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 a return of $0 with a probability of 1/3 and $3 with a probability of 2/3. For B, every dollar invested gives a return is $0 with a probability of 1/4 and $3 with a probability of 3/4. The individual has $120 to invest. Consider two investment choices: (1) invest an entire $120 in A and (2) invest $60 in A, $60 in B.

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

(b) Draw the diagram of the utility function and show your work, determine the expected utility of the individual from choice 2 when return from A is bad.

(c) Draw a diagram of the utility function and show your work, determine the expected utility of the individual from choice 2 when return from A is good.

(d) Draw a diagram of the utility function and show your work, determine the expected utility of the individual from choice 2.

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