Are the following preferences consistent with von Neumann Morgenstern’s axioms to maximize expected utility? Explain. a. You would rather have a sure $200 to a gamble with p=0.7 chance of $200, p=0.1 chance of $50, p=0.2 chance of $300. b. You prefer the gamble of p=2/3 chance of $300 and p=1/3 chance of $50 than a sure $250 win.
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Are the following preferences consistent with von Neumann Morgenstern’s axioms to maximize expected utility? Explain.
a. You would rather have a sure $200 to a gamble with p=0.7 chance of $200, p=0.1 chance of $50, p=0.2 chance of $300.
b. You prefer the gamble of p=2/3 chance of $300 and p=1/3 chance of $50 than a sure $250 win.
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- Consider the following prospects – A: (0.5, 0, 0.5: $100, $60, $10) B: (0, 0.9, 0.1: $100, $60, $10) C: (0.2, 0.5, 0.3: $100, $60, $10) D: (0.4, 0.2, 0.4: $100, $60, $10) Show that D>A>B>C is consistent with expected utility theory and that this preference ordering implies “risk-loving” preferences. Show that C>B>D>A is consistent with the expected utility theory.A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and if it does not. Assume that the Bernoulli utility function takes the form u(x) = with r > 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA? Alex plays football for a local club in Kumasi. If he does not suffer any injury by the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coach worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = Assume he could buy insurance at price P that could pay $9,900 in case of injury. What is the highest value of P that makes it worthwhile for Alex to purchase insurance? What is the certainty…Suppose that you graduate from college next year and you have two career options: 1) You will start a job in an investment bank paying a $100,000 annual salary. 2) You will start a Ph.D. in economics and, as a student, you will receive a $20,000 salary. You are bad with decisions, so you are letting a friend of yours decide for you by flipping a coin. The probabilities of options 1 and 2 are, therefore, each 50%. a) Illustrate, using indifference curves, your preferences regarding consumption choices in the two different states of the world. Assume that you are risk-averse. [Include also the 45 degrees line in your figure] b) Now show how the indifference curves would change if you were substantially more risk averse than before. Explain. c) Now show the indifference curves if you are risk neutral and if you are risk loving. d) Show your expected utility preferences from point a) mathematically.
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- Jacob is considering buying hurricane insurance. Currently, without insurance, he has a wealth of $80,000. A hurricane ripping through his home will reduce his wealth by $60,000. The chance of this happening is 1%. An insurance company will offer to compensate Jacob for 80% of the damage that any tornado imposes, provided he pays a premium. Jacob’s utility function for wealth is given by U(w) = In (w). (A) What is the maximum amount Jacob is willing to pay for this insurance? Show work and explain.Amy's utility depends upon her income, w. Her utility function is √w. She receives a prize that depends on the roll of a dice. If she rolls a 3 or 4 or 6, she will receive $400. Otherwise, if she rolls a 1 or 2 or 5, she will receive $100.1. What is the expected payoff from this prize? 2. What is the expected utility from this prize?3. What is the minimum payment that Amy will accept to forego the roll of the dice?. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . 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.
- 1 Consider an individual for whom utility is U = ln(I) There are two states of the world (G,B): Outcome G = 2000 with probability .4 Outcome B = 1000 with probability .6 W1 = 2000 L = 1000 π = .6 Option = invest $50 to lower π to .2 An insurance company is willing to offer a contract in which the individual pays a premium and gets full compensation for the loss (1000) in the bad state. a) With no insurance but the option of investing the $50, what is the utility of the individual? b) What is the first-best outcome for utility of the individual, insurance premium, and profits of the insurance company?Roger's utility/u as a function of wealth/w is u = { ln w, w < 1600 w1/2, w >= 1600 Roger has $1000 and 3 options. 1. spend $400 to enter the game with probabilities of winning or losing: Win/(Lose) (500) 0 1000 3000 P(Win/(Lose)) 0.2 0.1 0.6 0.1 a. Show with workings which option roger would choose.***PLEASE NOTE: QUESTION HAS TWO PARTS REQUIRING ANSWER*** Q: Johnny Football has a utility function of the form ? = √?. Johnny is beginning his senior year of college football. If he is not seriously injured, he will receive a $1,000,000 contract for playing professional football. If any injury ends his football career, he will take a job as a refuse removal facilitator in his hometown that pays $10,000. There is a 10% chance that Johnny will be injured badly enough to end his career. a. What is Johnny’s expected utility? b. How much would Johnny be willing to pay to remove the financial riskhe faces? That is, what $p would he pay for a $1,000,000 insurancepolicy so that he would have $1,000,000-$p even if he had a seriousinjury? Assume he wouldn’t work for $10,000 if he had the insuranceand he was injured. Hint: You should set his utility with certainty(U($1,000,000-$p)) equal to his expected utility with risk (found inpart a) and solve for p.