This preview shows page 1. Sign up to view the full content.
A RothschildStiglitz Problem
Consider the following economy with one physical commodity per state of nature and
three consumers, each of whom seek to maximize expected utility.
For i = 1,2, consumer i is risk
averse, with utility of certain consumption given by u
i
(x
i
) = log(x
i
).
For i = 1,2, consumer i is
endowed with 1 unit of consumption when she does not have an accident, 0 units of consumption
when she has an accident.
Consumer 1 is a “low risk” consumer, with a probability of an accident equal to 1/3.
Consumer 2 is a “high risk” consumer, with a probability of an accident equal to ½.
Consumer 1
having an accident and consumer 2 having an accident are independent events.
Consumer 3 is risk neutral, with utility of certain consumption given by u
3
(x
3
) = x
3
, and
has an endowment of 2 units of consumption in all states of nature.
For parts (i) and (ii), assume
that consumer 3 knows that consumer 1 is low risk and that consumer 2 is high risk, so
information is symmetric.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 07/17/2008 for the course ECON 805 taught by Professor Peck during the Spring '08 term at Ohio State.
 Spring '08
 PECK
 Utility

Click to edit the document details