4|Problem Set 3 Question Due Probability, Risk and Uncertainty (10 Marks) Copy the diagram beiow representing Investor Ian's risk preferences: Utility (a) (h) (C) (d) (1") Income Assume Investor Ian currently has $40,000 of which he has to invest $20,000 in a company with a 50% probability of doubling the $20,000 and a 50% probability of losing the $20,000. What is Investor Ian's total expected income after making the investment [including the $20,000 he does not invest)? (1 mark) On your diagram, show Investor Ian's expected utility from his expected income identied in (a) above. (2 marks) Assume Investor Inn is offered the opportunity to invest in two companies rather than one. Of his $40,000 assume Investor Ian puts $10,000 into company A and $10,000 in company B. Both companies have a 50% chance ofdoubling his money and a 50% chance of losing his money. What is Investor Ian's expected income after making the investment (including the $20,000 he does not invest)? (1 mark) On your diagram in (b) above, show Investor Ian's expected utility from his expected income identified in (c) above. (3 marks) Would Investor Ian prefer the investment in (a) above, the investment in (c) above, or would he be indifferent between the two? Explain why, and also explain the cause of any difference in utility between the investments in (a) and (c) above. (2 marks) Explain how you can tell Investor Ian's risk preferences are risk averse. (1 mark)