Paul has a utility function of U =[ i to the power 1/2] with income measured in thousands. He will get a job that either pays 25 thousand a year or 64 thousand a year. What is his expected utility, expected payoff, the utility of his expected payoff, and her risk premium? Additionally, plot Paul's utility and income. Show and label his utility curve, his expected utility, and risk premium. Note: Please solve only the bolded part of the question. The previous part was already answered

Paul has a utility function of U =[ i to the power 1/2] with income measured in thousands. He will get a job that either pays 25 thousand a year or 64 thousand a year. What is his expected utility, expected payoff, the utility of his expected payoff, and her risk premium? Additionally, plot Paul's utility and income. Show and label his utility curve, his expected utility, and risk premium. Note: Please solve only the bolded part of the question. The previous part was already answered

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.2P

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Paul has a utility function of U =[ i to the power 1/2] with income measured in thousands. He will get a job that either pays 25 thousand a year or 64 thousand a year. What is his expected utility, expected payoff, the utility of his expected payoff, and her risk premium? Additionally, plot Paul's utility and income. Show and label his utility curve, his expected utility, and risk premium.
Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why? I would like help with the unanswered last parts of the questions.
Suppose that Mira has a utility function given by U=2I+10√I. She is considering two job opportunities. The first job pays a salary of $40,000 for sure. The second job pays a base salary of $20,000 but offers the possibility of a $40,000 bonus on top of your base salary. She believes that there is a probability of p=0.50 that she will earn the bonus. What is the expected salary of the second job? Which offer gives Mira a higher expected utility? Based on this information, is Mira risk adverse, risk neutral, or risk-loving?
Natasha has utility function u(I) = (10*I)0.5, where I is her annual income (in thousands). (a) Is she a risk loving, risk averse or risk neutral individual? She is [risk loving, risk adverse, risk neutral] , as her utility function is [concave, convex, linear] (b) Suppose that she is currently earning an income of $40,000 (I = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. She should [take, not take] the new job because her expected utility of (approximately) [18.27,19.82,20,20.95,21.14] is [greater than, less than, equal to] her current utility of [18.27,19.85,20,20.95,21.14] .
A Risk Lover prefers the expected utility of wealth to the utility of the expected value of wealth. It is because a risk lover has a convex utility function It is because a risk lover has a concave utility function
Angie owns an endive farm that will be worth $90,000 or $0 with equal probability. Her Bernouilli utility function is u(w) =√w, where w is her wealth level (sum of initial wealth and the worth of the endive farm). 1. Suppose her firm is the only asset she has, that is, she has no initial wealth. What is the lowest price P at which she will agree to sell her endive farm before she knows how much it will be worth? 2. Redo part (1) assuming that she has $160,000 in her bank safe. 3. Compare and discuss your results in parts (1) and (2). What relationship can you find between Angie’s initial wealth level (zero versus $160,000) and her risk aversion?
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An investor has a power utility function with a coefficient of relative risk aversion of 3. Compare the utility that the investor would receive from a certain income of £2 with that generated by a lottery having equally likely outcomes of £1 and £3. Calculate the certain level of income which, for an investor with preferences as above, would generate identical expected utility to the lottery described. How much of the original certain income of £2 the investor would be willing to pay to avoid the lottery? Detail the calculations and carefully explain your answer.
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Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. a. b. c. d. Graph Jamal’s utility function. Is he risk averse? Explain. (2+2) Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why?
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