Question:

Sir James is very passionate about music. He has recently bought from a famous manufacturer in Palo Alto a beautiful lebanon clarinet, which has a value of 999 dollars. He is a bit worried since the probability p that musical instruments get stolen in California is 10%. If the instrument gets stolen, its value drops to zero. Sir James’s utility function takes the following form:

\(U\left( x \right)=\ln \left( x+1 \right)\)

where x is the value of the good (in this case, the clarinet). Notice that ln corresponds to the natural logarithm.

1. Derive analytically the two possible outcomes of the risky bundle, its expected value EV , its expected utility EU, its certainty equivalent CE, the utility of the expected value U(EV ), and the risk premium RP (round the results to one decimal).
2. Draw on a carefully labeled graph EV,EU,CE,U(EV ),RP.
3. State whether Sir James is risk averse, risk loving or risk neutral and explain why.
4. Sir James gathers some information on how to protect his new clarinet. He finds out that, for $600, he can buy a full insurance. Is Sir James willing to pay for such insurance? Why?
5. Molloy, a notorious cat burglar, makes his appearance in Palo Alto. The probability of theft rises to p = 20%. Will Sir James buy the insurance now? Why?
6. What is the maximum premium ! that Sir James is willing to pay to obtain full insurance? Answer this question for both scenarios, the one where the probability of theft is 10% and the one where the probability increases to 20%.

Price: $2.99

Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document