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 $24,000. With probability .2 the palace will be a failure and he'll lose $18,000, so that his wealth will be just $6,000. 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 $24,000 with certainty?

A) $28,500
B) $150,000
C) $96,000
D) $72,000
E) $30,000