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Answers to 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.
(i) Define a competitive equilibrium for the economy with complete statecontingent commodity
markets.
Specify how many states of nature there are and the probability of each state.
(ii) Calculate the competitive equilibrium price vector and allocation for the economy with
complete statecontingent commodity markets.
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 Spring '08
 PECK
 Utility

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