Ken Jennings has just been offered a job with a start-up company. The job pays $30,000 guaranteed per year. On top of that that there is a ½ probability that he can get a $50000 performance bonus making a total of $80,000. Ken, operates under the assumptions of expected utility theory and in general, has a strong preference for a job that pays a fixed amount per year. Ken's utility of wealth function is given by U(W) = $\surd$W. (U(W) is equal to the Square Root of W). Based on this information, you would conclude that:
A) Ken will be willing to accept any job that pays approximately $52,000 per year or higher.
B) Ken will be willing to accept any job that pays approximately $30,000 per year or higher.
C) Ken will be willing to accept a job that pays $50,000 per year.
D) Ken will be willing to accept a job that provides him with 200 utils of utility or less.

Question

Quizplus · Accepted Answer

CKen's expected wealth from the start-up job is $30,000 + 0.5 * $50,000 = $55,000. The utility of this expected wealth is the square root of $55,000, which is approximately 234.5 utils. A job that pays $52,000 per year would give him a utility of the square root of $52,000, which is approximately 228 utils, less than the utility from the start-up job but still desirable. A job that pays $50,000 per year would give him a utility of the square root of $50,000, which is approximately 223.6 utils, also less than the utility from the start-up job but desirable. Choices B and D do not directly relate to the calculation of utility based on his utility function and the given scenario.

Ken Jennings Has Just Been Offered a Job with a Start-Up