Answer
a) Please see the graph. Jamal isn't risk averse since the utility curve goes the same direction as the marginal utility curve.
b) Option B has the higher expected prize (4.2 million dollars, compared to Option A's expected prize of 4 million dollars).
c) Option B offers a higher expected utility.
d) If Jamal is a utility maximizing person, option B should be chosen (as that option offers the higher expected utility).
Work Step by Step
b)
Option A offers 4 million dollars for sure, so 4 million is the expected value.
Option B offers 1 million dollars with a 60% chance and 9 million dollars with a 40% chance.
$X = 1*.6 + 9*.4$
$X = .6 + 3.6$
$X = 4.2$
Option B's expected value is 4.2 million dollars.
c)
$U = W^{1/2}$
Option A
$U = 4000000^{1/2}$
$U = \sqrt {4000000}$
$U = 2000$
Option B
$U = 4200000^{1/2}$
$U = \sqrt {4200000}$
$U = 100*\sqrt {420}$
$U = 100*20.49$
$U = 2049$
d)
$U = W^{1/2}$
1 million dollars is awarded
$U = W^{1/2}$
$U = 1000000^{1/2}$
$U = 1000$
9 million dollars is awarded
$U = W^{1/2}$
$U = 9000000^{1/2}$
$U = 3000$
