James, whose Bernoulli utility function is given by u(w) = w0.5, participates in a lottery which pays him $4 with probability 0.3, $21 with probability 0.4, and $37 otherwise. What is his certainty equivalent?
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James, whose Bernoulli utility function is given by u(w) = w0.5, participates in a lottery which pays him $4 with probability 0.3, $21 with probability 0.4, and $37 otherwise.
What is his certainty equivalent?
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- Consider a worker, Janice, who has the option to purchase DI (disability insurance) on the private market. Janice becomes disabled with probability q = 0.01. She can purchase DI by paying the premium p. If the Janice is disabled, she will earn no income. But if she is insured, she will receive a total payment of $15,000 from the insurance company (her consumption will be $15,000). If the Janice is not disabled, she earns an income of $20,000. She has utility: U = 3Ci where C is the amount of consumption. a. Determine Janice's expected income without insurance. b. Determine Janice's expected utility without insurance. c. Is the insurance plan offered, full or partial insurance? Explain. d. Determine the actuarially fair insurance premium, p'. e. Write down the expected utility function for Janice if she purchases insurance at the actuarially fair price. f. Will Janice choose to purchase this disability insurance? Explain. 8. What is the most she would be willing to pay for DI insurance?An individual has a von Neumann-Morgenstern utility function of the form u(w) = Vw. What would the individual be willing to pay for a lottery that pays $1,000,000 with a probability of 0.0015 and zero otherwise?Nick is risk averse and faces a financial loss of $40 with probability 0.1. If nothing happens, his wealth is $260. If there is an actuarially fair insurance available to him, he buys the insurance so that his wealth would be the same in either state. True False Suppose that Jim has a von Neumann-Morgenstern utility function: U(c) = c². %3D Based on his utility function, we can tell that Jim is There is not enough information to determine his risk preference. risk averse. risk neutral. risk loving.
- # 4 Consider an individual with a utility function of the form u(w) = √w. The individual has an initial wealth of $4. He has two investments options available to him. He can eitffer keep his wealth in an interest-free account or he can take part in a particularly generous lottery that provides $12 with probability of 1/2 and $0 with probability 1/2. Assume that this person does not have to incur a cost if he decides to take part in the lottery. (a) Will this individual participate in the lottery? (b) Calculate this individual's certainty equivalent associated with the lottery. What is his risk premium?Adam is considering what skills to study in online school. Her utility function is based on the income she earns, and is defined by U(I) = I0.8. If she learns the skill of SPSS, she will earn $145,000 per year with probability 1. If she learns the skill of Tableau, she will earn $300,000 per year with probability 0.6 (assuming that she gets the certificate) and $30,000 with probability 0.4 (if she learns without earning a certificate and she has to find a waiter job). a. Is she risk averse, risk neutral, or risk loving? Explain.b. Write out the equation for her expected utility for each skill. c.Which skill will she learn? Show your work. d.Suppose someone offers her insurance for the possibility that she does not get a Tableau certificate. This insurance will provide her an amount of income in addition to the waiter job wages that makes her indifferent between learning SPSS and Tableau. What is this amount, and what is the cost of the insurance? (note: many possible answers)Lucy and Henry each have $1652. Each knows that with 0.1 probability, they will lose 85% of their wealth. They both have the option of buying a units of insurance, with each unit costing $0.1. Each unit of insurance pays out $1 in the event the loss occurs. The cost of the insurance policy is paid regardless of whether the loss is incurred. Lucy's utility is given by u²(x) = x, Henry's utility is given by u¹(x) = √√x. Answer the following: (If rounding is needed, only round at the end and write your answer to three decimal places.) a) Without insurance, what is the expected value of the loss? b) c) d). e) ( For Henry, facing the "lottery " above without any insurance is as bad as losing how many dollars for sure? Find Lucy's utility maximising choice of a. If more than 1 exist, enter the largest a. Now suppose insurance costs $0.2. Find Lucy's utility maximising choice of a. If more than 1 exist, enter the largest a. What is Henry's utility maximising choice of a with the new price of…
- 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 the lottery that assigns a probability T of obtaining a level of consumption CH and a probability 1-T an individual facing such a lottery with utility function u(c) that has the properties that more is better (that is, a strictly positive marginal utility of consumption at all levels of c) and diminishing marginal utility of consumption, u"(c) CL. Consider du(c) for the first derivative of the utility function with respect to dc du(c) du' (c) consumption and u"(c) (which is also the derivative of the first derivative of the utility function). to be the second derivative of the utility function dc dc2 1. Provide a definition for the certainty equivalent level of consumption for the simple lottery described above.You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $3 million to $4 million. If they are wrong, their prize is decreased to $2,250,000. You believe you have a 25% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is. Given that this is ______________ (POSITIVE/NEGATIVE), you___________ (SHOULD/ SHOULD NOT) play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is (Hint: At what probability does playing the final round yield an expected value of zero?)
- Roger's utility/u as a function of wealth/w is u = { ln w, w < 1600 w1/2, w >= 1600 Roger has $1000 and 3 options. 1. spend $400 to enter the game with probabilities of winning or losing: Win/(Lose) (500) 0 1000 3000 P(Win/(Lose)) 0.2 0.1 0.6 0.1 a. Show with workings which option roger would choose.Leo needs one unit of capital from a bank to launch a business. His profits depend on the interest rate of the contract r and the level of effort. Leo can either put high effort in the project, in which case his profits 7 equal y -r with probability 1/2 and 0 with probability 1/2. H | Leo incurs a cost of high effort c=2- Otherwise Leo can put low effort, in which case his profits 7 equals y,-r with probability 1/3 and 0 with probability 2/3. Leo incurs a cost of low effort L c=0: %3D Leo's utility function is 271/2- c where A represents his profits and c the cost of efforts. For a given an interest rate r, the risk-neutral bank receives r if the entrepreneur is successful or -1 if he is not. The bank knows that there are many entrepreneurs like Leo who either make high or low effort. It then proposes two types of loans. The first loan is designed for entrepreneurs who make high effort, with an interest rate r=r,. The second loan is designed for entrepreneurs who make low effort, with…Shane just bought a house worth $360,000 in an area that is known for floods. A flood occurs with a 5% chance and if it occurs, his home is ✓ for reduced in value to $202,500. Shane has utility function given by U(X)=√√X. He would be willing to pay a maximum of flood insurance. The fair insurance premium for flood insurance is Shane's risk premium is Suppose, instead, that Shane's utility function is given by U(X) = X². Then, the maximum he would be willing to pay for flood insurance is
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