Question

Suppose that there are only two goods, books and coffee. Justine gets utility from both books and coffee, but her indifference curves between them are concave rather than convex to the origin.

a. Draw a set of indifference curves for Justine.

b. What do these indifference curves tell you about Justine’s marginal rate of substitution between books and coffee?

c. What will Justine’s utility maximizing bundle look like?

d. Compare your answer to (b) to real world behaviors. Does the comparison shed any light on why economists generally assume convex preferences?

Answer 1

a.

10 HIC I Budget line Іс, т, IC L Books

b.

These set of indifference curve tells us that the marginal rate of substitution between books and coffee is not diminishing rather it increases. MRS of books for coffee increases when more of books are substituted for coffee. The concave indifference curve also tells us that Justin does not like much variety in his consumption and want to consume either of books or coffee. This is also clear from the diagram above. Equilibrium occurs at point O where budget line is tangent to IC2. However, Justing can move to point K or A and achieve a higher level of satisfaction. He will try to reach either to point B or L where he realizes the highest level of satisfaction. So, he can be either at point B or at point L. There exist corner solutions in the concave ICs.

c.

As discussed in above point Justin will either consume books or coffee. So, his utility-maximizing bundle will be (All Books, 0) or (0, All coffee)

d.

Economists generally assume convex preferences because they assume that the consumer will not spend his entire income only on one commodity. But in the case of concave preferences such as Justin's case, such cases are not seen in the real world. The consumer would like spend his entire income on different sets of commodities and not just on a single one. This is why the concavity of preferences has been ruled out from the economist's analysis.