Oskar's preferences over gambles in which the probability of events 1 and 2 are both 1/2 can be represented by the von Neuman-Morgenstern utility function .5y^.5₁ + .5y^.5₂, where y₁ is his consumption if event 1 happens and y₂ is his consumption if event 2 happens.A gamble that allows him a consumption of $9 if event 1 happens and $25 if event 2 happens is exactly as good for Oskar as being sure to have an income of A)$12.5. B)$9. C)$16. D)$17. E)None of the above.

Question

Quizplus · Accepted Answer

To find the answer, we need to set up two equations based on the given information. Let x be the consumption level that Oskar is indifferent between and solve for x:
0.5yU($9) + 0.5yU($25) = U(x)
0.5 + 0.5($16/x) = $15/x
Solving for x yields x=$16, so Oskar is indifferent between the gamble and an income of $16. Therefore, the answer is choice C, $16.

Oskar's Preferences Over Gambles in Which the Probability of Events