6.11 Graphing complements Graphing complements is complicated because a complementary relationship between goods (under Hicks’ definition) cannot occur with only two goods. Rather, complementarity necessarily involves the demand relationships among three (or more)

goods. In his review of complementarity, Samuelson provides a way of illustrating the concept with a two-dimensional indifference curve diagram (see the Suggested Readings). To examine this construction, assume there are three goods that a consumer might choose. The quantities of these are denoted by x1, x2, and x3. Now proceed as follows.

a. Draw an indifference curve for x2 and x3, holding the quantity of x1 constant at x0 1. This indifference curve will have the customary convex shape.

b. Now draw a second (higher) indifference curve for x2, x3, holding x1 constant at x0 1 % h. For this new indifference curve, show the amount of extra x2 that would compensate this person for the loss of x1; call this amount j. Similarly, show that amount of extra x3 that would compensate for the loss of x1 and call this amount k.

c. Suppose now that an individual is given both amounts j and k, thereby permitting him or her to move to an even higher x2, x3 indifference curve. Show this move on your graph, and draw this new indifference curve.

d. Samuelson now suggests the following definitions: