6. A person is a traveling salesman of goods for a large company (she travels by car). She earns 900 euros a week in fixed salary, but if she reaches the set for a week sales target, she receives a bonus of 325 euros that week. The probability of getting the bonus is 0.2. Her utility function over money is given by U=√W, where W is the wealth in SEK per week. 6a 6b What is her expected weekly bonus? Her boss offers her another job within the same company. If so, she would work in an office with a certain personnel responsibility and receive a fixed salary per week (no bonuses). What salary per week must her boss at
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- Seung's utility function is given by U - C^(1/2), where C is consumption and C^(1/2) is the square root of consumption. She makes $50,625 per year and enjoys jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $30,000, and lose an additional $5,000 from missing work. a. What is Seung's expected utility without insurance? b. Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is the expected utility if she buys it? Policy cost: $___ Expected utility: ___ c. Suppose Seung can buy insurance that will cover her medical expenses and foregone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it? Policy cost: $___ Expected Utility: ___Seung’s utility function is given by U = ln(C), where C is consumption. She makes $30,000 per year and enjoy jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $15,000, and lose an additional $5,000 from missing work. (a) What is Seung’s expected utility without insurance? (b) Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is her expected utility if she buys it? (c) Suppose Seung can buy insurance that will cover her medical expenses and forgone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it?PLS ANS 7 URGENT H = ($100, 0.4; $200, 0.6) K = ($120,p, $300, 1- p) 6. EV(H) =EV(K) What value of p makes this statement true? 7. Carol owns prospect H and is interested in selling it. Her utility of wealth function is given by u(x) = x^0.5 . What is the lowest price for which Carol would be willing to sell prospect H?
- Betty is looking for a job. She considers job opportunities intwo cities. Bettyís utility is given by y- x, where y is the lifetime income andx is the amount spent on buying a house. The income from City 1 fluctuatesalthough the house price is stable. On the contrary, the income from City2 is stable while the house price fluctuates. If she moves to City 1, Bettycan earn a lifetime income y1 with probability alpha and 1 + y1 with probability1-alpha . The house price in City 1 is x1. Moving to City 2 means that Bettycan earn an income of y2. However, the house price is x2 with probabilitygamma and 1 + x2 with probability 1-gamma . Do the following: (a) Write down theexpected utilities associated with living in the two respective cities, i.e., V1and V2. (b) Derive the condition under which Betty chooses City 1.Suppose Martha earns an of income 400 Birr currently, and her utility function is given by: U(m) = 4m, where m represents income. She has two options: Option 1: to buy a share. If she is successful her income will be 700 Birr and if she is not successful her income will be 100 Birr. Option 2: to do nothing and keep on earning 400 Birr. Assuming that success and failure are equally likely, a) What would be her expected income if she buys the share? b) What would be her expected utility of buying the share? c) Would Martha buy the share? Why? and Is Martha risk averse, risk lover or risk neutral?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?
- 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 if it does not. Assume that the Bernoulli utility function takes the form u(x) = with r > 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA? Alex plays football for a local club in Kumasi. If he does not suffer any injury by the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coach worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = Assume he could buy insurance at price P that could pay $9,900 in case of injury. What is the highest value of P that makes it worthwhile for Alex to purchase insurance? What is the certainty…Kindly assist on the questions below 1) Dan is an expected utility maximizer with a utility function over wealth given by : u(w) = 2√w +10 Dan faces a gamble of where there are equal chances to win $9 or $16. The certainty equivalent of this gamble is a) 3.5 b) 17 c)2√13 +10 d) not enough information to compute e) 20 2) Consider a expected utility maximizing consumer with preferences represented by u(w)= w2 If they face a loss that occurs with a 15% probability (select all that applies) a) fair insurance will be priced at 15% per dollar b) fair insurance will leave them with wealth equal to their certainty equivalent c)they will choose to fully insure themselves with fair insurance d)they will always buy more insurance than a risk neutral personAssume that Mary’s utility function is U(W) = W1/3, where W is wealth. Suppose that Mary hasan initial level of wealth of $27,000. How much of a risk premium would she require toparticipate in a gamble that has a 50% probability of raising her wealth to $29,791 and a 50%probability of lowering her wealth to $24,389?
- Amy's utility depends upon her income, w. Her utility function is √w. She receives a prize that depends on the roll of a dice. If she rolls a 3 or 4 or 6, she will receive $400. Otherwise, if she rolls a 1 or 2 or 5, she will receive $100.1. What is the expected payoff from this prize? 2. What is the expected utility from this prize?3. What is the minimum payment that Amy will accept to forego the roll of the dice?A risk-averse agent, Andy, has power utility of consumption with riskaversion coefficient γ = 0.5. While standing in line at the conveniencestore, Andy hears that the odds of winning the jackpot in a new statelottery game are 1 in 250. A lottery ticket costs $1. Assume his income isIt = $100. You can assume that there is only one jackpot prize awarded,and there is no chance it will be shared with another player. The lotterywill be drawn shortly after Andy buys the ticket, so you can ignore therole of discounting for time value. For simplicity, assume that ct+1 = 100even if Andy buys the ticket How large would the jackpot have to be in order for Andy to play thelottery? b) What is the fair (expected) value of the lottery with the jackpot youfound in (a)? What is the dollar amount of the risk premium that Andyrequires to play the lottery? Solve for the optimal number of lottery tickets that Andy would buyif the jackpot value were $10,000 (the ticket price, the odds of winning,and Andy’s…Natasha has utility function u(I) = (10*I)0.5, where I is her annual income (in thousands). (a) Is she a risk loving, risk averse or risk neutral individual? She is [risk loving, risk adverse, risk neutral] , as her utility function is [concave, convex, linear] (b) Suppose that she is currently earning an income of $40,000 (I = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. She should [take, not take] the new job because her expected utility of (approximately) [18.27,19.82,20,20.95,21.14] is [greater than, less than, equal to] her current utility of [18.27,19.85,20,20.95,21.14] .