Suppose that two investments have the same three payoffs, but the probability associated with each payoff differs, as illustrated in the table below: Probability (Investment B) Payoff $300 $250 $200 Probability (Investment A) 0.10 0.80 0.10 0.30 0.40 0.30 Nahoko has the utility function U= 51, where I denotes the payoff. Which investment should she choose?
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- First Player can invest $1.00 with Second Player (low reliance) or $2.00 (high reliance). Based on the payoffs shown below, what is the probability of performance that makes High Reliance optimal? Write your answer as a two digit integer. E.g., if the answer is 33%, write 33. Second Player Perform Breach Invest & Low Reliance 0.25 1.0 First Player 0.25 -1.0 Invest & High Reliance 0.5 1.0 0.75 -2.0A construction company needs to move lumber onto the roof of a building. If the lumber falls and hits someone it will cause $1,200,000 in damage. Assume that company must choose between the following levels of precaution: Spend $500 and the probability of an accident is .05 Spend $5,000 and the probability of an accident is .01 Spend $8,000 and the probability of an accident is .008 Spend $10,000 and the probability of an accident is .003 If the construction company is strictly liable for the costs of the accident, how much would they spend on precaution? A. $500 B. $5,000 C. $8,000 D. $10,000Consider a gamble/lottery in which a coin is tossed rapidly until a tail comes up. 2m rupee is given if the tail comes up at the mth toss. Let the individual be risk neutral, having u(x) = x where x is the amount of winning. Find the expected utility from the lottery.
- Y5 Alfred is a risk-averse person with $100 in monetary wealth and owns a house worth $300, for total wealth of $400. The probability that his house is destroyed by fire (equivalent to a loss of $300) is pne = 0.5. If he exerts an effort level e = 0.3 to keep his house safe, the probability falls to pe = 0.2. His utility function is: U = w0.5 – e where e is effort level exerted (zero in the case of no effort and 0.3 in the case of effort).a. In the absence of insurance, does Alfred exert effort to lower the probability of fire?HINT: Calculate and compare the expected utility i) with effort, and ii) without effort. If effort is exerted, then the effort cost is paid regardless of whether or not a fire occurs.b. Alfred is considering buying fire insurance. The insurance agent explains that a home owner’s insurance policy would require paying a premium α and would repay the value of the house in the event of fire, minus a deductible “D”. [A deductible is an amount of money that the…Suppose that a car - rental agency offers insurance for a week that costs $125. A minor fender bender will cost 34000 whereas a major accident might cost $16 comma 000 in repairs. Without the insurance, you would be personally liable for any damages. There are two decision alternatives: take the insurance, or do not take the insurance. You researched insurance industry statistics and found out that the probability of a major accident is 0.04% and that the probability of a fender bender is 0.18%. The expected payoff if you buy the insurance is $125.00. The expected payoff if you do not buy the insurance is $12.52. Develop a utility function for the payoffs associated with this decision for a risk-averse person. Determine the decision that would result using the utilities instead of the payoffs. Based on the expected payoffs, the best decision is to not purchase the insurance. Are these two decisions consistent?Given a choice between two investments with the same expected payoff: a. Most people will choose the one with the lower standard deviation b. Most people will opt for the one with the higher standard deviation c. Most people will be indifferent since the expected payoffs are the same d. Most people will calculate the variance to assess the relative risks of the two choices
- A risk-neutral plaintiff in a lawsuit must decide whether to settle a claim or go to trial. The defendants offer $50,000 to settle now. If the plaintiff does not settle, the plaintiff believes that the probability of winning at trial is 50% if the plaintiff wins, the amount awarded to the plaintiff is X Will the plaintif settle if x is $62,500? What if X-$250,000? What is the critical value of X that would make the plaintiff indifferent between setting and going to trial? it the plaintiff were risk averse instead of risk neutral, would this critical value of X be higher or lower? If the amount to be awarded at trial with a win (X) were $62,500, then the plaintiff would settle If the amount to be awarded at trial with a win (X) were $250,000, then the plaintiff would not settle The critical value of X that would make the plaintiff indifferent between settling and going to trial is $ (Enter your response using rounded to wo decimal places)The injured football player Bad news everyone! There is 1 second left in the game, and Tom Brady has injured himself. The matrices below depict the relative probabilities of winning givenan offensive and a defensive play call. (The row player is the New England Patriots and the column player is the opponent.) How much has the all star's home team probability of winning decreased due to the injury? Pass uny Patriots D Pass .4, .6 D Run .9,.1 .8,.2 .5,.5 Pass Run Opponent D Pass D Run .06, .94 .32, .68 .8,.2 .5,.5A risk-eutral plaintiff in a lawsuit must decide whether to settle a claim or go to trial. The defendants offer $70,000 to settle now. If the plaintiff does not settle, the plaintiff believes that the probability of winning at trial is 40%. If the plaintiff wins, the amount awarded to the plaintiff is X. Will the plaintiff settle if X is $87,500? What if X= $280,000? What is the critical value of X that would make the plaintiff indifferent between settling and going to trial? If the plaintiff were risk averse instead of risk neutral, would this critical value of X be higher or lower? If the amount to be awarded at trial with a win (X) were $87,500, then the plaintiff would settle If the amount to be awarded at trial with a win (X) were $280,000, then the plaintiff would not settle The critical value of X that would make the plaintiff indifferent between settling and going to trial is $. (Enter your response using rounded to two decimal places.)
- An author is trying to choose between two publishing companies that are competing for the marketing rights to her new novel. Company A has offered the author $10,000 plus $2 per book sold. Company B has offered the author $2,000 plus $4 per book sold. The author believes that four levels of demand for the book are possible are: 1,000, 2,000, 3000 and 5000 books are sold. If the probabilities of each level of demand are as follows: Demand Probability 1000 0.31 2000 0.32 3000 0.25 5000 0.12 Construct the payoff table for each level of demand for company X and company Y. What are the expected monetary value (EMV) and expected opportunity loss (EOL)? Hence determine the best decision that this author should do.A seller will run a second-price, sealed-bid auction for an object. There are two bidders, a and b, who have independent, private values v; which are either 0 or 1. For both bidders the probabilities of v; = 0 and v; = 1 are each 1/2. Both bidders understand the auction, but bidder b sometimes makes a mistake about his value for the object. %3| Half of the time his value is 1 and he is aware that it is 1; the other half of the time his value is 0 but occasionally he mistakenly believes that his value is 1. Let's suppose that when b's value is 0 he acts as if it is 1 with probability 1/2 and as if it is zero with 2 probability. So in effect bidder b sees value 0 with probability 1/4 and value 1 with probability 4. Bidder a never makes mistakes about his value for the object, but he is aware of the mistakes that bidder b makes. Both bidders bid optimally given their perceptions of the value of the object. Assume that if there is a tie at a bid of x for the highest bid the winner is…In a game, there are three values 1, 000, 2.500 and 5,000 and the cost of the game is 1, 500 . If each outcome has an equal probability of occurring, then what is the expected value of playing the game?