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

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 $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

Quizplus · Accepted Answer

To find the smallest value of x that would make Buck indifferent between investing in the palace and having a wealth of $24,000 with certainty, we need to set up the expected utility equation and solve for x:

Expected Utility of Investing in Palace = Expected Utility of Having $24,000 with Certainty

0.8(1 - (11e^(-0.000025x))) + 0.2(1 - (11e^(-0.00075(6000)))) = 1 - (11e^(-0.000025(24000)))

Solving for x, we get:

x = $96,000

Therefore, the smallest value of x that would make Buck want to invest in the pinball palace rather than have a wealth of $24,000 with certainty is $96,000.

So, the answer is C.

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