6. Suppose that Betty (a risk averse individual) has income of 100 . She has the opportunity to purchase ONE share of stock in Alpha Co. The share will be worth either $100 or $0 and the values are equally likely. a) What is the expected value of the stock? If the price of the stock is equal to its expected value then will Betty purchase it? Illustrate your answer in an expected utility diagram. Suppose that Betty is willing to pay a maximum of $40 for the share in Alpha Co. b) What is Betty's expected income if she purchases the stock at price X ? c) In a new expected utility diagram, illustrate Betty's expected utility when she does not purchase the stock and when she does purchase the stock at price $40. d) What is the risk premium associated with buying one share at $40 ? Illustrate it in your diagram. Suppose that Betty has the opportunity to purchase stock in a second company, the Omega Co. The stock in Omega will be worth either $200 or $0. The likelihood of the $200 valuation is .25 and the likelihood that it is worthless is .75 . e) Show that the expected value of Omega stock is the same as the expected value of Alpha stock. f) Show in your diagram above that Betty will NOT be willing to pay $40 for the stock in Omega company. Will she be willing to pay more or less for Omega company? g) Let Y be the maximum price that she will pay for stock in Omega company. In a new diagram illustrate the relationship between her expected utility from 1) purchasing no shares; 2 ) purchasing one share in Alpha at price $40 and; 3) purchasing one share in Omega at price Y. h) What is the relationship between the risk premia of Alpha and Omega company? i) We can define the expected return on an asset as the difference between the (expected value of the asset and its purchase price) divided by its purchase price. Which of the two assets has a higher expected return