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

90 CONSUMER DEMAND THEORY [CHAP. 4
(a)
Fig. 4-26
In panel A of Fig. 4-26, point E is the original point of consumer equilibrium in Problem 4-20. When the price of X
falls from $2 to $1 (ceteris paribus), we get budget line 4 and a new point of consumer equilibrium (point J on
indifference curve IV). Joining point E to point J, we get a segment of the consumer’s price-consumption curve
(PCC) for commodity X. From the points of consumer equilibrium in panel A of Fig. 4-26, we can derive a
segment of d x (panel B).
(b) Since the PCC is negatively sloped, d x is price-elastic over arc E 0 J 0 .[e ¼ 2(5/21) . (3/13) ¼ 15/
33 ffi 1.15; also, when the price of X falls from $2 to $1, the consumer increases expenditures on X
from $8 to $9 per time period. Thus, d x is price-elastic over arc E 0 J 0 .]
(c) At point E in panel A, the MRS xy ¼ MU x /MU y ¼ 2. At point J, the MRS xy ¼ MU x /MU y ¼ 1. Thus, in
moving from point E to point J, the MRS xy and the ratio of the MU x to the MU y falls. However, for the
MU x /MU y to fall it is not necessary for the MU x and the MU y to fall. For example, the MU x /MU y can
fall even if both the MU x and the MU y rise—as long as the rise in the MU x is less than the rise in the
MU y . Therefore, diminishing MRS xy does not necessarily imply diminishing MU x and MU y , and
diminishing MU is not necessary to derive a negatively sloped demand curve.