Chapter 6
Choice Under Uncertainty
Up until now, we have been concerned with choice under certainty.
A consumer chooses which
commodity bundle to consume. A producer chooses how much output to produce using which mix
of inputs. In either case, there is no uncertainty about the outcome of the choice.
We now turn to considering choice under uncertainty, where the objects of choice are not
certainties, but distributions over outcomes. For example, suppose that you have a choice between
two alternatives. Under alternative A, you roll a six-sided die. If the die comes up 1, 2, or 3, you
get $1000. If it comes up 4, 5, or 6, you lose $300. Under alternative B, you choose a card from
a standard 52 card deck. If the card you choose is black, you pay me $200. If it is a heart, you
get a free trip to Bermuda. If it is a diamond, you have to shovel the snow o
f
of my driveway all
winter.
If I were to ask you whether you preferred alternative A or alternative B, you could probably
tell me. Indeed, if I were to write down any two random situations, call them
L
1
and
L
2
,youcou
ld
probably tell me which one you prefer.
And, there is even the possibility that your preferences
would be complete, transitive (i.e., rational), and continuous. If this is true then I can come up
with a utility function representing your preferences over random situations, call it
U
(
L
)
, such that
L
1
is strictly preferred to
L
2
if and only if
U
(
L
1
)
>U
(
L
2
)
.T
h
u
s
,w
i
t
h
o
u
t
t
o
om
u
c
he
f
ort, we can
extend our standard utility theory to utility under uncertainty. All we need is for the consumer
to have well de
f
ned preferences over uncertain alternatives.
Now, recall that I said that much of what we do from a modeling perspective is add structure
to people’s preferences in order to be able to say more about how they behave. In this situation,
what we would like to be able to do is say that a person’s preferences over uncertain alternatives
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