer will give up 3 units of clothing: to obtain an additional unit offood,whileiftheMRSisK, only y2 aunitofclothingwillbegivenup.

To be consistent throughout the book, we will describe the MRS in terms of the amount of the good drawn on the vertical axis that must be given up to obtain one extra unit of the good drawn on the horizontal axis. Thus, in Figure 3.5 we refer to the amount of clothing given up to obtain an additional unit of food. If we denote the change in clothing by AC and the change in food by AF, the MRS can be written as - AC/AF. The negative sign, is included to make the marginal rate of substitution a positive number (AC is always negative). As a result, the marginal rate of substitution at any point is equal in absolute value to the slope of the indifference curve at that point,

At this point it is useful to add an additional assumption regarding consumer preferences to the three we discussed earlier in the chapter:

4. The fourth assumption is that indifference curves are convex, that is, bowed inward. The term convex means that the slope of the indifference curve increases (i.e., becomes less negative) as we move down along the curve. In other words, an indifference curve is convex if the MRS diminishes along the curve. The indifference curve in Figure 3.5 is convex. Starting with market basket A in Figure 3.5 and moving to market basket B, we note that the MRS of food F for clothing C is -AC/AF = — (—6)/l = 6. However, when starting at market basket B and moving from B to D, the MRS falls to 4. Starting at market basket D and moving to E, the MRS is 2, and starting at E and moving to G, the MRS is 1. As food consumption increases, the slope of the indifference curve falls in magnitude, so the MRS also falls.1

Is it reasonable to assume that indifference curves are convex? Yes. As more and more of one good is consumed, we would expect that a consumer would prefer to give up fewer and fewer units of a second good to get additional units of the first one. As we move down along the indifference curve in Figure 3.5 and consumption of food increases, the consumer's desire for still more food should diminish. Thus, he should be willing to give up less and less clothing to obtain additional food.

Another way of describing this is to say that consumers generally prefer a balanced market basket to market baskets that contain all of one good and none of the other. Note from Figure 3.5 that a relatively balanced market basket containing 3 units of food and 6 units of clothing (basket D) generates as

1 With nonconvex preferences, the MRS increases as the amount of the good measured on the horizontal axis increases along any indifference curve. This unlikely possibility might arise if one orboth goods are addictive. For example,the willingness to substitute an addictive drug for other goods might increase as the use of the addictive drug increased.

much satisfaction as another market basket that contains only 1 unit of food, but 16 units of clothing (basket A). It follows that a balanced market basket containing (for example) 6 units of food and 8 units of clothing would generate a higher level of satisfaction.