5. True or False. Explain your reasoning. Assume that an agent's preferences can be represented by a strictly increasing vNM utility function. If a prospect gives an agent higher wealth than another prospect in each possible state, the agent must prefer the former to the latter.
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- Betty is looking for a job. She considers job opportunities intwo cities. Bettyís utility is given by y- x, where y is the lifetime income andx is the amount spent on buying a house. The income from City 1 fluctuatesalthough the house price is stable. On the contrary, the income from City2 is stable while the house price fluctuates. If she moves to City 1, Bettycan earn a lifetime income y1 with probability alpha and 1 + y1 with probability1-alpha . The house price in City 1 is x1. Moving to City 2 means that Bettycan earn an income of y2. However, the house price is x2 with probabilitygamma and 1 + x2 with probability 1-gamma . Do the following: (a) Write down theexpected utilities associated with living in the two respective cities, i.e., V1and V2. (b) Derive the condition under which Betty chooses City 1.If 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 False1. 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…
- Consider an agent who has to choose how many donuts to eat. He exhibits the choices C({1, 2}) = {1, 2} and C({1, 2, 3}) = {2, 3}. Can these choices be explained by : (i) maximization of a complete and transitive preference? (ii) satisficing? (iii) regret aversion? %3Dayesha 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 $8000. find ayesha's utility maximizing choice of days travelling and dining outside. and alsoo find uutility level from consuming that bundles .show findings graphicallySuppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 -2 -2 2 Guitars 2$ Losses Losses i-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., "10o0", not "$1000"
- 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 unitsIn the standard notation of our revealed preference analysis, suppose p^cC < p^CA < p^cB and p3cB < pBcC. Select one: Select one: a. These conditions are consistent with well-behaved preferences and imply only that situation A is revealed weakly preferred to situation C. b. These conditions are consistent with well-behaved preferences but tell us nothing about the preference ranking of the three situations. O c. These conditions are not mutually consistent with well- behaved preferences. O d. These conditions are consistent with well-behaved preferences and imply that situation C is revealed weakly preferred to situation B and situation A is revealed weakly preferred to situation C.4 Lata gets to consume 16 units of food (FS) if there is sunshine (probability 3/4) and 4 units of food (FH) if there is hurricane (probability 1/4). Will she accept a bundle (9,25) with same probabilities? Find out the equation of indifference curve that passes through the new bundle. Also calculate certainty equivalent and risk premium for the new bundle. Explain your answer with the help of appropriate diagrams if her benefit function for food is given by (i) W(F) = F^2 (ii) W(F) = F^1/2 (iii) W(F) = F
- Ann can finish a project either this week or next week. The delayed rewards are 10 in either case. (The project can be done only once or not at all).Next week is busy and the cost of finishing the project are lower this week. The immediate costs are 4 this week and 6 next week. Ann has a quasi-hyperbolic utility withδ= 1 andβ <1. Imagine that Anndoes not finish the project this week. Then she should finish it next week (A) ifβ >0.6; (B) ifβ >0.4; (C) only ifβ= 1; (D) for anyβ.11. Suppose that β= 0.5 and Ann correctly anticipates her choice next week. Then she should finish the project (A) this week; (B) next week; (C) never; (D) not enough information. can you help me with the bolded question? thank you!Suppose Jessica has two choices: receive $12000 and 30 utils or take a gamble that has a 55% chance of a $20000 and 45 utils, and a 45% chance of a $0 payoff and zero utility. Assuming Jessica is a utility maximizer, what will she likely choose? a) Jessica will not take the gamble b) Jessica will take the gamble c) It cannot be determined d) Jessica is indifferentAn individual is o ered a choice of either $50 or a lottery which may result in $0and $100, each with equal probability 1/2 . If the individual has a utility function u(w) = 5 + 2w, which one would they choose? If the individual has a utility function u(w) =w1/2 + 1?