Nelson has a utility function given by U = y0.5. Suppose that Nelson is offered a job that will pay 100 with probability 0.6 and 225 with probability 0.4. a.The expected value of Nelson's income is 12. b.Nelson's expected utility is 12. c.Nelson is risk neutral. d.b. and c. e.None of the above.
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- Bob earn 60,000 a year and an accounting firm each year he receives Reyes Bob has determined that the probability that he receives a 10% raise is .7 the probability that he earns a 3% raise is .2 and the probability that he earns a 2% raise is .1 a competing company has offered Bob a similar position for 65,000 a year Bob wonders if he should take the new job or take his chances with his current job. a. Find the mathematical expectation of the dollar amount of his raise at his current job b.Suppose that Mary has a utility function U(W) W power of 0.5. Her only asset is the shares in the start-up e-com company. Next week she will learn the stock's value. She believes that it is worth $225 with the probability 1/3, $196 with the probability 1/2 and $144 with the probability 1/6. Write down the prospect and calculate the expected value and her expected utility.The manager of XYZ Company is introducing a new product that will yield N$1000 in profits if the economy does not go into a recession. However, if a recession occurs, demand for normal good will fall so sharply that the company will lose N$4000. If economists project that there is a 10 percent chance the economy will go into a recession, what are the expected profits to XYZ Company of introducing the new product? How risky is the introduction of the new product?
- 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)?Both jobs provide base salary and commissions. Base salary is garunteed But the probability of getting the commissions is 50% every month Job 1 base salary is 1k but commission is 3k Job 2 base salary is 2k but commission is 1k A) Calculate the expected value for both jobs. b.whats the standard deviation for both jobs. C) Use utility-income diagram to show if the applicant is risk-averse, which job should he accept and why.Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)
- Economics Yuki has a utility function given by u(x) = In(x). She faces a gamble that pays 10 with probability 0.5 and 15 with probability 0.5. Comment on how Yuki's certainty equivalent relative to the expected value varies as her utility function goes from concave from convex.Johnny is "paid" by his parents $2o if he gets a grade A, $10 if he gets a grade B, whereas he has to pay his parents back $5 if he gets a grade other than A or B. On average 20% of the grades he gets are A, and 30% are grades B. What is the expected value of what he "earns" per grade ? What is the expected value of what he "earns" at school weekly if on average he gets five grades a week ? How long should Jim save until he collects enough money to buy a pair of brand new Hi-Fi headphones that cost $225?Jamal has a utility function 1/2 U W5 , where W is hiswealth in millions of dollars and U is the utility heobtains from that wealth. In the final stage of agame show, the host offers Jamal a choice between(A) $4 million for sure and (B) a gamble that pays$1 million with probability 0.6 and $9 million withprobability 0.4.a. Graph Jamal’s utility function. Is he risk averse?Explain.b. Does A or B offer Jamal the higher expectedprize? Explain your reasoning with appropriatecalculations. (Hint: The expected value of arandom variable is the weighted average of thepossible outcomes, where the probabilities arethe weights.)c. Does A or B offer Jamal the higher expectedutility? Again, show your calculations.d. Should Jamal pick A or B? Why?
- Charles is participating in an experiment. His payoff in the experiment is tied to his effort e doing a mundane task. There is also some risk involved by design-there is a chance p that Charles is going to get a fixed payment L regardless of his effort. Charles' payoff is thus: with probability p w.e with probability 1- p Charles has to pay a cost C, which increases with his effort. First, let us assume that Charles' utility is the expected payoff net of this cost: U(e) = pL + (1 – p)we – c(e) Derive the first order condition with respect to e. b. How doesp affect Charles' effort e? c. How does L affect e?a) Explain what is meant by risk aversion, and illustrate with the help of a figure out what we mean by the term "risk premium". Suppose Donald runs hotels and casinos, which makes one very insecure income. With probability 1 the income becomes 100 and with probability 1 the 64th Donald's expected income is thus equal to 82. Further assume that the utility to Donald is a a function of income, and that it is given by U (x) = 2x 12 x is the income level. b) Calculate Donald's expected utility.Consider Bob's decision problem: Sunny Cloudy Rainy Beach 2 3 2 Park 3 3 2 Mall -1 1 x Suppose the probability of Sunny is 0.25, the probability of Cloudy is 0.25, and the probability of Rainy is 0.5. What is the smallest value of x for which Mall is an expected utility maximiser? Round your answer to one decimal place (e.g. 0.5).
