Consider the following decision problem with monetary outcomes: State: Si S2 Probability: a $100 $0 Act: $0 $100 (a) Ann is risk neutral. What is the maximum price that she is willing to pay for perfect information? (b) Bob is risk averse with von Neumann-Morgenstern utility function U($x) = vx and zero initial wealth. What is the maximum price that he is willing to pay for perfect information?
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- 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.5. 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?5. 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. I Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. 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?
- 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. Utility2. Suppose you asked the following question to Person A and Person B: "How much are you willing to pay to avoid the following fair gamble – win $100 with 50% chance and lose $100 with 50% chance (thus, Variance is equal to 10,000)?" A's answer- $2 B's answer-$10 Assuming that A and B have CARA utility function, a) compute their absolute risk aversion coefficients (approximately) and b) compute their risk premiums for avoiding the following new gamble - win $500 with 50% chance and lose $500 with 50% chance.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)
- 5. In economics, an index of risk aversion is defined as: -U" (m) U'(m) I (m) where m measures how much of a commodity is owned and U(m) is a utility function. Find the index of aversion, I(m), for both utility functions U₁(m) = √m and U,(m) = m5/8, and determine which indicates a greater aversion to risk.Utility functions incorporate a decision maker’s attitude towards risk. Let’s assume that the following utilities were assessed for Danica Wary. x u(x) -$2,000 0 -$500 62 $0 75 $400 80 $5,000 100 Would a risk neutral decision maker be willing to take the following deal: 30% chance of winning $5,000, 40% chance of winning $400 and a 30% chance of losing $2,000? Using the utilities given in the table above, determine whether Danica would be willing to take the deal described in part a? Is Danica risk averse or is she a risk taker? What is her risk premium for this deal?3. Suppose that Jon Snow's utility function is given by U(I)=501 where I represents annual income in thousands of dollars. a. Is Jon risk loving, risk neutral, or risk averse? Explain b. Suppose that Jon is currently earning an income of $1000 and can earn that income next year with certainty. He is offered a chance to take a new night watch job that offers a 0.25 probability of earning $2000 and a 0.75 probability of earning $500. Should he take the new night watch job?
- Question 3: Jane has utility function over her net income U(Y)=Y2 a. What are Jane's preferences towards risk? Is she risk averse, risk neutral or risk loving? [Briefly explain your answer] b. Jane drives to work every day and she spends a lot of money on parking meters. She is considering of cheating and not paying for the parking. However, she knows that there is a 1/4 probability of being caught on a given day if she cheats, and that the cost of the ticket is $36. Her daily income is $100. What is the maximum amount of she will be willing to pay for one day parking? c. Paul also faces the same dilemma every single day. However, he has a utility function U(Y)-Y. His daily income is also $100. What is Paul's preference towards risk? Is he risk averse, risk neutral or risk loving? d. If the price of one day parking is $9.25, will Paul cheat or pay the parking meter? Will Jane cheat or pay the parking meter?Khalid has a utility function U = W1/2, where W is his wealth in millions of dollarsand U is the utility he obtains from the wealth. In a game show, the host offershim a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with probability 0.6 and $9 million with probability 0.4.i. Graph Khalid’s utility function with the help of above utility function. Ishe risk lover? Explain. ii. Does A or B choice offer Khalid a higher expected prize? Explain yourreasoning with appropriate calculations. iii. Does A or B offer Khalid a higher expected utility? Again, show yourcalculations. iv. Should Jamal pick A or B choice? Why?1. Show if the following utility functions represent risk averse, risk neutral or risk loving preferences. u(c) = 10° + 3 u(c) = C2 + 3C i. ii. ii. u(c) = e4C iv. u(c) = 1 – e-C