A Rothschild-Stiglitz 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.
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