Oskar's preferences over gambles in which the probability of events 1 and 2 are both 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 out what Oskar's preference is, we need to calculate the expected utility of the gamble and compare it to the expected utility of a certain income. Let's start by finding the expected utility of the given gamble.

Expected utility of the gamble:

EU(gamble) = .5u(9) + .5u(25)
EU(gamble) = .5(9)^(.5) + .5(25)^(.5)
EU(gamble) = 1.5 + 2.5
EU(gamble) = 4

Now let's compare this to the utility of a certain income. To find out what that income is, we need to solve for y in the utility function.

.5u(y) + .5u(y) = 4
u(y) = 4
y = 16

So the income that would be as good for Oskar as the given gamble is $16. Therefore, the answer is C) $16.

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