Economics 206
Spring 2007 (Prof. G. Loury)
Assignment 1: Choice under Uncertainty
1. Concerning the Independence Axiom:
L
”
L
0
⇐⇒ ∀
α
∈
[0
,
1]
,
∀
L
00
:
αL
+ (1

α
)
L
00
”
αL
0
+ (1

α
)
L
00
(a) (
The Axiom extends to strict preference and to indifference.
) Show that the In
dependence Axiom implies:
(i)
L
´
L
0
⇐⇒ ∀
α
∈
(0
,
1]
,
∀
L
00
:
αL
+ (1

α
)
L
00
´
αL
0
+ (1

α
)
L
00
(ii)
L
∼
L
0
⇐⇒ ∀
α
∈
[0
,
1]
,
∀
L
00
:
αL
+ (1

α
)
L
00
∼
αL
0
+ (1

α
)
L
00
(b) (
The Axiom implies there is a best and a worst lottery
.) Let the set of consequences
be finite:
C
=
{
c
1
, ..., c
N
}
, and let
L
n
be the lottery giving consequence
c
n
with
probability 1,
n
= 1
, ..., N
. Assume, WLOG, that
L
1
”
L
2
”
...
”
L
N
. Then,
show that the Independence Axiom implies:
∀
lotteries
L
:
L
1
”
L
”
L
N
2. Try to work through the following exercises from the text: page 208 number 6.B.4;
and, page 209 number 6.B.6.
3. (
The demand for insurance
.)
An expected utility maximizing agent with wealth
W
either suffers a loss,
D
, reducing his wealth to
W

D
; or, loses nothing and maintains
his wealth at
W
. Let
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 Spring '07
 G.LOURY
 Economics, Microeconomics, Utility, independence axiom

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