U C b 30 50 75 100 16.2.5) The above figure shows Bob's utility function. He currently has $100 of wealth, but there is a 50% chance [NB1] that it could all be stolen. To reduce the chance of theft to zero, Bob is willing to pay A) $20. $70. Answer: C B) $50. D) $80. C)
Q: Lucy and Henry each have $8082. Each knows that with 0.1 probability, they will lose 85% of their…
A: Given: Lucy and Henry each have = $8082 The probability here is = 0.1 They both buy units of…
Q: Figure 27-2. The figure shows a utility function for Britney. Unlity B $750 $1,050 $1,350 Wealth…
A: Risk-averse people are those who prefer not to take any risk or want to reduce the uncertainty.
Q: Suppose that you have two opportunities to invest $1M. The first will increase the amount invested…
A: Utility function = 2.3ln(1+4.5x) First opportunity : Returns = + or - 50% Probability of gain =…
Q: Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the…
A: Answers. Part - 1 By dividing the utility gained from each conceivable outcome by the corresponding…
Q: Draw a utility function in U - I space that fits this description. b) Explain the connection…
A: Risk refers to the uncertainty associated with an event. People have different bearing capacities of…
Q: 5. True or False. Explain your reasoning. Assume that an agent's preferences can be represented by a…
A: VNM utility functions define the risk appetite of an investor under uncertainty through its utility…
Q: Natasha has utility function u(I) = (10*I)0.5, where I is her annual income (in thousands). (a) Is…
A: The expected utility theory is a well known idea in economic aspects that fills in as a kind of…
Q: Leo owns one share of Anteras, a semiconductor chip company which may have to recall millions of…
A: The stock price is the current value of stock for buyers and sellers.
Q: Calculate the risk premium of John when he faces the risky prospect X = {1, 4, 9, 16; 0.2, 0.4, 0.4,…
A: We are going to calculate Certainty equivalent and Expected Value to answer this question.
Q: Consider the following decision problem with monetary outcomes: State: Si S2 Probability: a $100 $0…
A: (a) A risk neutral individual will pay the expected value of the lottery. Therefore, For act "a" Ann…
Q: Consider a risk averse individual who has utility function u(a) which is increasing with u(0) = 0.…
A: As per our bartleby guidelines i only have to do first 3 questions
Q: Amy likes to go fast in her new Mustang GT. Their utility function over wealth is v(w) where w is…
A: We are going to find he expected utility for Anna in both scenarios when she is insured and she…
Q: Suppose he faces the following scenario. He can keep his current level of income or he can take the…
A: Fair bit the the bit that gives 0 expected payoff.
Q: Khalid has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the…
A: The utility function is given as, Answer (i) Figure (1) below depicts the given utility…
Q: Consider the following compound lottery, described in words: "The probability that the price of…
A: Probability can be characterized as the proportion of the number of positive results to the absolute…
Q: 2. If h(y) denotes an individual's happiness (called “utility" in economics) when having income y,…
A: Answer: Given: Coefficient of relative risk aversion: Ry=-yh''yh'ywher h''y means second order…
Q: 4. Consider the following variant of the Prisoner's Dilemma game: Player 1 is unsure whether Player…
A: Given information Probability of player 2 is selfish=p Probability of player 2 is nice=1-p Pay off…
Q: Let W0 represents an individual’s current wealth and U(W) is this individual’s von…
A: Utility analysis is a quantitative method which in turn estimates the dollar value of benefits being…
Q: Fin has $216 dollars in income and has the following preferences over income: U(1) = Suppose he…
A: We are going to find risk aversion coefficient and risk premium to answer this question.
Q: Vhat is the behavior of a person with the following utility function? 1 0.8 0.6 5 0.4 0.2 $0 $50…
A: Each and every investment is associated with risk. Thus a person taking a risk can be of three types…
Q: Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both…
A: The total income of Tess = $40,000 The probability that Tess experiences adverse event (π) = 1% or…
Q: Can you explain how Constant Relative Risk Aversion utility function should be understood and how it…
A:
Q: 22. Consider the same set up as in the previous exercise but now consider the case of incomplete…
A: Please find the answer below.
Q: Consider two individuals whose utility function over wealth I is ?(?) = √?. Both people face a 10…
A: Insurance: It refers to protection from financial loss.
Q: Compute the RELATIVE risk aversion measure rr(W) of the following utility function (the form of…
A: Given: U=W1-γ-11-γ, when γ≥0,γ≠1U=lnW, when γ=1 Relative risk aversion formula…
Q: 1. Show if the following utility functions represent risk averse, risk neutral or risk loving…
A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…
Q: A risk averse agent, a risk neutral agent, and a risk loving agent each face the risky situation…
A: EV = Expected Value We need to find the Expected values in each scenario to answer this question.
Q: You participate in a coin-toss gamble with a weighted coin. The coin has a 70% chance of landing…
A: Expected utility refers to the aggregate economy utility due to which individuals can make…
Q: 3. In the second example, we will consider the case where the insurance contract involves a…
A: We are going to find the optimal insurance coverage level to answer this question.
