## Perfect Substitutes and Perfect Complements

The shapes of indifference curves can imply different degrees of willingness to substitute one good for another. To see this, look at the two polar cases illustrated in Figure 3.6. Figure 3.6a shows Philip's preferences for apple juice and orange juice. These two goods are perfect substitutes for Philip, since he is entirely indifferent between having a glass of one or the other. In this case, the marginal rate of substitution of apple juice for orange juice is 1; Philip is always willing to trade a glass of one for a glass of the other. In general, we say that two goods are perfect substitutes when the marginal rate of substitution of one good for the other is a constant; that is, the indifference curves that describe the trade-off between the consumption of the goods are straight lines.

Figure 3.6b illustrates Jane's preferences for left shoes and right shoes. For Jane, the two goods are perfect complements, since a left shoe will not increase her satisfaction unless she can obtain the matching right shoe. In this case, the

Apple Juice (glasses)

(a) Perfect Substitutes

(a) Perfect Substitutes

2 3 4 Orange Juice (glasses)

(b) Perfect Complements

Left Shoes

2 3 4 Orange Juice (glasses)

Right Shoes figure 3.6a and b Perfect Substitutes and Perfect Complements. In (a), Philip views orange juice and apple juice as perfect substitutes; he is always indifferent between a glass of one and a glass of the other. In (b), Jane views left shoes and right shoes as perfect complements. An additional left shoe gives her no extra satisfaction unless she also obtains the matching right shoe.

marginal rate of substitution of left shoes for right shoes is zero whenever there are more right shoes than left shoes, since Jane would not give up any left shoes to get additional right shoes. Correspondingly, the marginal rate of substitution is infinite whenever there are more left shoes than right, since Jane will give up all but one of the excess left shoes she has in order to obtain an additional right shoe. Two goods are perfect complements when the indifference curves for the goods are shaped as right angles.