Hey can someone help me on the following questions please.
After graduating, John receives a job offer which pays 42000/year. He knows that their is 1% chance the comapny might go bankrupt. Alternatively, he is thinking of opening his own firm with predicted net payoffs:
Probability 0.1 Value After 1 Year 0
Probability 0.7 Value After 1 Year 40000
Probability 0.2 Value After 1 Year 80000
a) John's utility function is U(I) = sq. root ( I ). Which occupation would he prefer?
b)Assume that John decided in favour of starting his firm. However, just before starting John is offered a position at Pepsi with a fixed salary. John's utility function is U(I) = sq. root (I) . Calculalte the fixed salary that makes John indifferent between starting his own firm and taking Pepsi's job offer. Calculate John's risk-premium.
c) How would your preferences from part a) change if John's utility was represented by U(I) = I^2. Show mathematically. What is the economic intuition behind the new risk-premium.
Thanks for all the help in advance.
Mar 14th 2010, 03:31 PM
I hope this will still be useful to you.
Expected utility takes the form of EU(.)=p1*u(c1)+p2*u(c2)... where p are the probability of states c1, c2, ...
He prefers the job.
U"(I)=2 Function is convex therefore John is a risk-seeker.