Zac has a current wealth of £400. He gets an email offering him the chance to enter a prize draw that gives £500 prize with a 25% chance and £0 the rest of the time. Zac is an expected utility maximiser with a von Neumann-Morgenstern utility in wealth w of u (w) = Vw. What is the minimum price at which Zac will sell his rights to enter the draw? O £106.25 £506.25 £31.25 £22.5 O E56.25
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- 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.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.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?
- 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)Johnny owns a house that is worth $100,000. There is a O.1% chance that the house will be completely destroyed by fire, leaving Johnny with $0. Johnny's utility function is u(x) = vx, where x represents final wealth. Assuming that Johnny has no other wealth, what's the maximum amount that he would be willing to pay for an insurance policy that completely replaces his house if destroyed by fire? Make sure to answer with the dollar sign and then the number, i.e. $532.17. Be accurate up to the second decimal. You should not need to round. Hint: The hundredths place should be 0. Enter your answer hereJoe's wealth is $100 and he maximizes his expected utility. Joe’s utility as a function of his wealth is U(W) = W1/2. Joe might oversleep his economics exam. He figures there is only a 1 in 10 5 chance that he will, but if he does, it will cost him $100 in fees to the University to take an exam later. Joe's neighbor, Mary, never oversleeps. She offers to wake Joe one hour before the test, but he must pay her for this service. What is the most that Joe would be willing to pay for this wake-up service? a. $10 b. $9 c. $19 d. $100 e. $12.7
- . 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.Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary's boat wins, Donna would give him $31. If Gary's boat does not win, Gary would give her $31. Gary's utility function is p1x^21+p2x^22, where P₁ and p2 are the probabilities of events 1 and 2 and where x₁ and x₂ are his wealth if events 1 and 2 occur respectively. Gary's total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). 1. Taking the bet would reduce his expected utility. 2. Taking the bet would leave his expected utility unchanged. 3. Taking the bet would increase his expected utility. 4. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. 5. The information given in the problem is self-contradictory.Max is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $15,000. With probability p = 0.7 the palace will succeed and Max's wealth will grow from $15,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $10,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $15,000 with certainty? (Please round your final answer to the whole dollar, if necessary)
- Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.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?Your utility function is given by M1/2. You have $100 and are planning to invest in a venture where you can win or lose 50 with equal probability. Will you accept the venture? What is the minimum gain you need to make in the good scenario such that you will invest in the venture?