Ski Utility

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Posted by admin | Posted in Parts And Stuff | Posted on 23-09-2010

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Ski Utility

Ski Utility
Help with this economics expected utility problem?

BJ is planning a skiing trip to Big Sky Montana. The utility from the trip is a function of how much she spends (y) and is given by U(y) = log y. BJ has $10,000 to spend on the trip. If she spends it all, her utility will be U(10,000) = log 10,000 = 4. (Note: we are using logarithms to base 10).
(a)If there is a 25% probability that BJ will lose $1,000 of her cash on the trip, what is the trip’s expected utility?
(b)Suppose BJ can buy insurance against losing the $1,000 at an actuarially fair premium of $250. Will BJ buy the insurance?
(c)What is the maximum amount that BJ would be willing to pay to insure her $1,000.
(d)Suppose that people who buy insurance tend to become more careless with their cash than those that don’t, and assume that the probability of their losing $1,000 is 30%. What will be the actuarially fair insurance premium? Will BJ buy insurance at the actuarially fair price?

Don't have a calculator handy, so I'll trust you to do it:

a) .75*log(10000) + .25*log(9000)

b) you need to compare the answer in a to log(9750). If log(9750) is greater than the answer from a, BJ will buy the insurance. Otherwise, he will not.

c) Calculate the value of x in the equation: .75*log(10000)+.25*log(9000)=log(10000-x)

d) In the case of moral hazard, the actuarially fair premium is $300 (.3*1000+.7*0). Will he buy it at this price? Compare $300 to your answer from c. If $300 is greater than your answer from c, then he will not. If your answer from c is greater than $300, then he will.

Ski-Doo 2011 Sport-Utility Sleds: Skandic, Tundra, Tundra Xtreme