Risk Aversion In economics, an index of absolute risk aver-sion is defined as-U"(M)U'(M)(м)where M measures how much of a commodity is owned andU(M) is a utility function, which measures the ability of quan-tity M of a commodity to satisfy a consumer's wants. Find I(M)for U(M) = VM and for U(M) = MB, and determine whichindicates a greater aversion to risk.

A ‘risk-averse investor’ prefers to avoid risks. He or she escapes from ‘high-risk investments’…

Answered: Risk Aversion In economics, an index of…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 2 -2 -2 Guitars 24 Losses Losses -600 -2 What is the least amount of money Jimi is willing to accept to sell one of his guitars? (just enter a dollar amount, i.e., "1000", not "$1000"
Suppose you have an exponential utility function given by U(x) =1- exp(-x/R) where, for you, R = 1000. Further, suppose you have an investment with a 50/50 chance of returning either 0 or 2000 dollars. Note U(0) = 0 and U(2000) = 0.865, so the utility of the lottery is 0.432. What is the certain equivalent of that investment?
Consider the lottery that assigns a probability T of obtaining a level of consumption CH and a probability 1-T an individual facing such a lottery with utility function u(c) that has the properties that more is better (that is, a strictly positive marginal utility of consumption at all levels of c) and diminishing marginal utility of consumption, u"(c) CL. Consider du(c) for the first derivative of the utility function with respect to dc du(c) du' (c) consumption and u"(c) (which is also the derivative of the first derivative of the utility function). to be the second derivative of the utility function dc dc2 1. Provide a definition for the certainty equivalent level of consumption for the simple lottery described above.
A pirate is about to set sail on a 2-period journey (trip). He has 100 bags of barley (food). He must decide how much to consume in period 1 and how much to consume in period 2: (C1, c2). He gets all the barley in period 1 and none in period 2. Unfortunately, rats will eat 50% of any barley that he saves to consume in period 2. If the pirate's utility function is U(C1, C2) = C1C2, what levels of consumption does he choose in each period? (Hint: The "price" of barley in each period can be assumed to be 1.)
An individual is offered a choice of either $50 or a lottery which may result in $0 or $100, each with equal probability 1/2. If the individual has a utility function u(w) = w, which one would they choose? If the individual has a utility function u(w) =sqr(w)?
Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, where there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is UA(XA,S)=XA+In(1+s), where xA is the amount of money Person A owns. Person B's utility function is uB(XB,1s)%3D3XB+2(1-s), where Xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Persch B has the legal right to a smoke-free room and there is a market for "emission right." At the Walrasian equilibrium, what will be the (per unit of smoke index) price p of the emission rights if the price of money is 1? O a. None of the other answers. O b. p=2/3 O c. p=1 O d. p=3/2 О е. р31/6
Steve has received a stock tip from Monica. Monica has told him that XYZ Corp. will increase in value by 100%. Steve believes that Monica has a 25% chance of being correct. If Monica is incorrect, Steve expects the value of XYZ Corp. will fall by 50%. a. If Steve's utility of income is U(I)=50I. What is Steve's expected utility from buying $1,000 worth of XYZ Corp. stock? b. If Steve's utility of income is U(I)=I0.5. What is Steve's expected utility from buying $1,000 worth of XYZ Corp. stock?
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
Scenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function (sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 Suppose that insurance companies do not know specific probabilities of adverse events for Tess or Lex, but do know the average probability of an adverse event. If they assumed that both Tess and Lex purchase full insurance, what is the actuarially fair premium charged? Round to two decimal places
Problem 3. Carol's risk preference is represented by the following expected utility formula: U(T, C₁; 1 T, C₂) = π √√ √₁+ (17) √√C₂. i) Suppose Carol is indifferent between the following two options: the first option A returns $100 with probability and $X with probability, and the second option B returns $49 for sure. Determine X. ii) Consider the following three lotteries: L₁ = (0.9, $100; 0.1, $49), L2 = (0.7, $225; 0.3, $49), and L3= (0.5, $400; 0.5, $0). What is the ranking of these lotteries for Carol? Calculate the risk premiums of these lotteries for Carol. 1
Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, when there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is ua(XA,s)=Xa.S, where xA is the amount of money Person A owns. Person B's utility function is ug(xg, 1s)=Xg .(1-s)³, where xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Person A has the legal right to a fill up the room with smoke and there exists a market for smoke "abatements". At the Walrasian equilibrium, how much money will person B be left with? а. Хв31.25 ОБ. Хв32.25 O c. XB=0.25 O d. Xg=0.25 е. None of the other answers.
Draw a utility function over income u(I) that describes a man who is a risk lover when his income is low but risk averse when his income is high. 1.) Using the 3-point curved line drawing tool, draw the low income portion of his utility function. Label it U₁. 2.) Using the 3-point curved line drawing tool, draw the high income portion of his utility function. Label it UH. Carefully follow the instructions above, and only draw the required objects. C 500- 450- 400- 350- 300- 250- 200- 150- 100- 50- 0 Utility 20,000 40,000 60,000 80,000 100,000 Income

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