1.) Consider a consumer with expected utility function U(X) = 1n(X). The consumer has wealth equal to $100,000 and faces the following risk: lose $1,000 with probability 0.1, lose $10,000 with probability 0.01, and lose nothing with probability 0.89. a. Is the consumer risk averse? b. What is the maximum this consumer would be willing to pay (WTP) for full insurance against this risk? c. What is this consumer?s risk premium? 2.) Consider a consumer with utility function U(W) = a + bWC where W is wealth and a,b, and c are constants with the following restrictions: b>0, c>0, and a can be any number. Assume the consumer has a wealth endowment of $25,000 and faces the following risk: lose 5,000 with probability 0.05 and lose nothing with probability 0.95. a. For what values of a, b, and c, would this consumer be considered risk averse? b. Suppose a=0, b=2, and c=0.8. What is this consumer?s risk premium for full insurance against this risk? c. How would your answer to part b change if a 7t 0? d. Use the answer to part b to draw an expected utility diagram showing the consumer?s WTP, expected loss, and risk premium.
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