Fin has $216 dollars in income and has the following preferences over income: U(1) = Suppose he faces the following scenario. He can keep his current level of income or he can take the following gamble: with probability equal to 91/218 he wins $127 or with probability equal to 127/218 he loses $91. Please answer the following questions: 1. Is this a fair gamble? Please provide support for your assertion. 2. Will Fin opt for the gamble? Provide support for your assertion. 3. If Fin were forced to take the gamble, then determine the maximum amount that he would be willing to pay to avoid the gamble?
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- Clarice has a utility function: U(Y) = 1000 - (100/Y), where Y is her income. clarice has just graduated from college and has a career choice for her first job of either working as a teacher and earning $40,000 or trying to become a theatre lighting director and earning $70,000 (if there is growth in the demand for theatre) or $20,000 (if there isn't growth in the demand for theatre). there is a 50% probability of growth. a consulting firm guarantees Clarice that it already knows whether there will be growth in the demand for theatre next year. what is the maximum amount Clarice should be willing to pay for this information?1. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,00 A. Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. B. What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8 logx2+ 0.72 logx3over her incomes x1, x2, x3 in the next three years. This is an example of(A) expected value;(B) quasi-hyperbolic utility function;(C) standard discounted utility;(D) none of the above. Emma’s preferences can exhibit which of the following behavioral patterns?(A) preference for flexibility;(B) context effects;(C) time inconsistency;(D) intransitivity.
- Sanjay won a poker game against his friends. Now he has to choose between $600 (the winnings) and the chance to play a new game. In this new game, Sanjay has a 50% chance of winning nothing and a 50% chance of winning $1000. The following graph presents the utility function of Sanjay with respect to money: 1. By how much money would his winnings need to increase or decrease so that Sanjay isindifferent between the $600 and the new game? At a different table, Juan wins $800 in a blackjack game. Similarly, he has to choose between $800 or the chance to win a new game. In this game, Juan has a 45% chance of winning nothing and a 55% chance of winning $1000. The following graph presents the utility function of Juan with respect to money: 2. By how much money would his winnings need to increase or decrease so that Juan is indifferent between the $800 and the new game? Please enter a positive number for an increase or a negative number for a decrease.Emma has a utility function U(x1, x2, x3) = log x1 + 0.8 log x2 + 0.72 log x3 over her incomes x1, x2, x3 in the next three years. This is an example of (A) expected value; (B) quasi-hyperbolic utility function; (C) standard discounted utility; (D) none of the above. Emma’s preferences can exhibit which of the following behavioral patterns? (A) preference for flflexibility; (B) context effffects; (C) time inconsistency; (D) intransitivity.Economics Consider a potential criminal with a lawful income of $121. Potential loot from robbery is $75. The probability of being caught and imprisoned is 0.50 and a prison term for this type of crime is 0.33 units of time. Round to one decimal place in all calculations. Utility is given by: Utility = (income)1/2 A. Calculate the guaranteed utility from lawful income and the expected utility of committing the crime. What will the potential criminal do? Explain why. Would your answer change if there were an anguish cost of 1 util involved? Explain. B. Suppose all the information given above holds true, except there is no anguish cost. You are a city official who has some extra room in the budget to dedicate towards fighting crime. For the use of these resources, you can choose between either increasing the length of prison term for criminals to 0.595 units of time or investing in GIS technologies and improved policing strategies that will increase the probability of criminals being…
- Jacob is considering buying hurricane insurance. Currently, without insurance, he has a wealth of $80,000. A hurricane ripping through his home will reduce his wealth by $60,000. The chance of this happening is 1%. An insurance company will offer to compensate Jacob for 80% of the damage that any tornado imposes, provided he pays a premium. Jacob’s utility function for wealth is given by U(w) = In (w). (A) What is the maximum amount Jacob is willing to pay for this insurance? Show work and explain.Suppose that you graduate from college next year and you have two career options: 1) You will start a job in an investment bank paying a $100,000 annual salary. 2) You will start a Ph.D. in economics and, as a student, you will receive a $20,000 salary. You are bad with decisions, so you are letting a friend of yours decide for you by flipping a coin. The probabilities of options 1 and 2 are, therefore, each 50%. a) Illustrate, using indifference curves, your preferences regarding consumption choices in the two different states of the world. Assume that you are risk-averse. [Include also the 45 degrees line in your figure] b) Now show how the indifference curves would change if you were substantially more risk averse than before. Explain. c) Now show the indifference curves if you are risk neutral and if you are risk loving. d) Show your expected utility preferences from point a) mathematically.‘‘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.
- Student question Time Left :00:09:43Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = 2X + Y UB(X,Y) = Min(X,Y) The initial endowments are: A: X = 5; Y = 3 B: X = 2; Y = 2 a. Illustrate the initial endowments in an Edgeworth Box. Be sure to label the Edgeworth Box carefully and accurately, and make sure the dimensions of the box are correct. Also, draw each consumer’s indifference curve that runs through the initial endowments. Is this initial endowment Pareto Efficient? b. Now suppose Consumer A gets all of both goods. Is this allocation Pareto Efficient? (You do not need to draw a new graph or illustrate this on the existing graph. Simply answer “yes” or “no.”) c. Now suppose Consumer B gets all of both goods. Is this allocation Pareto Efficient? (You do not need to draw a new graph or illustrate this on the existing graph. Simply answer “yes” or “no.”)Draw a utility function (with income on the horizontal axis) for an individual who is risk-loving at low levels of income, risk-neutral at moderate levels of income, and risk-averse at high levels of income (with each of these three regions clearly labeled). How would someone who looked at this graph (and had no other information about the individual) be able to figure out the individual’s attitude toward risk (averse/loving/neutral) in each region?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.