Paul hires Amy to manage his bakery shop. The following table gives the shop's profits (without subtracting payments to Amy) under 2 different levels of Amy's effort and two different states of the world (good and bad weather). There is a 50% probability that the weather will be good. Bad weather (50%) Good weather (50%) Low Effort High Effort 300 The cost of low effort is 10 and the cost of high effort is 41. Paul offers a fixed salary of 100 and bonus B if revenue is strictly higher than 300. What is the value of the lower bound of B, above which Amy would be incentivized to put in high effort? 100 300 500
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- 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…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?For the following questions consider this setting. The deciding shot in a soccer game comes down to a penalty shot. If the goal-keeper jumps in one corner and the striker shots the ball in the other, then it is a goal. If the goalie jumps left and the striker shoots left, then it is a goal with probability 1/3. If the goalie jumps right and the striker shots right, it is goal with probability 2/3. QUESTION Say the goalie's strategy is to jump left with probability 1 and the striker shoots left with probability 0.5, then the probability of a goal is (round to two digits) QUESTION If the striker shoots in either corner with probability 0.5 and the goalie likewise shoots in either corner with probability 0.5, then the probability of a goal is (round to 2 digits)
- Max is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $15,000. With probability p = 0.7 the palace will succeed and Max's wealth will grow from $15,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $10,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $15,000 with certainty? (Please round your final answer to the whole dollar, if necessary)For the following questions consider this setting. The deciding shot in a soccer game comes down to a penalty shot. If the goal-keeper jumps in one corner and the striker shots the ball in the other, then it is a goal. If the goalie jumps left and the striker shoots left, then it is a goal with probability 1/3. If the goalie jumps right and the striker shots right, it is goal with probability 2/3. Say the goalie's strategy is to jump left with probability 1 and the striker shoots left with probability 0.5, then the probability of a goal is (round to two digits) If the striker shoots in either corner with probability 0.5 and the goalie likewise shoots in either corner with probability 0.5, then the probability of a goal is (round to 2 digits)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!
- Roger's utility/u as a function of wealth/w is u = { ln w, w < 1600 w1/2, w >= 1600 Roger has $1000 and 3 options. 1. spend $400 to enter the game with probabilities of winning or losing: Win/(Lose) (500) 0 1000 3000 P(Win/(Lose)) 0.2 0.1 0.6 0.1 a. Show with workings which option roger would choose.Consider a risk averse individual who has utility function u(a) which is increasing with u(0) = 0. There are two risky assets: A,B. For A, every dollar invested gives return $0 with probability 1/3 and $3 with probability 2/3. For B, every dollar invested gives return is $0 with probability 1/4 and $3 with probability 3/4. The individual has $120 to invest. Consider two investment choices: (1) invest entire $120 in A and (2) invest $60 in A, $60 in B. (a) Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 1. (b)Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 2 when return from A is bad. (c) Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 2 when return from A is good. (d) Drawing diagram of the utility function and showing your work, determine the…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…
- 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.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 stepsHow much is his risk on any random day due to late arrival?