(13.1) Sempronius has to choose between two lotteries X and Y. Lottery X is distributed as (4, 1: 16, ; 36, ), whereas Y is distributed as (1, ; 49, ). Which lottery will Sempronius prefer in each case below? (a) If he is an expected utility maximizer with u = v VR, where R is the result of the lottery as in the good old times of Bernoulli and Cramer. (b) If he is infinitely risk averse (or infinitely pessimistic). (c) If he is an RDEU decision maker with u = R and a function f(p) such that: 0 for 0
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- Suppose that Mike, with utility function, u(x) = v x+5000, is offered a gamble where a coin is flipped twice, and if the coin comes up heads both times (probability - .25), he gets $40,000. Would he prefer this gamble or $7,500 for sure? What is his Certainty Equivalent?Arielle is a risk-averse traveler who is planning a trip to Canada. She is planning on carrying $400 in her backpack. Walking the streets of Canada, however, can be dangerous and there is some chance that she will have her backpack stolen. If she is only carrying cash and her backpack is stolen, she will have no money ($0). The probability that her backpack is stolen is 1/5. Finally assume that her preferences over money can be represented by the utility function U(x)=(x)^0.5 Suppose that she has the option to buy traveler’s checks. If her backpack is stolen and she is carrying traveler’s checks then she can have those checks replaced at no cost. National Express charges a fee of $p per $1 traveler’s check. In other words, the price of a $1 traveler’s check is $(1+p). If the purchase of traveler’s checks is a fair bet, then we know that the purchase of traveler checks will not change her expected income. Show that if the purchase is a fair bet, then the price (1+p) = $1.25.Y5 Alfred is a risk-averse person with $100 in monetary wealth and owns a house worth $300, for total wealth of $400. The probability that his house is destroyed by fire (equivalent to a loss of $300) is pne = 0.5. If he exerts an effort level e = 0.3 to keep his house safe, the probability falls to pe = 0.2. His utility function is: U = w0.5 – e where e is effort level exerted (zero in the case of no effort and 0.3 in the case of effort).a. In the absence of insurance, does Alfred exert effort to lower the probability of fire?HINT: Calculate and compare the expected utility i) with effort, and ii) without effort. If effort is exerted, then the effort cost is paid regardless of whether or not a fire occurs.b. Alfred is considering buying fire insurance. The insurance agent explains that a home owner’s insurance policy would require paying a premium α and would repay the value of the house in the event of fire, minus a deductible “D”. [A deductible is an amount of money that the…
- Consider an individual who gets a utility of u(x) - x^1/2 from his total wealth x. Amsume that he has 160.000 AZN in the bank and owns a car with a value of 90,000 AZN. It is expected that will be stolen within the next year with 20% probability, whereas nothing will happen with. Your company tries to sell him an insurance package with the following properties; as an insurance premium now. (ii) if his car is stolen, your company will pay him a partial ation of 55,000 AZN. (iii) if his car is not stolen, there will be no paytent made by your .Should the individund buy this package, if the insurance premium in 12,500 AZN? ExplainCost-Benefit Analysis Suppose you can take one of two summer jobs. In the first job as a flight attendant, with a salary of $5,000, you estimate the probability you will die is 1 in 40,000. Alternatively, you could drive a truck transporting hazardous materials, which pays $12,000 and for which the probability of death is 1 in 10,000. Suppose that you're indifferent between the two jobs except for the pay and the chance of death. If you choose the job as a flight attendant, what does this say about the value you place on your life?(Derive the coefficients of absolute and relative risk aversion of the following functions, and point out th conditions to make each function increase and concave: (а) и (х) —х- (b/2)x2 (b) µ (x) = (B/(B –- 1))x!-1/B (c) µ (x) = (1/ (B – 1)) [A +Bx]'¬1/B
- 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?There is an urn containing 90 balls: 30 of them are red, and the other 60 are either black or white. One ball will be drawn randomly, and its color will be inspected. R denotes the event of a red ball drawn from the urn and the events B, W are defined similarly. Gambling on an event means receiving $100 if the even obtains and zero otherwise. Consider the following gambles: The most common preferences are r>r and yy. x= (R: 100, B:0, W:0), a = (R: 0, B: 100, W:0), y= (R: 100, B:0, W: 100), = (R: 0, B: 100, W: 100). a. Can the majority choice pattern be explained by (subjective) EU? O No YesConsider the choice between the following two lotteries.L1 = (0, 0.2; 200, 0.8) ;L2 = (0, 0.6; 300, 0.4).Now consider a choice between another pair of lotteriesL3 = (0, 0.6; 200, 0.4) ;L4 = (0, 0.8; 300, 0.2)Suppose that a decision maker prefers the lottery L1 to the lottery L2 andderives zero utility from an outcome of zero. If the decision maker followsexpected utility theory, which lottery among L3 and L4 will the decision makerchoose?
- Deborah is at the casino and is considering playing Roulette. In Roulette, a ball drops into one of 36 slots on a spinning wheel. 17 of the slots are red, 17 are black, and 2 are green. Each slot is equally likely and occurs with probability 1/36. Deborah bets $1.00 on black. If the ball drops into a black slot she receives $2.00 and if it drops into a red or green slot, she receives nothing. The expected value of Deborah's bet (after subtracting the $1.00 she bet) is $ Given that Deborah makes this bet, she must beDeborah is at the casino and is considering playing Roulette. In Roulette, a ball drops into one of 36 slots on a spinning wheel. 17 of the slots are red, 17 are black, and 2 are green. Each slot is equally likely and occurs with probability 1/36. Deborah bets $1.00 on black. If the ball drops into a black slot she receives $2.00 and if it drops into a red or green slot, she receives nothing. a) The expected value of Deborah’s bet (after subtracting the $1.00 she bet) is $________________ b) Given that Deborah makes this bet, is she risk adverse, risk neutral, or risk loving?Obi-Wan is considering whether to buy a lightsaber. With probability 0.50 he will value the lightsaber at $4,000, and with probability 0.50 he will value it at $1,000. If new lightsabers sell for $2,500, then buying a new lightsaber is a: Multiple Choice fair gamble. better-than-fair gamble. less-than-fair gamble. less-than-fair gamble if Obi-Wan risk neutral.