Vhat is the behavior of a person with the following utility function? 1 0.8 0.6 5 0.4 0.2 $0 $50 $100 $150 $200 Wealth a) Risk-averse. b) Risk-seeking. c) Risk-seeking up to $100 wealth, then risk-averse after $100. d) Risk-averse up to $100 wealth, then risk-seeking after $100. e) Risk-neutral. Utility
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- Sanjay won a poker game against his friends. Now he has to choose between $600 (the winnings) and the chance to play a new game. In this new game, Sanjay has a 50% chance of winning nothing and a 50% chance of winning $1000. The following graph presents the utility function of Sanjay with respect to money: 1. By how much money would his winnings need to increase or decrease so that Sanjay isindifferent between the $600 and the new game? At a different table, Juan wins $800 in a blackjack game. Similarly, he has to choose between $800 or the chance to win a new game. In this game, Juan has a 45% chance of winning nothing and a 55% chance of winning $1000. The following graph presents the utility function of Juan with respect to money: 2. By how much money would his winnings need to increase or decrease so that Juan is indifferent between the $800 and the new game? Please enter a positive number for an increase or a negative number for a decrease.35. Your current disposable income is $10,000. There is a 10% chance you will get in a serious car accident, incurring damage of $1,900. (There is a 90% chance that nothing will happen.) Your utility function is U = √√T, where I is income. If this policy is priced at $40, what is the change in your expected utility if you purchase the policy rather than no insurance? b) 0.8 c) 0.2 d) 04. Show how to construct the reference dependent utility function for two friends Kate and Mary whose gains and losses are listed as follows : Kate's net worth is $ 4.5 million ( decreased from $ 5.5 to $ 4.5 million ) Mary's net worth $ 3.2 million ( increased from $ 3 to $ 3.2 million ) ( First determine the reference point ( use a parameter ) and then derive reference utility function for each ) .
- 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)1. Rosie has just written a book. Assume that her preferences are consistent with expected utility theory. There is 30% chance that her book will be a best-seller and make $500,000 in profit (after the costs of production) and a 70% chance it will just break even (i.e. no profit after the costs of production). Her current income is $150,000 (which she will receive regardless of what happens with her book) and her utility function is u (I) = ln (I) (a) Is Rosie risk-averse, risk-neutral, or risk-loving? How do you know? (b) Assume that Rosie will receive all of the profits (if any) from her book. Draw a diagram illustrating (i) Rosie's total income if her book just breaks even, (ii) her total income if her book is a best-seller, (iii) her expected income, (iv) her expected utility, (v) her certainty equivalent, and (vi) her risk premium. (c) Compute the numerical values associated with each of the six amounts you found in (b). (d) Acme Publishing Company has offered Rosie $100,000 for…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.
- 2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.If Kelly is first given $1000, she strictly prefers lottery A=$500 over lottery B=($0,0.5; $1000,0.5). If Kelly is instead first given $2000, she strictly prefers lottery C=($0,0.5; -$1000,0.5) over lottery D=-$500 a. Briefly explain why Kelly's preference are inconsistent with expected utility maximization. b. Briefly describe how Prospect Theory can resolve this paradox c. Are Kelly's attitudes toward risk consistent with the attitudes toward risk K&T propose when there is a reasonable chance of winning/losing? Briefly explain5. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) = √√x. There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. b) What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?
- Oliver takes $2500 with him to a camp and there is 50% chance he will lose $900 on his way. Suppose Oliver can buy an insurance policy that will totally cover his loss, what maximal amount will he be willing to pay for such insurance? Oliver’s utility function is given by the function U(E) = E0.5 where E is the amount that he spends on the camp without any saving. a. $325 b. $475 c. $650 d. $535Scenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function (sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 Suppose that insurance companies do not know specific probabilities of adverse events for Tess or Lex, but do know the average probability of an adverse event. If they assumed that both Tess and Lex purchase full insurance, what is the actuarially fair premium charged? Round to two decimal places6. Joe and Sam wish to complete the Auckland marathon. They each have the following two options: (a) training for the marathon at time 1 (utility=0) and completing the marathon at time 2 (utility=16); and (b) going to the beach at time 1 (utility=8} and not completing the marathon at time 2 (utility=0). a. Joe discounts the future exponentially. His & =3/4. 1. From the point of view of time 0: What is his utility of a? What is his utility of b? it. From the point of view of time 1: What is his utility of a? What is his utility of b? b. Sam discounts the future hyperbolically. His B=1/4 and his 6 = 1. i. From the point of view of time 0: What is his utility of a? What is his utility of b? ii. From the point of view of time 1: What is his utility of a? What is his utility of b? C. Who will not complete the marathon? Why? d. Who will complete the marathon? Why?