Which of the following is true about utility-income model? The individual prefers an uncertain outcome to a certain one with the same expected income The individual prefers the utility she would get from her expected income to th- expected utility she will get from the uncertain income The individual is risk tolerant All of the above
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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.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.You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…
- 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 100,00012. A consumer who conforms to the von Neumann-Morgenstern axioms is faced with four situations A, B, C, and D. She prefers A to B, B to C, and C to D. Experimentation reveals that the consumer is indifferent between B and a lottery ticket with probabilities of 0.4 and 0.6 for A and D respectively, and that she is indifferent between C and a lottery ticket with probabilities of 0.2 and 0.8 for B and D respectively. Construct a set of von Neumann- Morgenstern utility numbers for the four situations.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
- 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…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.
- Consider IC1. Good X • B • D E Good Y If given a choice between A and D the person will always choose D If given a choice between A and E the person will always choose E O If given a choice between A and G the person will always choose G If given a choice between A and B the person will always choose B Moving from B to D, the person is giving up Good X and getting Good Y. It is uncertain if the person prefers B over D because it's uncertain if he values the extra Y he gets give more enjoyment than the enjoyment he loses from having less X.‘‘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.An individual is oered 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?