There are four axioms that underpin Expected Utility Theory. Match the names of these axioms to the four descriptions below. Prompts If lottery A is preferred to lottery B; and lottery B is preferred to lottery C; then lottery A must be preferred to lottery C. For every pair of possible lotteries, A and B; either A is preferred to B, B is preferred to A, or A is valued indifferently to B. There is nothing so good (or so bad) that it does not become insignificant if it occurs with small enough probability. Submitted Answers Choose a match Choose a match Choose a match
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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 1.1. 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…ayesha 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
- 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!Bob's utility function implies O time stationarity O transitivity O impatience O all of the above I need help with the questionsAnn can finish a project either this week or next week. The delayed rewardsare 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 thisweek. Theimmediate 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 thatβ= 0.5 and Ann correctly anticipates her choice next week. Thenshe should finish the project (A) this week; (B) next week; (C) never; (D) not enough information. Suppose thatβ= 0.5, and Ann can commit to finish the project next week (e.g.by imposing a heavy cost on herself if the project is not finished nextweek).Then she will (A) do the project this week;(B) commit to do it next week and finish it then;(C) do it next week without commitment;(D) commit and then not finish it.
- 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 with δ= 1 and β <1. Imagine that Anndoes not finish the project this week. Then she should finish it next week A) if β >0.6; (B) if β >0.4; (C) only if β= 1; (D) for any β.Ann can finish a project either this week or next week. The delayed rewardsare 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 thisweek. Theimmediate 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 thatβ= 0.5 and Ann correctly anticipates her choice next week. Thenshe should finish the project (A) this week; (B) next week; (C) never; (D) not enough information. Suppose thatβ= 0.5, and Ann can commit to finish the project next week (e.g.by imposing a heavy cost on herself if the project is not finished nextweek).Then she will (A) do the project this week;(B) commit to do it next week and finish it then;(C) do it next week without commitment;(D) commit and then not finish it. Can you…In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w, b) = w¹/4b³/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is T. Question 3 Part a Express Ben's expected utility function. (Hint: find Ben's optimal consumption in each state of nature first) Question 3 Part b Let's assume = 0.5. Knowing that bad weather…
- In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w, b) = w¹/46³/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is π. Question 3 Part a Express Ben's expected utility function. (Hint: find Ben's optimal consumption in each state of nature first) Question 3 Part b Let's assume π = 0.5. Knowing that bad weather…. Answer all parts (a) (c) of this question. (a) Consider an agent whose preferences over any couple (x1, x2), where 2₁ ER+ and x2 € R+, e.g., apples and oranges, is such that she prefers the bundle that is closest to having the same number of apples and oranges. Write a utility function u: R² → R+ which represent these preferences. A politician remarks "Our recent increases in the wage rates of teachers has been a total suc- cess! The shortage of teachers has been reduced drastically. Another, similar wage increase should eliminate this shortage entirely" (b) Explain and illustrate in a diagram what is meant by "income effects" and "substitution effects" of a wage rate change. (c) Explain and illustrate how you would model the labour supply decision of a potential teacher. Do you agree that the wage increase will increase the labour supply in this case? Carefully outline the assumptions underlying your argument.Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 -2 -2 2 Guitars 2$ 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"