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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(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.
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