Vivien has just graduated from SSB and plans to run her own business for one year. Her preferences are described by this utility function: U(I) = I 0.5 , where I is her income. Vivien considers these two opportunities: A: to open a spa on Princess Street, which requires an investment of $10; B: to open a small Greek restaurant in downtown Ottawa, which requires an investment of $8. Vivien has no savings but her dad offers to lend her money for the up-front investment (the money will be repaid with zero interest after income has been generated). Vivien will donate her business to a local charity after a one year. She has the following beliefs about her prospective income for each alternative: A: Spa B: Restaurant Income Probability Income Probability $15 10% $8 15% $20 25% $21 70% $25 65% $38 15% (a) (2 points) Which business opportunity will provide Vivien with higher expected income? Calculate Viviens expected income for each business opportunity. (b) (2 points) Which business opportunity will Vivien choose? (c) (3 points) How does your answer in (b) compare of that in (a) and why? Provide an intuitive explanation. (d) (4 points) Viviens mom, who runs a small but very successful trading company, wants to employ Vivian for a fixed salary. What minimum salary S she must offer Vivien so that Vivien chooses the safe job with her mom instead of starting her own business? What is Vivians risk premium? (e) (4 points) Immediately after opening, Vivien is told that two prospective buyers, Ms. Smith and Mr. Jones, are interested in purchasing the spa. Smith has constant marginal utility of income, and Jones has increasing marginal utility of income. Vivien knows that if she bargains with either Smith or Jones, the negotiated price will be half way between her minimum price and the buyers maximum price. Assuming Vivien wants to sell the spa, which prospective buyer should she negotiate with? Carefully explain your reasoning