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

CHAP. 5] ADVANCED TOPICS IN CONSUMER DEMAND THEORY 111
THE THEORY OF REVEALED PREFERENCE
5.3 Starting from Fig. 5-2, draw a figure showing haw we can derive the entire (a) lower boundary and
(b) upper boundary of the indifference curve.
(a)
The consumer can be induced to purchase basket C on PP in Fig. 5-7, if P x /P y is sufficiently low, as
indicated by budget line RR. Thus, area CPR can also be removed from the lower zone of ignorance by
reasoning analogous to that used in Example 2. Hence, the lower boundary for the indifference curve is
TFDABCR.
Fig. 5-7
(b) From Fig. 5-8, we can see that baskets above and to the right of H are preferred to H, which is preferred to G,
which is preferred to A. Thus, we can remove the areas to the right of the boundary AGH from the upper zone
of ignorance. By analogous reasoning, we know that the indifference curve must be below the AJK boundary.
Thus, the upper boundary for the indifference curve is HGAJK.
5.4 Draw a figure showing the lower and upper boundaries found in Problem 5.3 and also showing
indifference curve II from Fig. 5-1 that we seek to derive.
In Fig. 5-9, indifference curve II that we seek to derive must be above TFDABCR and below HGAJK. The exact
location of indifference curve II can be pinpointed more closely by chipping away still more areas from the
lower and upper zones of ignorance. While not very practical, the theory of revealed preference thus shows how
a consumer’s indifference curve can be derived from observed market choices and without direct questioning of
the consumer about personal preferences.