ECONOMICS 100A
Professor Dan Acland
09/28/10
Lecture 10
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TURN IN PROBLEM SET #2
ICLICKER QUIZ
ANNOUNCEMENTS
A student in the front row just said to me that
convexity is equivalent to riskaversion, not
concavity, which is not what was on the iClicker
question. So I will look into that, and if I find the
question wrong relative to what it says in the book,
then I will not include that question.
LECTURE
Today we will talk about expected utility and
insurance contracts. We will talk about risk
preferences, but before we get into buying
insurance, I want to point something out about
expected utility theory and what it does for us and
what it says about an individual’s utility function.
Slide
: Lecture outline:
1.
Risk preference and the shape of the utility
function.
A.
Preferences over certain outcomes tell us
the horizontal shape of utility.
B.
Preferences over risky outcomes tell us
the vertical shape of utility.
2.
How much will people pay for complete
insurance:

Certainty equivalent, risk premium, and
maximum willingness to pay
You’ll notice that up until now, we’ve been talking
exclusively about the horizontal curvature of
individuals’ utility functions. We’ve been
pretending that people actually have utility
functions that help them make decisions. So far, all
we’ve said is that the only thing we know about is
the horizontal curvature of that function. That’s
because the vertical dimension is utils, and because
we said utils don’t exist, we can’t say anything
about the vertical dimension of the curve.
BUT
, if
we allow ourselves to assume the independence
axiom with respect to people’s preferences over
risky outcomes, the vertical curvature (the utility
function that we’ve been looking at all along)
suddenly starts to matter. And it matters crucially.
I’m going to try to show you that the utility
function, u(x), that we have started looking at is
actually directly related to the utility function that
we’ve been looking at so far that tells us about
people’s preferences over certain outcomes.
Then I’ll go over a specific insurance application.
Slide
: A. Preferences over certain outcomes tell us
the horizontal shape of utility.

Three sisters, Magda, ZsaZsa, and Eva, each
have CobbDouglas preferences over clothing, x
1
,
and all other goods, x
2
, so their utility function is
U(x
1
, x
2
) = x
1
α
x
2
β
.
