Thread: 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 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.

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 risk-seeker.