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?

Question

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?

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The Answer of 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?

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