[Problem Set 3 Question One Probability, Risk and Uncertainty (10 Marks) Copy the diagram beiow representing Investor Ian 's risk preferences: Utility Income (a) (h) (C) (d) (9) (0 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 identified 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) Copy the diagram below for Fred into your answer book: Utility U1 $401100 Income (a) What does the curved line drawn on the axis represent? Explain why the line is shaped the way it is. (2 marks) Assume there is a 50% chance that Fred will become ill, and require an operation costing $20,000. He currently has an income of $40, 000. (b) Show on your diagram F red's expected income and associated utility in this uncertain situation. (2 marks) (C) Show on your diagram the utility Fred would receive if he was able to take out 'fair' insurance against becoming ill. (1 mark} ((1) Explain what 'fair' insurance is, and how the fair insurance would be calculated in the example above. (2 marks) (e) On your diagram, show the amount that Fred would be prepared to pay to take out insurance. (You can use an estimate of the dollar amount for the premium, it doesn't have to be exact so long as you have drawn it correctly). Be sure to state the premium Fred would be prepared to pay. (2 marks) (f) Explain why insurance companies don't charge a 'fair premium'. (1 mark}