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84 CHAPTER 3 CONSUMER PREFERENCES AND THE CONCEPT OF UTILITY

12

10
A
y, units of clothing 6 B U = 8
8

FIGURE 3.5 Indifference Curves for 4 C U = 6
the Utility Function U 1xy 2
The utility is the same for all baskets U = 4
on a given indifference curve. For U = 2
example, the consumer is indifferent 0
between baskets A, B, and C in the 2 4 6 8 10 12
graph because they all yield the same x, units of food
level of utility (U 4).

equally satisfied with (or indifferent in choosing among) all baskets on that curve. For
example, Brandon would be equally satisfied with baskets A, B, and C because they all
lie on the indifference curve with the value U 4. (Compare Figures 3.4 and 3.5 to see
how the indifference curve U 4 looks in a three-dimensional and a two-dimensional
graph of the same utility function.) A graph like Figure 3.5 is sometimes referred to
as an indifference map because it shows a set of indifference curves.
Indifference curves on an indifference map have the following four properties.
1. When the consumer likes both goods (i.e., when MU and MU are both posi-
x
y
tive), all the indifference curves have a negative slope.
2. Indifference curves cannot intersect.
3. Every consumption basket lies on one and only one indifference curve.
4. Indifference curves are not “thick.’’

We will now explore these properties in further detail.

1. When the consumer likes both goods (i.e., when MU and MU are both positive), all the
x
y
indifference curves will have a negative slope. Consider the graph in Figure 3.6. Suppose
the consumer currently has basket A. Since the consumer has positive marginal utility
for both goods, she will prefer any baskets to the north, east, or northeast of A. We
indicate this in the graph by drawing arrows to indicate preference directions. The
arrow pointing to the east reflects the fact that MU 7 0. The arrow pointing to the
x
north reflects the fact that MU 7 0.
y
Points to the northeast or southwest of A cannot be on the same indifference
curve as A because they will be preferred to A or less preferred than A, respectively.
Thus, points on the same indifference curve as A must lie either to the northwest or
southeast of A. This shows that indifference curves will have a negative slope when
both goods have positive marginal utilities.