Danielle has the following VonNeumannMorgenstern utility fun

Danielle has the following VonNeumann-Morgenstern utility function with v(c)=pc. (i.e. If there are only two possible states of the world with probabilities L and H and consumption levels cL and cH; expected utility will be LpcL +HpcH) She is a soccer player. If she does not get injured she will get 40000 dollars per month to play. There is a 20% chance she may be injured and only make 1600 dollars per month instead.

(a) What is her expected consumption?

(b) Someone o§ers her a coaching job where she will get 10000 dollars a month without any risk of injury. Will she accept this job?

(c) She is thinking about buying insurance against injury. What is the fair price for her insurance and how much insurance will she buy at this fair price?

Solution

a)

40000 * 0.80 + 0.20 * 1600

3520

(b) Someone o§ers her a coaching job where she will get 10000 dollars a month without any risk of injury. Will she accept this job?

yes, because the expected value for the other job is $3520 is less than $10000