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- Define risk aversion and give an example of a risk-averse person?4. You wish to hire Ricky to manage your Dallas operations. The profits from the operations depend partially on how hard Ricky works, as follows. Probabilities Profit $10,000 Profit= $50,000 Lazy worker 40% 60% 20% Hard worker 80% If Ricky is lazy, he will surf the Internet all day, and he views this as a zero cost opportunity. However, Ricky would view working hard as a "personal cost" valued at $1,000. What fixed percentage of the profits should you offer Ricky? Assume Ricky only cares about his expected payment less any "personal cost."3. Suppose that Jon Snow's utility function is given by U(I)=501 where I represents annual income in thousands of dollars. a. Is Jon risk loving, risk neutral, or risk averse? Explain b. Suppose that Jon is currently earning an income of $1000 and can earn that income next year with certainty. He is offered a chance to take a new night watch job that offers a 0.25 probability of earning $2000 and a 0.75 probability of earning $500. Should he take the new night watch job?
- 2. Ronald has $18,000. But he is forced to bet it on the flip of a fair coin. If he wins he has $36,000. If he loses he has nothing. Ronald's expected utility function is 0.5x0.5 + 0.5y0.5, where x is his wealth if heads comes up and y is his wealth if tails comes up. What safe income would make him exactly as well off as this bet?1. A person with U(w) = w² is facing the following lottery: there are four tickets sold, or which only one wins the prize of $100. a. Calculate the expected value of the lottery. b. Calculate the certainty equivalent. c. Comparing parts (a) and (b), what is this person's risk preference and why?ease use utility of wealth function in the booK, 8-1 (see below). Certainty Utility B D 200 198 194 D' Total utility 170 of wealth C' Expected Utility A 140 10,000 15,000 19,000 20,000 Wealth FIGURE 8-1 Total Utility of Wealth and the Impact of Insurance Please explain the difference between the certainty utility line and the expected utility line b. Calculate your E(U), given an 80% change of being healthy and 20% of being sick, knowing that your income falls to $10,000 and your utility is 140 if you get sick. Calculate your E(W), given an 80% change of being healthy and 20% of being sick. d. Given that your Certainty Utility Function is U = 200Y-0.00154 and Y is your income, what is your Certainty Utility with insurance (if you are risk averse) What insurance premium will you pay to guarantee a utility of 197? Please provide a calculation.
- Sarah has a coefficient of risk aversion of 2. Sheng has a coefficient of risk aversion of 4. Given their risk preferences, we do not expect that... Select one: a. The indifference curves of Sheng are steeper than those of Sarah. b. Sheng holds a higher weight of the risky assets than Sarah does. c. None of the options provided. d. Sarah and Sheng hold the same risky assets in their portfolios.The chief executive officer of a publishing company says she is indifferentbetween the certainty of receiving $7,500 and a gamble where there is a 0.5 chance of receiving $5,000 and a 0.5 chance of receiving $10,000. a). Does she seem to be a risk averter, a risk lover, or risk- neutral? Explain. b). What is the coefficient of variation of the risky option (gamble)?4. Kate has von Neumann-Morgenstern utility function U(x1,x2) = m7. She currently has $2025. a. Would she be willing to undertake a gamble that involves a gain $2875 with probability + and a loss of $1125 with probability ? Show your work and explain your answer. b. Would she be willing to undertake a gamble that involves a gain $2599 with probability and a loss of $800 with probability ? Show your work and explain your answer.