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

CHAP. 5] ADVANCED TOPICS IN CONSUMER DEMAND THEORY 115
(b)
Since the individual is just induced to accept the gamble when the probability of winning is 0.60 and would
gain 100 utils upon winning, we can measure the utility lost in losing the gamble as follows:
Expected gain in utility ¼ expected loss in utility
(0:6)(100 utils) ¼ (0:4)(utils lost)
(0:6)(100 utils)
utils lost ¼ ¼ 150 utils
0:4
Since the individual would gain 100 utils upon winning $1000 and lose 150 utils on losing the $1000,
the MU of money decreases, making the individual an insurer. Note that in choices involving risk, the
consumer maximizes expected utility rather than utility. This general method of calculation is often
referred to as modern utility theory.
5.9 Do the calculations in Problem 5.8(b) give a cardinal measure of utility? Why?
The calculations of Problem 5.8(b) (and modern utility theory) do not really give us a cardinal measure of
utility, since the results obtained are arbitrary with regard to both origin and scale. For example, if we assigned
200 utils to the winning of $1000, the utility lost in losing the $1000 would have been 300 utils instead of 150
utils. Furthermore, 300 utils should only be taken to imply more utility than 150 utils, and not twice as much
utility. Thus, modern utility theory only gives a method of ordering utility in conditions involving risk.
A NEW APPROACH TO CONSUMER THEORY—THE DEMAND FOR CHARACTERISTICS
5.10 Starting with panel A of Fig. 5-4, draw a figure that shows a hypothetical equilibrium with (a) 33%
increase in the consumer’s income and (b) 40% reduction in the price of honey (with no change in
the price of sugar and in the consumer’s income).
(a)
A 33% increase in the consumer’s income extends ray OA by 33% to OA 0 in Fig. 5-11 or OB to OB 0 . The
budget frontier is then A 0 B 0 , and equilibrium may take place at C 0 on indifference curve III, with OB characteristics
from honey and BC 0 (equals OG) from sugar. See Fig. 5-11.
Fig. 5-11 Fig. 5-12
(b)
A 40% reduction in the price of honey extends ray OB by 40% to OB 00 in Fig. 5-12, so that the budget frontier
becomes AB 00 . Equilibrium may then take place at point C 00 on indifference curve V and is reached with ON
characteristics from honey and NC 00 (equals OR) from sugar. See Fig. 5-12.