1. An expected utility maximizing individual has utility of end-of-period wealth given by wl-r –1 , if y #1 u(W)={ 1-y In(W), if y = 1 (1) Show that this individual has constant relative risk aversion and decreasing absolute risk aversion. (2) Consider the special case where y = 2. Suppose that this individual is endowed with an initial wealth W, but his end-of-period wealth is subject to a random income shock given as follows: S $y, with probability p s0, with probability 1-p where 0

1. An expected utility maximizing individual has utility of end-of-period wealth given by wl-r –1 , if y #1 u(W)={ 1-y In(W), if y = 1 (1) Show that this individual has constant relative risk aversion and decreasing absolute risk aversion. (2) Consider the special case where y = 2. Suppose that this individual is endowed with an initial wealth W, but his end-of-period wealth is subject to a random income shock given as follows: S $y, with probability p s0, with probability 1-p where 0

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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9) A risk-neutral individual with current wealth w has already decided investing all his wealth in a project that has two possible net wealth outcomes wn and we (with probabilities pr and pe, respectively) where wr > w > we > 0, PrPe E (0,1), and pr + Pe = 1. Before he invests, he realises that there is a source of information that tells the individual which outcome will be realised with truth, what is the value of this information for the individual? a) pe(@ – w;), b) (Pn – Pe)w, c) Phwn + PeWe – w, d) Pr(w – wn).
2. Maria has $100. There is a 50% that she will lose all of it. Her utility as a functionof wealth is u(c) = √c. a. What is the maximum amount she would be willing to pay to fully insure againstthe 50% probability of the loss? b. Is she risk averse, risk loving, or risk neutral?
Find the attached file.
(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.
A widely used utility function in the economics literature is the constant rate of risk aversion utility function. It is given by: utc) = c*(1-n) (1-n) Assume that an agent lives tor three periods (t-0,1,2) and discounts future utity at rate B (per period), The agent is born with asset level ag and his/her labour market income is yo and y, for periods O and 1 respectively, the agent retire in the last period (no labour income). The interest rate in this economy is Please answer the following questions based on the information displayed here. Choose the best option avallable. Select one: O a. The budget constrain in period te2 is given by: C2 + ay = az(1+r) O b. The budget constrain in period te2 is given by: c2= az{1+1) O G. The budget constrain in period t=2 is glven by: ute, )+ ag = a;(1+1) +ya d. The budget constrain in period t=2 is given by: C2= az(1+r) +y3 e. The budget constrain in period te2 is given by: c, + ag = az(1+) +ya
Which of the following utility functions exhibits constant absolute risk aversion? a. U(W) =W-0.5W² b. U(W) = -e-w c. U (W) = W d. U(W) = In W
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When the second order derivative of a function is greater than zero than the agent is risk lover. question; Asses the risk attitude of an agent represented by the expected utility function u(x)= 2x2-5. However my course material writes that this agent is risk neutral because it is affine. My question is that whys is this so despite the fact that the second order derivative is '4' which is >0. Kindly explain this to me with complete steps.
Millicent’s utility function is U(w) = W0.5 , where W is her wealth. She owns a “pure water” producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability. a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree to sell her pure water? (Hint: price=amount that will give her the same expected utility) b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at which she will agree to sell her “pure water” producing firm c. From your answers in parts (a) and (b), what is the relationship between her wealth and her degree of risk aversion?
Consider an individual with an expected utility function of the form u(w) = √wwhere wrep-resents this individual’s wealth. This individual currently has wealth of $100. This individualfaces a risk of losing $64 with a probability of (1/2). The maximum price that this individualwould pay for insurance that covers the entire $64 loss is?
Which of the following shapes is the most likely plot of the utility-of-wealth function for a risk-averse person? Utility OA B D B D A Wealth C