An individual can play a lottery X. You know that the individual's instantaneous utility is u(w) = √w. Suppose you wanted to know whether the certainty equivalent of playing the lottery for that individual is higher than, equal to, or lower than the expected value of the lottery. Which additional piece of information, if any, would you need to answer that question? (a) The values of the possible outcomes of the lotteries, the corresponding probabilities, and initial wealth of the individual. (b) The values of the possible outcomes of the lotteries and the corresponding probabilities. (c) The probabilities associated with each possible outcome and the initial wealth of the individual. (d) The values of the possible outcomes of the lotteries and the initial wealth of the indi- vidual. (e) No additional information is needed.
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- 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?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…Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.
- Suppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability ofwinning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. How much utility does one lose if one loses the gamble?1. Now, imagine that Port Chester decides to crack down on motorists who park illegally by increasing the number of officers issuing parking tickets (thus, raising the probability of a ticket). If the cost of a ticket is $100, and the opportunity cost for the average driver of searching for parking is $12, which of the following probabilities would make the average person stop parking illegally? Assume that people will not park illegally if the expected value of doing so is negative. Check all that apply. A. 9% B. 18% C. 17% D. 10% 2. Alternatively, the city could hold the number of officers constant and discourage parking violations by raising the fine for illegal parking. Suppose the average probability of getting caught for parking illegally is currently 10% citywide, and the average opportunity cost of parking is, again, $12. The fine that would make the average person indifferent between searching for parking and parking illegally is ____ , assuming that people will not…In the final round of a TV game show, contestantshave a chance to increase their current winnings of$1 million to $2 million. If they are wrong, theirprize is decreased to $500,000. A contestant thinkshis guess will be right 50% of the time. Should heplay? What is the lowest probability of a correctguess that would make playing profitable?
- 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.Becky is deciding whether to purchase an insurance for her home againtst burglary. the payoff for her is shown as follow: Net worth of her Net worth of her home: $ 20000 burglary(10%) Net worth of her Net worth of her home: $50000 burglary (90%) The insueance would cover all the loss from burlary and the insurance fee is $8000. Her utility funtion is given as u=w ^0.3 Should Beck purchase the insurance Explain.4. Marvin is given a number of choices between various lotteries where the possible outcomes include a vacation, a motorbike, a pair of shoes and a round of applause, or X = {v,m, s, a}. It is known that, according to Marvin's preferences, v > m > s > a. In addition, he claims he would be indifferent between the motorbike and a lottery that results in a vacation with probability 0.4 and a pair of shoes with probability 0.6, and he would furthermore be indifferent between a pair of shoes and a lottery that results in a motorbike with probability 0.5 and a round of applause with probability 0.5. Marvin has a utility function u: X → R (in other words u maps each element in X to a real number) and he in an expected utility maximiser (in other words his preferences conform to the axioms G1 to G6). 4.1. Assuming Marvin's claims about indifference are correct, derive u(m) and u(s) in terms of u(v) and u(a). 4.2. Von Neumann-Morgenstern utility functions are only unique up to positive affine…
- To go from Location 1 to Location 2, you can either take a car or take transit. Your utility function is: U= -1Xminutes -5Xdollars +0.13Xcar (i.e. 0.13 is the car constant) Car= 15 minutes and $8 Transit= 40 minutes and $4 What is your probability of taking transit given the conditions above? What is your probability of taking transit if the number of buses on the route were doubled, meaning the headways are halved? Remember to include units.2. Christiaan can go hiking, or he can stay at home. Hiking would be fun if nothing bad happens, but there is a risk if he goes hiking that he will meet a bear (not fun) or get bitten by a snake (very not fun). Christiaan decides that if there is a 5% chance of meeting a bear and a 1% chance of getting bitten by a snake, he would prefer to go hiking rather than stay at home. However, if the chance of meeting a bear is 10% and the chance of a snake bite is 5%, he definitely would rather stay at home. then (a) Consider the utility function: U (stay home) = 25, U (hike no event) = 100, U (hike & snake) -1000, U (hike & bear) = -200. Does this utility function represent Christiaan's pref- erences? Explain. (b) Suppose that the utility function in (a) does represent Christiaan's preferences. Would Christiaan prefer to hike or stay home if the probability of meeting a bear is 6% and the probability of being bitten by a snake is 4%? Show your work.When playing roulette at a casino, a gambler is trying to decide whether to bet $10 on the number 30 or to bet $10 that the outcome is any one of the three possibilities 00, 0, or 1. 3 The gambler knows that the expected value of the $10 bet for a single number is - 53¢. For the $10 bet that the outcome is 00, 0, or 1, there is a probability of 38 of making a net profit of $30 and a probability of losing $10. 35 38 a. Find the expected value for the $10 bet that the outcome is 00, 0, or 1. b. Which bet is better: a $10 bet on the number 30 or a $10 bet that the outcome is any one of the numbers 00, 0, or 1? Why? a. The expected value is $. (Round to the nearest cent as needed.) b. Since the expected value of the bet on the number 30 is C than the expected value for the bet that the outcome is 00, 0, or 1, the bet on is better.