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Consider an individual with expected utility preferences and Bernoulli utility index u(x)=lnx. Suppose she is facing a lottery L with equal probability of having 2 and 4 yuan. Find a mean-preserving spread of L such that the level of expected utility in L is twice as much as in the new lottery. Consider an expected utility maximizer with Bernoulli utility index u(x)=〖x 〗^(1-ρ)/((1-ρ)), where ρ>0 and ρ≠1. Assuming her initial wealth is w=1 and she can invest her wealth in two assets. A safe asset gives a net return of 0 and the risky asset gives a net return v>0 with probability 1>π>0.5, and -v with probability 1-π. Show the proportion of wealth invested in the risky asset is strictly positive. Find a condition under which the proportion of wealth invested in the risky asset is less than 1. Assuming the condition you found in (b) holds, find the demand for risky asset. How does it vary with π and v? Comment on your findings.
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