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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- 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 explain4. 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.You are trying to decide between rescuing a puppy or an older dog. You decide to try to assign some numbers to your preferences so you can compare options. You estimate that your utility for a dog that will chew your furniture is 0.1 and your utility for a dog that can go on hikes with you is 0.8. You expect that a puppy will have an 70% chance of chewing your belongings and a 90% chance of going on hikes. What is your expected utility for getting the puppy?
- Q11. What is the behavior of a person with the following utility function? 1 0.8 0.6 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. UtilityEconomics Consider a potential criminal with a lawful income of $121. Potential loot from robbery is $75. The probability of being caught and imprisoned is 0.50 and a prison term for this type of crime is 0.33 units of time. Round to one decimal place in all calculations. Utility is given by: Utility = (income)1/2 A. Calculate the guaranteed utility from lawful income and the expected utility of committing the crime. What will the potential criminal do? Explain why. Would your answer change if there were an anguish cost of 1 util involved? Explain. B. Suppose all the information given above holds true, except there is no anguish cost. You are a city official who has some extra room in the budget to dedicate towards fighting crime. For the use of these resources, you can choose between either increasing the length of prison term for criminals to 0.595 units of time or investing in GIS technologies and improved policing strategies that will increase the probability of criminals being…The following four figures show the utility of wealth functions for 4 different consumers. Which consumer is the most likely to accept a coin toss gamble where she could win $10 if heads and lose $10 if tails? A B C D نان A Wealth B Wealth C Wealth D Wealth
- 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.6. 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?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).
- Select the correct option : When the expected utility of offer A is larger than offer B, a rational individual would always prefer offer A to offer B. 1. True 2.FalseMicroeconomics 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)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. $535