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CHAPTER 18
UNCERTAINTY AND RISK AVERSION
Most of the problems in this chapter focus on illustrating the concept of risk aversion. That is,
they assume that individuals have concave utility of wealth functions and therefore dislike
variance in their wealth. A difficulty with this focus is that, in general, students will not have
been exposed to the statistical concepts of a random variable and its moments (mean, variance,
etc.). Most of the problems here do not assume such knowledge, but the Extensions do show how
understanding statistical concepts is crucial to reading applications on this topic.
Comments on Problems
18.1
Reverses the riskaversion logic to show that observed behavior can be used to place
bounds on subjective probability estimates.
18.2
This problem provides a graphical introduction to the idea of risktaking behavior. The
FriedmanSavage analysis of coexisting insurance purchases and gambling could be
presented here.
18.3
This is a nice, homey problem about diversification. Can be done graphically although
instructors could introduce variances into the problem if desired.
18.4
A graphical introduction to the economics of health insurance that examines costsharing
provisions. The problem is extended in Problem 19.3.
18.5
Problem provides some simple numerical calculations involving risk aversion and
insurance. The problem is extended to consider moral hazard in Problem 19.2.
18.6
This is a rather difficult problem as written.
It can be simplified by using a particular
utility function (e.g.,
U
(
W
) = ln
W
). With the logarithmic utility function, one cannot use
the Taylor approximation until after differentiation, however.
If the approximation is
applied before differentiation, concavity (and risk aversion) is lost.
This problem can,
with specific numbers, also be done graphically, if desired.
The notion that fines are
more effective can be contrasted with the criminologist’s view that apprehension of law
breakers is more effective and some shortcomings of the economic argument (i.e., no
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 Spring '09
 Smith
 Utility

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