Buck Columbus Is Thinking of Starting a Pinball Palace near a Large

Multiple Choice

Buck Columbus is thinking of starting a pinball palace near a large Midwestern university. Buck is an expected utility maximizer with a von Neuman-Morgenstern utility function, U(W) = 1 - ( ) , where W is his wealth. Buck's total wealth is $12,000. With probability .2 the palace will be a failure and he'll lose $9,000, so that his wealth will be just $3,000. With probability .8 it will succeed and his wealth will grow to $x. What is the smallest value of x that would be sufficient to make Buck want to invest in the pinball palace rather than have a wealth of $12,000 with certainty?

A) $75,000
B) $14,250
C) $36,000
D) $48,000
E) $15,000