1. Consider the figure below, which depicts the matching of jobs and workers. There are two jobs at firms X and Y and two workers A and B. Wage Rate B2 Way R WAX RAX Ray Risk of Injury a. Which worker is more risk averse? A or B? Which job does he take? How much does he carn? What is the highest utility he can achieve given the job opportunities?
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- 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…Both jobs provide base salary and commissions. Base salary is garunteed But the probability of getting the commissions is 50% every month Job 1 base salary is 1k but commission is 3k Job 2 base salary is 2k but commission is 1k A) Calculate the expected value for both jobs. b.whats the standard deviation for both jobs. C) Use utility-income diagram to show if the applicant is risk-averse, which job should he accept and why.7 3. How would the utility of a risk lover look like? a. Graph the utility function. Will this person be willing to pay for insurance?
- 4. A taproom owner is trying to determine how to structure his manager's compensation. One option he considers is a flat salary of $70,000 per year. The second option is a base salary of $30,000 plus 15% of the taproom's profit. If the manager puts a lot of effort into her job, the taproom's annual profit will be $500,000 with 75% probability and $100,000 with 25% probability. If the manager exerts only modest effort, the taproom's profit will be $500,000 with 25% probability and $100,000 with 75% probability. The manager's opportunity cost of putting a lot of effort into her job is $50,000, while her opportunity cost of exerting only modest effort is $25,000. a. Draw the game tree for the interaction between the taproom owner and the manager. Assume that the taproom owner moves first. b. What is the equilibrium outcome for this game? What kind of contract should the taproom owner offer? What level of effort will the manager choose? Explain.The manager of XYZ Company is introducing a new product that will yield N$1000 in profits if the economy does not go into a recession. However, if a recession occurs, demand for normal good will fall so sharply that the company will lose N$4000. If economists project that there is a 10 percent chance the economy will go into a recession, what are the expected profits to XYZ Company of introducing the new product? How risky is the introduction of the new product?23. Captain Kidd has a map that has a 20% probability of leading him to a treasure worth 400,000 guineas. Independent of the fact of having a map, Capitan Kidd already has his own income equal to 90,000 guineas. Another pirate wants to buy the map from the Capitan Kidd (after selling the map Capitan Kidd has no chance to find a treasure). What is the minimum price for a map which the Captain Kidd will accept if Capitan Kidd has von Neuman- Morgenstern utility function is U(w) = w0.5, where w is his income level? a) 54,400 b) 32,500 c) 45,000 d) 90,000 e) There is no correct answer
- Bob earn 60,000 a year and an accounting firm each year he receives Reyes Bob has determined that the probability that he receives a 10% raise is .7 the probability that he earns a 3% raise is .2 and the probability that he earns a 2% raise is .1 a competing company has offered Bob a similar position for 65,000 a year Bob wonders if he should take the new job or take his chances with his current job. a. Find the mathematical expectation of the dollar amount of his raise at his current job b.Economics Shawn's consumption is subject to risk. With probability 0.75 he will enjoy 10000 in consumption, but with probability 0.25 he will have only 3600. His utility function for consumption is given by v(c) = Vc. -What is the expected value of Shawn's consumption? -What is his expected utility? -What is his certainty equivalent of having 10000 with probability 0.75 and 3600 with probability 0.25?Jamal has a utility function 1/2 U W5 , where W is hiswealth in millions of dollars and U is the utility heobtains from that wealth. In the final stage of agame show, the host offers Jamal a choice between(A) $4 million for sure and (B) a gamble that pays$1 million with probability 0.6 and $9 million withprobability 0.4.a. Graph Jamal’s utility function. Is he risk averse?Explain.b. Does A or B offer Jamal the higher expectedprize? Explain your reasoning with appropriatecalculations. (Hint: The expected value of arandom variable is the weighted average of thepossible outcomes, where the probabilities arethe weights.)c. Does A or B offer Jamal the higher expectedutility? Again, show your calculations.d. Should Jamal pick A or B? Why?
- Choice under uncertainty. Consider a coin-toss game in which the player gets $30 if they win, and $5 if they lose. The probability of winning is 50%. (a) Alan is (just) willing to pay $15 to play this game. What is Alan’s attitude to risk? Show your work.(b) Assume a market with many identical Alans, who are all forced to pay $15 to play this coin-toss game. An insurer offers an insurance policy to protect the Alans from the risk. What would be the fair (zero profit) premium on this policy? i need help with question B please.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?2. Consider a cheap talk game in which Nature moves by choosing a sender's type, where the type space has four elements: −1, 1, 2, and 3, each occur- ring with equal probability of 1½. The sender learns his type and chooses one of three possible messages: bumpy, smooth, and slick. The receiver observes the sender's message and then chooses one of three actions: 0, 5, and 10. The sender's payoff equals his type multiplied by the receiver's action. The receiver's payoff equals the sender's type multiplied by twice the receiver's payoff. a. Find a separating perfect Bayes-Nash equilibrium. b. Find a semiseparating perfect Bayes-Nash equilibrium.