Q: 5. You are a risk-averse decision maker with a utility function U(1) = VI, where I denotes your…
A: Risk premium is defined as the maximum amount that an individual investor desires to pay to…
Q: 21. Suppose that the utility function for nonnegative amounts of money for some risk-averse agent…
A: Two lotteries A and B are given where A gives 36 with certainty and B given 0 with probability p and…
Q: Lottery A gives $2 million with 10%, $1 million with 80%, and $0 with 10%. ⚫ Lottery B gives $2…
A: Given information Case 1: Lottery A gives $2 million with 10%, $1 million with 80%, and $0 with 10%.…
Q: Recall Janet's proposal from Question 2 and Sam's solution from Question 3. Which of the following…
A: It is assumed that Janet and Sam have identical preferences, i.e., they are both risk-averse. When a…
Q: Consider a risk-neutral agent who maximizes expected utility of wealth facing a lottery with a "bad"…
A: Risk-neutral people will be indifferent if the expected income will be equal to the actual income.…
Q: Two workers independently choose how much effort to put in their jobs. If worker 1 chooses e₁ ≥ 0…
A: Two workers independently choosing the level of effort to put in , so as to maximize payoffs take…
Q: 5. You are a risk-averse decision maker with a utility function U(1)= VI, where I denotes your…
A: The term insurance premium refers to the amount that a person or a firm pays to the insurance…
Q: Clancy has $5,000. He plans to bet on a boxing match between Sullivan and Flanagan. He finds that he…
A: Money = 5,000 If Sullivan Wins Coupon = $3 with payoff$10 If Flanagan wins Coupon = $1 with…
Q: Question 20 An island community has two residents: Katie and Dylan. Katie has a utility function of…
A: Utilitarian perspective of welfare is provided by the sum of individual utilities whereas Rawlsian…
Q: Let us consider a utility function: U(x) = ()/2x -1. (200sxs800) We have LiL2 where L1=(1, Y) and…
A:
Q: Consider the following prospects: A: (0.5, 0, 0.5: $100, $60, $10) B: (0, 0.9, 0.1: $100, $60, $10)…
A:
Q: Victoria founded a start-up several years ago, together with her Macedonian friends. At first, she…
A: The satisfaction or pleasure that consumers get from consuming a commodity or service is referred to…
Q: Consider the following claim: “If a decision maker prefers one given lottery that yields $x with…
A: Answer - Risk averse :- Risk-averse under which an individual is avoid taking risks
Q: Jin's Utility Function Wealth Utility (Dollars) 60,000 4,000 61,000 4,110 62,000 4,209 63,000 4,288…
A: We are first going to derive the properties of risk averse function to answer this question.
![d
a
30 50
75
100
16.2.5) The above figure shows Bob's utility
function. He currently has $100 of wealth,
but there is a 50% chance [NB1] that it could
all be stolen. To reduce the chance of theft
to zero, Bob is willing to pay
A) $20.
$70.
Answer: C
B) $50.
D) $80.
C)
bo](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd557876f-a295-433c-ae28-ff0b06d3f70c%2F2d04a3f7-ab90-4661-9e37-d29a83454f0d%2Fhb13wyc_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
- 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?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.1. A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and o if it does not. Assume that the Bernoulli utility function takes the form u(x) = -e-rx with r>0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA?
- 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.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?Jamal has a utility function U= W1/2 where Wis his wealth in millions of 'dollars and Uis 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 $1million with a probability of 0.6 and $9 million with a probability of 0.4. a. Graph Jamal's utility function. Is he risk-averse? Explain. b. Does A or B offer, Jamal, a higher expected price? Explain your reasoning with appropriate calculations. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.) c. Does A or B offer Jamal a higher expected utility? Again, show your calculations. d. Should Jamal pick A or B? Why?
- [**] Simon has current wealth of $36, including $20 in cash. With probabil- ity Simon's money will be stolen (contingency 1), leaving him with only $16 to spend on consumption, and with probability his cash will not be stolen (contingency 2) so he can spend the entire $36 on consumption. Simon has utility function u (0₁.0₂) = √6 + 2√ where c is consumption spending in contingency i. Show Transcribed Text 1. What is the expected value of Simons contingent consumption? 2. What is the expected utility of Simons contingent consumption? 3. What is Simons MRS at his current contingent consumption bundle 4. An insurance company offers to fully insure Simon against the risk of theft for a premium (price) of $P. That is, if Simon pays $P to the insurance company, then the insurer will replace Simons $20 in contingency 1. If Simon buys the insurance his contingent consumption bundle is therefore (36 P; 36 P). i. What is Simons MRS at the fully insured contingent consumption bundle? ii. At what…5. Consider a decision-maker who expects to have a car accident with chance ; if this occurs, he will incur $L in damages. He can purchase as much auto insurance, q, as he likes, at a price of p per dollar of coverage: this means that if he pays pq upfront (as the insurance premium), he'll receive a payment of q from the insurance company if an accident occurs. (a) Write out his expected utility from purchasing insurance level q, assuming a utility-of- wealth function u(w) and initial wealth wo. 1 (b) Show that the optimal level of insurance, q, solves u' (wo - L + (1 - p)q)) u' (wo - pq) = p(1 - π) T(1-P) (c) Now assume that u(w) 1 - e-aw, where a > 0 (this is known as a "CARA", or "constant absolute risk aversion", utility function; a parametrizes risk aversion). Solve explicitly for the optimal insurance, and show that it does not depend on wealth.6) Leia has $11,000 and she wants to invest in financial market. There are two types of assets. The first one guarantees 0.1 percent return next year. The second one is a risky asset which will yield 0.5 percent return in good times and 0.4 percent of loss in bad times. Suppose the chance of good and bad times is half-half and Leia's utility function is U(Y) = Y 0.5 %3D a). What is the expected utility if she invest in the first asset? b). What is the expected utility if she invest in the second asset? Will Leia chooses the first or the second asset? c). Suppose that Leia can purchase a financial insurance which cost her $100 and cover all her lost when bad times happen. Will she purchase this insurance?
- 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?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?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?