Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

CHAP. 4] CONSUMER DEMAND THEORY 79
4.12 (a) Is a cardinal measure of utility or satisfaction necessary in order to sketch a set of indifference
curves? (b) What are the characteristics of indifference curves?
(a)
(b)
In sketching a set of indifference curves, we need only an ordering or ranking of consumer preferences. A
cardinal measure of utility or satisfaction is neither necessary nor specified. That is, we do not need
to know either the absolute amount of utility that a consumer receives by being on a particular indifference
curve or by how much utility increases when the consumer moves to a higher indifference curve. All we
need to know to get the indifference curves of a consumer is whether the consumer is indifferent, prefers,
or does not prefer each combination of X and Y to other combinations of X and Y.
Indifference curves are negatively sloped, they are convex to the origin and do not cross. Indifference curves
need not be and are usually not parallel to one another.
4.13 (a) Find the MRS xy between all consecutive points on the four indifference curves of Problem 4.11.
(b) What is the difference between MRS xy and the MU x ?
(a) See Table 4.12.
(b) The MRS xy measures the amount of Y a consumer is willing to give up to obtain one additional unit of X (and
still remain on the same indifference curve). That is, the MRS xy ¼ –(DQ y /DQ x ). The MU x measures the
change in the total utility a consumer receives when changing the quantity of X consumed by one unit.
That is, MU x ¼ DTU x /DQ x . In measuring the MRS xy , both X and Y change. In measuring MU x , the quantity
of Y (among other things) is kept constant. Thus, the MRS xy measures something different from the MU x .
Table 4.12
I II III IV
X Y MRS xy X Y MRS xy X Y MRS xy X Y MRS xy
2 13 .. 3 12 .. 5 12 .. 7 12 ..
3 6 7 4 8 4 5.5 9 6 8 9 3
4 4.5 1.5 5 6.3 1.7 6 8.3 1.4 9 7 2
5 3.5 1 6 5 1.3 7 7 1.3 10 6.3 0.7
6 3 0.5 7 4.4 0.6 8 6 1 11 5.7 0.6
7 2.7 0.3 8 4 0.4 9 5.4 0.6 12 5.3 0.4
4.14 On the same set of axes, draw three indifference curves showing perfect substitutability between X and Y.
Fig. 4-14
For X and Y to be perfect substitutes, the MRS xy must be constant. That is, no matter what indifference curve
we are on and where we are on it, we must give up the same amount of Y to get one additional unit of X. For
example, in going from point A to point B on indifference curve III, the MRS xy equals 2. Similarly, in going
from point B to point C, the MRS xy is also equal to 2. If the indifference curves had throughout a slope of 21
(and thus a MRS xy ¼ 1), X and Y would not only be perfect substitutes but could be considered as being the