Chapter 6
The Economics
of Information
and Choice
Under
Uncertainty
Slide 1
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 6-1
The Information
Implicit in Silence
If only those toads with
a pitch below 6.0 bother
to croak, toads who
remain silent reveal that
their pitch is, on the
average, significantly
higher than 6.0.
Slide 2
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 6-2
A Concave Utility
Function
Any arc of a concave
utility function lies above
the corresponding chord.
Slide 3
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 6-3
A Risk-Averse Person
Will Always Refuse a
Fair Gamble
The expected utility of a
gamble lies on the chord
joining points A and C. If
the probability of winning
is 1/2, the expected utility
lies halfway between A
and C. Since a point on
the arc of a concave
function always lies above
the correspond-ing point
on the chord, the expected
utility of a fair gamble
will always be less than
the utility of refusing the
gamble.
Slide 4
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 6-4
The Utility Function of
a Risk-Seeking Person
Is Convex in Total
Wealth
Any arc of a convex
function lies below the
corresponding chord. For a
risk seeker, the expected
utility of a
fair gamble, EUG, will
always exceed the
utility of refusing the
gamble, U(M0).
Slide 5
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 6-5
Risk Neutrality
A risk-neutral
consumer is indifferent
between accepting or
refusing a fair gamble,
because the expected
utility of accepting,
EUG, is the same as the
certain utility of
refusing, U(M0).
Slide 6
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 6-6
The Value of
Reducing Uncertainty
Under the assumed
payoffs, the expected
utility of becoming an
actress is less than the
expected utility of
becoming a teacher. But
because a successful
actress earns so much
more than a teacher,
information about
whether an acting career
would be successful has
obvious economic value.
Slide 7
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 6-7
Career Prospects
After Attending
Colleges A and B
If you go to college B,
you get an adequate
job with certainty. If
you go to the more
prestigious college
A, you get a great job
with probability .6. But
with probability .4 you
will flunk out of A, in
which case you will get
a bad job.
Slide 8
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 6-8
The Expected
Utilities of
Alternative College
Choices
The expected value of
lifetime wealth is
higher when you go to
A ($700,000) than
when you go to B
($690,000). But a riskaverse person will
nonetheless choose B,
because it has higher
expected utility (830.6)
than A (800).
Slide 9
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 6-9
The Reservation
Price for Insurance
The consumer’s initial
wealth is $700, and he
faces a loss of $600 with
probability 1/3. His
expected utility is 30
utils. Because he gets the
same expected utility
from a certain wealth
level of $370, he would
be willing to pay as
much as
$700 – $370 = $330 for
insurance against the
loss.
Slide 10
Copyright © 2004 McGraw-Hill Ryerson Limited
FIGURE 6-10
The Reservation Price
for Insurance Against
a Loss L Occurring
with Probability p
If this consumer paid R
for an insurance policy
against a loss of L that
occurred with probability
p, her utility, U(M0 – R),
would be the same as her
expected utility without
the insurance,
pU(M0 – L) +
(1 – p)U(M0).
Slide 11
Copyright © 2004 McGraw-Hill Ryerson Limited
PROBLEM 1
Slide 12
Copyright © 2004 McGraw-Hill Ryerson Limited
ANSWER 6-1
Slide 13
Copyright © 2004 McGraw-Hill Ryerson Limited