3. Suppose Chelsea has the following utility function over wealth: v (y) = ln y %3D (a) Show that Chelsea is risk averse. (b) Consider the lottery that yields the outcome $2 with probability ; and the outcome $8 with probability . How much money would you need to offer Chelsea to buy the lottery from her if the lottery is all she owns? (c) What is the Chelsea's risk premium for this lottery? (d) Suppose Antonio has utility function over wealth given by Va (y) = Vy and suppose Dillon has the following utility function over wealth:

3. Suppose Chelsea has the following utility function over wealth: v (y) = ln y %3D (a) Show that Chelsea is risk averse. (b) Consider the lottery that yields the outcome $2 with probability ; and the outcome $8 with probability . How much money would you need to offer Chelsea to buy the lottery from her if the lottery is all she owns? (c) What is the Chelsea's risk premium for this lottery? (d) Suppose Antonio has utility function over wealth given by Va (y) = Vy and suppose Dillon has the following utility function over wealth:

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Janet's broad attitude to risk (risk averse, risk neutral, or risk loving) is independent of her wealth. She has initial wealth w and is offered the opportunity to buy a lottery ticket. If she buys it, her final wealth will be either w + 4 or w – 2, each equally likely. She is indifferent between buying the ticket and not buying it. Janet offers her friend Sam (who has identical preferences and initial wealth) the following proposition: They buy the ticket together, and share the cost and proceeds equally. Sam has another idea: They buy two tickets (that have independent outcomes) and share the costs and proceeds equally. Suppose that Janet's and Sam's utility of income is given by u(x) = In x and the initla wealth of each one of them is equal to w = 4. Which of the following statements is true? O a. Both agents prefer Sam's solutions to Janet's solution. b. Both agents prefer Janet's solutions to Sam's solution. The agents are indifferent between Janet's solutions to Sam's solution.…
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2. Two individuals have the same income ($100,000), but different potential healthcare expenses. Person A's probability of having $80,000 in healthcare expenses is 0.5 percent. Person B's probability of having $800 in healthcare expenses is 50 percent. Assume your utility is U = VI where I is your income. Calculate each person's expected income and expected utility. Calculate each person's certainty equivalent. What does value of the certainty equivalent tell you about how much each person would be willing to insure against their loss?
A10.
(d) Suppose Antonio has utility function over wealth given by Va (y) = Vy and suppose Dillon has the following utility function over wealth: va (y) = In %3D Who is more risk aversc, Antonio or Dillon? Show this using two approachcs. (e) Who is more risk averse, Chelsca or Dillon'? Explain.
Please answer question on screenshot (which of the folowing statements....) q1) Janet offers her friend Sam (who has identical preferences and initial wealth) the following proposition: They buy the ticket together, and share the cost and proceeds equally.
4. A taproom owner is trying to determine how to structure his manager's compensation. One option he considers is a flat salary of $70,000 per year. The second option is a base salary of $30,000 plus 15% of the taproom's profit. If the manager puts a lot of effort into her job, the taproom's annual profit will be $500,000 with 75% probability and $100,000 with 25% probability. If the manager exerts only modest effort, the taproom's profit will be $500,000 with 25% probability and $100,000 with 75% probability. The manager's opportunity cost of putting a lot of effort into her job is $50,000, while her opportunity cost of exerting only modest effort is $25,000. a. Draw the game tree for the interaction between the taproom owner and the manager. Assume that the taproom owner moves first. b. What is the equilibrium outcome for this game? What kind of contract should the taproom owner offer? What level of effort will the manager choose? Explain.
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Choice under uncertainty. Consider a coin-toss game in which the player gets $30 if they win, and $5 if they lose. The probability of winning is 50%. (a) Alan is (just) willing to pay $15 to play this game. What is Alan’s attitude to risk? Show your work.(b) Assume a market with many identical Alans, who are all forced to pay $15 to play this coin-toss game. An insurer offers an insurance policy to protect the Alans from the risk. What would be the fair (zero profit) premium on this policy? i need help with question B please.
1. ) Suppose a driver has a 6% of having one accident a year. In case of an accident the value of the car is reduced from $25,000 to $5,000. If driver buys an insurance policy the insurance company would completely cover damage to the car (essentially restoring its value to its initial level). Assume that the driver's utility function is U = VW. a) If price of the insurance policy (premium) is $1500, would this driver be willing to purchase the policy? Explain Show you computations b) What would be the maximum price a driver with 10% chance of accident be willing to pay for the insurance policy?
1. Risk Premium: Assume your wealth is $100 and like in the Veritassium video you're offered a bet of a 50% chance of winning $10 and a 50% chance of losing $10. Assume you have square root utility. a. What is the utility you enjoy by holding the $100 of current wealth? b. What is the expected utility you foresee by entering the bet? Will you take the bet? c. What is your risk premium? Do you think someone would pay this to avoid the bet? d. Draw a diagram and label the relevant values.