Results 1 to 2 of 2

Math Help - Economics- Preferences

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    19

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie CaesarXXIV's Avatar
    Joined
    Mar 2010
    Posts
    5
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Economics
    Posted in the Business Math Forum
    Replies: 4
    Last Post: October 26th 2010, 11:08 PM
  2. Economics
    Posted in the Business Math Forum
    Replies: 5
    Last Post: October 14th 2010, 08:34 AM
  3. Transitive preferences in a circular order
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 9th 2010, 09:11 AM
  4. economics
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: May 14th 2009, 07:33 PM
  5. economics
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: May 14th 2009, 06:05 AM

Search Tags


/mathhelpforum @mathhelpforum