Consider a risk averse individual who has utility function u(a) which is

increasing with u(0) = 0. There is one safe asset which gives $1 for every dollar invested. There

are two risky assets: A,B. For A, every dollar invested gives return $0 with probability 4/5 and

$3 with probability 1/5. For B, every dollar invested gives return is $0 with probability 2/3 and

$3 with probability 1/3.

The individual has $60 to invest. Out of $60, the individual must invest $30 in the safe asset and

the remaining $30 can be invested in risky assets. Consider two investment choices: (1) invest

entire $30 in A and (2) invest $15 in A, $15 in B.

(a) [3 points] Drawing diagram of the utility function and showing your work, determine the

expected utility of the individual from choice 1.

(b) [3 points] Drawing diagram of the utility function and showing your work, determine the

expected utility of the individual from choice 2 when return from A is bad.

(c) [3 points] Drawing diagram of the utility function and showing your work, determine the

expected utility of the individual from choice 2 when return from A is good.

(d) [3 points] Drawing diagram of the utility function and showing your work, determine the

expected utility of the individual from choice 2.

(e) [2 points] Comparing expected utility from choices 1,2 in a diagram, determine which choice

is better.