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.
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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.
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Solved in 2 steps
- 1. A standard model of choice under risk is Expected Utility Theory (EUT) in which preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities (P1, P2, ..., Ps) with Eps = 1 are represented by the function L S (a) What does it mean to say that a function represents the consumer's prefer- ences? Σpsu(xs) Choice 1 8=1 (b) State and briefly comment on the axioms required for the EUT representation. (c) Consider the following experiment of decision making under risk in which sub- jects are asked which lottery they prefer in each of the following two choices: Lottery B 0 with prob. 0.01 10 with prob. 0.89 50 with prob. 0.10 Lottery D Choice 2 Lottery A 0 with prob. 0 10 with prob. 1 50 with prob. 0 Lottery C 0 with prob. 0.90 10 with prob. 0 50 with prob. 0.10 Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in Choice 2. Assume that utility of zero is equal to zero and illustrate why it is not possible to reconcile these experimental…a) Compute the (absolute) risk aversion measure dependent r(W) of utility function -e -aW Is r(W) on W?Suppose that Natasha's utility function is given by u(I) = √/10/, where I represents annual income in thousands of dollars. Is Natasha risk loving, risk neutral, or risk averse? Explain. A. She is risk averse because her utility function exhibits diminishing marginal utility. OB. She is risk loving because her utility function exhibits increasing marginal utility. OC. She is risk neutral because her utility function exhibits constant marginal utility. Suppose that Natasha is currently earning an income of $40,000 (1 = 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. Should she take the new job? Natasha should not take the new job because her expected utility of 19.85 is less than her current utility. (Round expected utility to three decimal places.)
- 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 UL. 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. 500- 450- 400- 350- 300- 250- 200- 150- 100- 50- 0- Utility 20.000 40.000 60,000 80,000 Income 100,000If agent is preferences under uncertainty can be represented by the utility function u = 10x, then they can also be represented by the utility function u = 20x - 10. O True Falseayesha derives utility from travelling and outdoor dinning o weekends as given utility function U(t,d)=TD.the price of a day spent travelling is $160{Pt=160} and price of dining outdoor $200{Pd=200}.ayesha annual budget for this is $8000. find ayesha's utility maximizing choice of days travelling and dining outside. and alsoo find uutility level from consuming that bundles .show findings graphically
- 3. Let us consider a utility function: U(x) = ()V2x -1. (200sxs800) We have L¡iL2 where L1=(1, Y) and L2=(0.3, 450, 0.7,648). a. Determine the value of Y. b. Determine RP (Risk Premium) of L2.The chief executive officer of a publishing company says she is indifferentbetween the certainty of receiving $7,500 and a gamble where there is a 0.5 chance of receiving $5,000 and a 0.5 chance of receiving $10,000. a). Does she seem to be a risk averter, a risk lover, or risk- neutral? Explain. b). What is the coefficient of variation of the risky option (gamble)?The following figure shows a utility function for Dexter UTILITY 1,300 1.000 WEALTH (Dollars) 800 Refer to Figure 28-3. Suppose the vertical distance between the points (0, A) and (o, B) is 12. If his wealth increased from $1,300 to $1,800, then OaDexter would be more likely to buy insurance. Ob Dexters subjective measure of his well-being would increase by less than 12 units Dexter would change from being a misk-averse person into a person who is not risk averse Od Dexters subjective measure of his well being would increase by more than 12 units
- Utility functions incorporate a decision maker’s attitude towards risk. Let’s assume that the following utilities were assessed for Danica Wary. x u(x) -$2,000 0 -$500 62 $0 75 $400 80 $5,000 100 Would a risk neutral decision maker be willing to take the following deal: 30% chance of winning $5,000, 40% chance of winning $400 and a 30% chance of losing $2,000? Using the utilities given in the table above, determine whether Danica would be willing to take the deal described in part a? Is Danica risk averse or is she a risk taker? What is her risk premium for this deal?‘‘Risk-averse people should only be averse to big gambles with a lot of money at stake. They should jump on any small gamble that is unfair in their favor.’’ Explain why this statement makes sense. Use a utility of income graph like Figure 4.1 to illustrate the statement. For a challenge, demonstrate the statement using a two-state graph like Figure 4.6.Consider an agent with the following utility function: %3D where o ("sigma") is a parameter that we fix and does not vary. (a) For which values of o is the agent risk averse? (hint: use the mathematical definition of risk aversion) (b) Compute the coefficient of absolute risk aversion and relative risk aversion. How do they vary with x? Consider the case where o = 2 and the lottery L that pays $ 3, $ 5 and $ 10 with equal probability. The agent has an initial wealth of $ 6. In order to participate to this lottery, the agent has to pay an amount of dollars p. (c) Let p = 3. Does the agent prefer to participate to the lottery or not participate? (d) What is the amount of dollars you should give the agent so that he is indifferent between participating to the lottery and not participating but getting the money?