Fin has $216 dollars in income and has the following preferences over income: U(1) = Suppose he faces the following scenario. He can keep his current level of income or he can take the following gamble: with probability equal to 91/218 he wins $127 or with probability equal to 127/218 he loses $91. Please answer the following questions: 1. Is this a fair gamble? Please provide support for your assertion. 2. Will Fin opt for the gamble? Provide support for your assertion. 3. If Fin were forced to take the gamble, then determine the maximum amount that he would be willing to pay to avoid the gamble?
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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.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.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.
- 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.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?Draw a utility function over income u(I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. 1.) Using the 3-point curved line drawing tool, draw the low income portion of his utility function. Label it UL. 2.) Using the 3-point curved line drawing tool, draw the high income portion of his utility function. Label it UH- Carefully follow the instructions above, and only draw the required objects. 500- 450- 400- 350- 300- 250- 200- 150- 100- 50- 0- Utility 20.000 40.000 60,000 80,000 Income 100,000
- Billy's income Is equal to / = 100 and his utility function is U = [?. There is a 10% chance that he will be in an accident next year with his skateboard that will cause $70 worth of damage. Get the risk premium for Billy. b. An Insurance company offers a policy that will cover all the damages if an accident occurs Calculate the fair price for the insurance. %3D a.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.You are considering two options for your next family vacation. You can visit Disney World or Chicago. Your utility from Disney World is 100 if the weather is clear, and 0 if it rains. Chicago is worth a utility of 70 if the weather is clear and a utility of 40 if the weather is rainy. Also assume that the chance of rain at Disney World is going to be 50% and the chance of rain in Chicago is 40%. As a utility maximizer, should you plan to go to Disney World or Chicago? (Explain using relevant equations)
- Suppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability ofwinning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. How much utility does one lose if one loses the gamble?1) to avoid an accident at work or not exert any effort (e John is deciding whether to exert effort (e = 0). If e = 1, the probability of an accident is 0.5. If e = 0, the probability of an accident is 1. John's income without the accident is $100. In case of an accident, medical expenses will be $64. John utility of income is VI. The cost of effort, C(e), is 0 if effort is e = 0 and 1 if effort is e = 1. John's utility function is u(I, e) = Vī – C(e). (a) What are the expected utility values that John would face when he exerts effort and when he does not exert effort? Based on your calculations, should he exert effort? Briefly explain the intuition behind his decision in one or two sentences. Now suppose there is a risk neutral insurance company. Suppose the insurance company cannot monitor whether John exerts effort or not. The insurance company considers two plan contracts. Contract Plan A: Premium: p = $36. Payout in the event of accident: d = $64 Contract Plan B: Premium: p = $19.…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.