A principal is considering hiring a lawyer to represent him or her in a lawsuit. The principal gets $ 250 000 if the suit is won and $0 otherwise. If the agent works hard (100 hours), there is a 50% chance that the principal will win the suit. If the agent does not work hard (10 hours), there is a 15% chance that the principal will win the suit. Without a lawyer, the principal is sure to lose the suit. The principal can monitor the agent, and both parties are risk neutral. The agent's utility function is m-50e, where m is money in dollars and e is effort in hours. The agent's fee for this case is $100 per hour, and the outside opportunity is worth $500. Write down the game in extensive form and solve it.
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- 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!Matthew is playing snooker (more difficult variant of pool) with his friend. He is not sure which strategy to choose for his next shot. He can try and pot a relatively difficult red ball (strategy R1), which he will pot with probability 0.4. If he pots it, he will have to play the black ball, which he will pot with probability 0.3. His second option (strategy R2) is to try and pot a relatively easy red, which he will pot with probability 0.7. If he pots it, he will have to play the blue ball, which he will pot with probability 0.6. His third option, (strategy R3) is to play safe, meaning not trying to pot any ball and give a difficult shot for his opponent to then make a foul, which will give Matthew 4 points with probability 0.5. If potted, the red balls are worth 1 point each, while the blue ball is worth 5 points, and the black ball 7 points. If he does not pot any ball, he gets 0 point. By using the EMV rule, which strategy should Matthew choose? And what is his expected…First Fiddler's Bank has foreclosed on a home mortgage and is selling the house at auction. There are three bidders for the house, Ernie, Teresa, and Marilyn. First Fiddler's 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 $600,000, a probability of 1/3 of valuing at $500,000, and a probability of 1/3 of valuing it at $200,000. First Fiddler's believes that these probabilities are in de pendent among buyers. If First Fiddler's sells the house by means of a second- bidder, sealed- bid auction (Vickrey auction), what will be the bank's expected revenue from the sale? (Choose the closest option.) The closest option is 448, 148. Please explain in details thank you.
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- You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $1 million to $3 million. If they are wrong, their prize is decreased to $750,000. You believe you have a 25% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is [$ blank]. Given that this is positive [blank (positive/negative)], you should [blank (should/should not)] play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is [blank]. (Hint: At what probability does playing the final round yield an expected value of zero?)The table below shows that a sales agent can work with either low, or high amount of effort. Low effort generates$30,000, $60,000 or $100,000 profit (with probability given below), while high effort generates 60,000; 100,000 or 150, 000 (with probability given below) depending on some random factors. Bad luck (P=0.3) Medium luck (P=0.3) Good luck (P=0.4) Low effort (a=0) $30,000 $60,000 $100,000 High effort (a=1) $60,000 $100,000 $150,000 The cost of low effort is 0 and the cost of high effort is $10,000 (Formally, c=$10,000a). The net wage is wage minus cost of effort and the net profit is total profit minus wage. Suppose the firm offers the repair person a fixed wage of 13,000, what will be the net wage of the repair person and the net profit of the owner? Suppose now the owner offers the repair person the following bonus arrangement What will be the net wage of the repair person? What will be the net profit of the owner? Specify…A thousand used cars are for sale in Boston. Some of the cars are of good quality (“plums”), and some are not (“lemons”), but the buyer cannot tell the difference between the two qualities; of course the seller knows whether the car is a lemon or a plum. Suppose that consumers are willing to pay $4,000 for a lemon and $6,400 for a plum; and sellers are willing to sell a lemon for $3,500 and a plum for $5,600. a. If there is a 40% chance that a car is a lemon, how many cars will be sold? And what is the maximum consumer surplus in this case. b. If there is a 10% chance that a car is a lemon, how many cars will be sold? And what is the maximum consumer surplus in this case? Kindly answer in detail with all steps and answer should b typed not hand written.