irst 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 -1.0 0.25 Invest & High Reliance 0.5 1.0 0.75 -2.0
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- In a final round of a MegaMillion TV show, a contestant has won $1 millionand has a chance of doubling the reward. If he loses his winnings drop to$500,000. The contestant thinks his chances of winning are 50%. Should heplay? What is the lowest probability of a correct guess that will make his betprofitable? Show workYou have determined that your risk tolerance is 60. Calculate your utility for the following payoffs: (Round your answers to 2 decimal places.) Payoff Utility 8 15 20Bill owes Bob $36. Just before Bill pays him the money, he gives Bob the opportunity to play a dice game to potentially win more money. The rules of this game are as follows: If Bob rolls doubles (probability 1/6), Bill will Bob double ($72). If he misses doubles on pay the first try, he can try again or settle for half the money ($18). If he makes doubles on the second try Bill will again pay-up double ($72), but if Bob misses doubles on the second try Bill will only pay him one-third ($12). Should Bob decide to play the dice game with Bill, or insist that he pay the $36 now? Use a decision tree to support your answer.
- Consider a game where there is a $2,520 prize if a player correctly guesses the outcome of a fair 7-sided die roll.Cindy will only play this game if there is a nonnegative expected value, even with the risk of losing the payment amount.What is the most Cindy would be willing to pay?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?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.
- A Bank has foreclosed on a home mortgage and is selling the house at auction. There are two bidders for the house, Zeke and Heidi. The bank does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $800,000, a probability of 1/3 of valuing at $600,000, and a probability of 1/3 of valuing it at $300,000. The bank believes that these probabilities are independent among buyers. If the bank sells the house by means of a second- bidder, sealed-bid auction, what will be the bank’s expected revenue from the sale? The answer is 455, 556. Please show the steps in details thank you!Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. The game consists of tossing a coin. The player gets a payoff of 2^n where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses yields TTTH, you get a payoff of 2^4 this payoff occurs with probability (1/2^4). Compute the expected value of playing this game. Next, assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game? Finally, what is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function (found in Data, What-If Analysis) in Excel.Shimadzu, a manufacturer of precise scientific instruments, relies heavily on the efforts of its local salespeople. Selling an instrument requires either luck, high effort, or some combination of the two. A salesperson who chooses to work hard (put in high effort) has a 40 percent chance (probability of 0.4) of selling an instrument in a given year while a salesperson who chooses to slack off (put in low effort) has a 20 percent chance (probability of 0.2) of making a sale. Practically no one manages to sell more than one instrument in a single year. Contracts for salespeople are designed on a year-by-year basis. Sales staff members do not mind risk; they choose employers based only on expected wage and the disutility of effort. Disutility of effort is equivalent to $20,000 per year if they work hard and $0 if they slack off. Even if a salesperson slacks off, he or she requires a salary of at least $50,000 not to seek alternate employment. (So, the worker's net payoff in alternative…
- 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)A 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.)Find an equilibrium in the following game, with Nature moving first, with fixed probabilities as shown. (0,2) (2,2) B Q 2 (4,0)N N (6,0) .1 (0,0) (2,0) F .9 F B Q (6,2) N 2 1 -(4,2)