ECN 712
Fall 2009
Professor Schlee
Problem Set VIIa, Additional Practice
For problems 1 and 2, consider the insurance problem in MWG, exercise
6.C.1
, with the following
change of notation:
W
is wealth in the absence of a loss, and
L
is the magnitude of a loss if it
occurs,
π
2
is the probability of a loss,
I
is the indemnity level, and
r
2
∈
(
π
2
,
1) is the price per
dollar of coverage. The vNM utility
u
is diﬀerentiable with
u
0
>
0 and is strictly concave.
1. How does an increase in risk aversion aﬀect insurance demand? If the household’s preferences
satisfy decreasing absolute risk aversion, how does an increase in wealth aﬀect insurance
demand?
2.
Demand for statecontingent consumption
(a) Show that this insurance problem can be reformulated as follows (by substituting
I
out
of the problem using the budget constraint which follows). The consumer has a state
contingent endowment of
ω
= (
W,W

L
). Let
x
= (
x
1
,x
2
), where
x
1
is consumption
in the noloss state and
x
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 Spring '10
 schlee
 Microeconomics, absolute risk aversion, risky asset

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