Decision Problem of Investing an Amount of Wealth W Into a Risky Asset Economics Assignment Help

MICROECONOMICS
Consider the decision problem of investing an amount of wealth W into a risky asset with return
R={0.1with probability
?0.05with probability1?p
and into a risk-less asset with risk-free interest rate r=2%. You are a risk-averse investor with a utility function
U(WT)=10+ln(WT)
where WTWT is the amount of wealth at the end of the investment.
a) Find the optimal allocation in risky and risk-less assets as a function of the probability pp and the initial amount of wealth WW invested.b) Compute the optimal allocation for a probability value p=0.5c) What is the lower bound of the probability pp for investing a positive share into the risky asset?d) What is the lower bound of p for starting to borrow money at the risk-less interest rate and invest an amount larger than W in the risky asset?
PROBLEM  2

Consider a risky asset with return expressed by
R={0.5with probabilityp0.05with probability1?p
and a utility function U(WT)=ln(WT), where WT is the final value from investing wealth W.
a) Find the Certainty Equivalent of the investment for such utility as a function of probability p and invested wealth W. How does it depend on p? Comment on your result.b) Compute the Certainty Equivalent for a probability p=50%.c) Compute the Risk Premium for a probability p=50%.d) What is the risk premium if p=0? And if p=1? Comment on your results, and show how the risk premium is a non-monotonic function of probability p.e) Find the probability  P that maximises the risk premium (for this it may 

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