
Economics Preferences
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 riskpremium.
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 riskpremium.
Thanks for all the help in advance.

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, ...
a)
EU(Job)=0.99U(42,000)+0.01U(0)=0.99*42,000^0.5+0.0 1*0^0.5=202.89
EU(Firm)=0.7*40,000^0.5+0.2*80,000^0.5=196.57
He prefers the job.
b)
EU(Pepsi)=salary^0.5=196.57
salary=196.57^2=$38,639,19
c)
EU(Job)=.99*42,000^2=1.7B (approx)
EU(Firm)=.7*40,000^2+.2*80,000^2=2.4B (approx)
U"(I)=2 Function is convex therefore John is a riskseeker.