Maria has $100. There is a 50% that she will lose all of it. Her utility as a function of wealth is u(c) = √c. a. What is the maximum amount she would be willing to pay to fully insure against the 50% probability of the loss? b. Is she risk averse, risk loving, or risk neutral?
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2. Maria has $100. There is a 50% that she will lose all of it. Her utility as a function
of wealth is u(c) = √c.
a. What is the maximum amount she would be willing to pay to fully insure against
the 50% probability of the loss?
b. Is she risk averse, risk loving, or risk neutral?
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- 5) Philippina's utility of wealth function is VW. She has stocks, bonds and cash worth $360,000 and a house worth $280,000. There is a 1% chance of her house being completely destroyed by fire. Unfortunately, if she has insurance, she is less responsible and so the risk of her house being burned down rises to 2%. a. What is the most Philippina is willing to pay for insurance?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?Jin's Utility Function Wealth Utility (Dollars) 60,000 4,000 61,000 4,110 62,000 4,209 63,000 4,288 Refer to Table 27-1. If Jin's current wealth is $61,000, then O his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Jin is not risk averse. O his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Jin is not risk averse. O his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Jin is risk averse. his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Jin is risk averse.
- 4) Luke is planning an around-the-world trip on which he plans to spend $10,000. The utility from the trip is a function of how much she spends on it (Y ), given by U(Y) = InY a). If there is a 25 percent probability that Luke will lose $1000 of his cash on the trip, what is the trip's expected utility. b). Suppose that Luke can buy insurance to fully against losing the $1,000 with a actuarially fair insurance. What is his expected utility if he purchase this insurance. Will he purchase the insurance? c). Now suppose utility function is U(Y) = Y/1000 What is his expected utility if he purchase the insurance in b). Will he purchase the insurance?a) Explain what is meant by risk aversion, and illustrate with the help of a figure out what we mean by the term "risk premium". Suppose Donald runs hotels and casinos, which makes one very insecure income. With probability 1 the income becomes 100 and with probability 1 the 64th Donald's expected income is thus equal to 82. Further assume that the utility to Donald is a a function of income, and that it is given by U (x) = 2x 12 x is the income level. b) Calculate Donald's expected utility.Jamal has autility function U=W1/2,where W is his wealth in millions of dollars and U is the utitlity he obtains from that wealth.Inthe final stage of a game show,the host offers offers Jamal a choice(A)$4 million dollar for sure,or (B) a gamble that pays $1 million with probability 0.6 and $9million with probability 0.4. a.Graph Jamal's utitility function.Is he risk averse?Explain. b.Does A or B offers Jamal a higher expected price?Explain your reasoning with appropriate calculations. c.Does A or B offer Jamal a higher expected utility? d.Should Jamal pick A or B? Why?
- 1. 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 £10,00 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?# 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?2. Ronald has $18,000. But he is forced to bet it on the flip of a fair coin. If he wins he has $36,000. If he loses he has nothing. Ronald's expected utility function is 0.5x0.5 + 0.5y0.5, where x is his wealth if heads comes up and y is his wealth if tails comes up. What safe income would make him exactly as well off as this bet?
- 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?10. Karl's utility function is U(w) = 20 is w. = 300. He considers a gamble in which he could win 200 with probability p or lose 200 with probability 1 described by expected utility theory. He is indifferent between keeping his initial wealth for sure or taking the gamble if the value of p is where w is wealth. His initial wealth %3D w+200 - p. Karl's preferences in the face of risk are (a). 4 (b) .5 (c) .6 (d) .7 (e) .85. 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?