Consider a risk averse individual who has utility function u(a) which is increasing with u(0) = 0. There are two risky assets: A,B. For A, every dollar invested gives return $0 with probability 1/3 and $3 with probability 2/3. For B, every dollar invested gives return is $0 with probability 1/4 and $3 with probability 3/4.

The individual has $120 to invest. Consider two investment choices: (1) invest entire $120 in A and (2) invest $60 in A, $60 in B.

(a) Drawing a diagram of the utility function and showing your work, determine the expected utility of the individual from choice 1.

(b) Drawing a 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)Drawing a 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)  Drawing a diagram of the utility function and showing your work, determine the expected utility of the individual from choice 2.

(e) Comparing expected utility from choice 1,2 in a diagram, determine which choice is better.