Derive the utility function of a worker who is aiming to maximize his utility in the market for risky jobs. Explain and illustrate graphically how this worker will be making his choice among different alternatives of risk/wage combinations.
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Derive the utility function of a worker who is aiming to maximize his utility in the market for risky jobs. Explain and illustrate graphically how this worker will be making his choice among different alternatives of risk/wage combinations.
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- Consider a competitive economy that has four different jobs that vary by their wage and risk level. The table below describes each of the four jobs.Job Risk ( r ) Wage ( w)A 1/5 $ 3B 1/4 $12C 1/3 $23D 1/2 $25All workers are equally productive, but workers vary in their preferences. Consider a worker who values his wage and the risk level according to the following utility function:u(w, r) = w + 1/r2Where does the worker choose to work? Suppose the government regulated the workplace and required all jobs to have a risk factor of 1/5 (that is, all jobs must become A jobs). What wage would the worker now need to earn in the A job to be equally happy following the regulation?Jim Range is the manager at a USPS office which requires arduous physical labor of their employees. Jim wants to hire an employee. During the interview, Sofia Caster tells Jim that she is a hard worker. But Sofia Caster realizes once she is hired that the federal government and its agencies cannot fire their employees unless their performance is extremely poor. She thus decides to work minimally as a result of this information. The problem was created because of? Misaligned incentives. Moral hazard. A OB c Asymmetric information. OD. The principle agent problem.There are 50 workers in the economy in which all workers must choose to work a safe or a risky job. When it comes to accepting a risky job, Worker 1’s reservation price is $5; worker 2’s reservation price is $6, worker 3's reservation wage is $7, and so on. Assume there are exactly 12 risky jobs. (a) What is the equilibrium wage differential between safe and risky jobs? Which workers will be employed at the risky firm? (b) Suppose now that an advertising campaign, paid for by the employers who offer risky jobs, stresses the excitement associated with “the thrill of injury,” and this campaign changes the attitudes of the work force toward being employed in a risky job. Worker 1 now has a reservation price of $1, worker 2’s reservation price is $2, and so on. There are still only 12 risky jobs. What is the new equilibrium wage differential? c) What is the maximum the firm should be willing to pay for its ad campaign?
- Suppose Lesley is deciding on career paths. She could choose career A, which earns $50,000 per year and has a 10% chance of layoff each year, or career B, which earns 80,000 per year and has a 30% chance of layoff each year. When laid off, she earns 0. Suppose her utility over annual earnings is equal to U(E) = VE (a) What would be her preferred job if she had to choose one or the other? If she could allocate her time to both jobs (e.g., could spend 90% of time in job A and 10% in job B) what would be her ideal allocation of time between jobs?Q) Suppose that utility for a worker is u(w)=w^.5. If the wage (w) offered is $64, there is a 50% chance of being fired, and switching costs are $28. What is the expected utility for the worker? Explain it earlySuppose an individual can decide between two careers: (1) a surgeon and (2) a business analyst. Salaries for four periods a displayed in the table below. OCCUPATION Surgeon Period 0 -$40 Business Analyst -$10 Period 1 $100 $41 SALARY Period 2 $115 $43 Period 3 $300 $45 (Questions) (a) Assume the individual's discount factor is 0.90. Calculate the net present value of becoming a surgeon. Show all steps to your work. (b) Again, assume the individual's discount factor is 0.90. However, this time, calculate the net present value of becoming a business analyst. Show all steps to your work. (c) For which occupation did the individual have a higher net present value (NPV)? Based on this information, discuss potential intrinsic characteristics that this person might have? (d) Explain why a large internal rate of return for an occupation, such as being a surgeon, can persist over a long period of time.
- Paul has a utility function of U =[ i to the power 1/2] with income measured in thousands. He will get a job that either pays 25 thousand a year or 64 thousand a year. What is his expected utility, expected payoff, the utility of his expected payoff, and her risk premium? Additionally, plot Paul's utility and income. Show and label his utility curve, his expected utility, and risk premium.A firm is considering adopting a plan in which it would pay employees less than their MRPL early in their careers and more than their MRPL late in their careers. For a typical worker at the firm MRPL = 10 + 0.1T, where T = the number of years which the worker has been employed at the firm and MRPL is measured in dollars per hour. The worker’s wage per hour is W = 8 + 0.2T. Assume that this wage is high enough to attract workers from alternative jobs, that the discount rate for the firm is zero, and that the expected tenure of a typical worker is 35 years. If workers retire after 35 years, will this plan be profitable for the firm? Explain. For how many years will the firm “underpay” it workers? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Sophie is offered a performance based wage that will either be equal to $4,200 or to $3,600, each with a probability of 50%. Sophie says that getting $3,900 for certain would be as good as being offered that random wage. Which, of the following sentences, is true? options: Sophie is risk averse and her risk premium is zero. Sophie is risk neutral and her risk premium is zero. Sophie is risk averse and her risk premium is $300. Sophie is risk neutral and her risk premium is $300.
- Suppose you manage a factory with ten workers. Each worker’s output is determined by the equation q = e. Output sells in the market for a price of 40. The firm has fixed cost equal to 800, and variable costs aside from labor are 8 per unit of output. Worker utility is U = w – e2. Suppose you are paying workers a wage equal to bq. What is the profit- maximizing value of b? Suppose that the probability of worker error increases as the worker increases effort, and that worker error results in unusable output. Suppose that the probability of worker error is Pr[Error] = e/10. Then for worker effort level e, expected (usable) output is now determined by the equation E[q] = (1-Pr[Error]) x e. However, the problem is that you cannot detect errors until after the product is shipped to customers, meaning you pay workers for output before you know whether it is usable or not, and you have to refund your customers for unusable output. Demonstrate why you should not pay your workers the same…Question 13 Consider a market in which there are two types of workers L and H. Each type of worker has a different level of productivity, but that productivity is unobservable ex ante to potential employers. Before seeking employment at a firm in the market, all workers can (if they choose) get some level of education e. This choice of education e is observable to all, including potential employers. Assume that the market is competitive, so expected profits must be zero in equilibrium. The L-type workers have a productivity of 2 if they work for a firm in the market. They also have an outside option of 2. The utility function of the L-type workers UL - wL- eL, where wl is the wage received and eL is the level of education they obtain. The H type worker has an outside option of 2 and a productivity of 4 if they are employed by a firm in the market. The utility function for a H-type worker is UH=wH - (%)eH, where wH is the wage paid to a H-type and eH is the education they choose to get.…2. Suppose, as in class, that the utility function of a worker is U (w, e) = Vw - e, where w is the wage and e € {0, .8} is the level of effort. Suppose the reservation utility is 1. Suppose the outcome is $10 or $0 and that the probability of the $10 outcome is .6 if the worker works hard and .2 if the worker chooses low effort. (a) If you could costlessly monitor the worker's effort, would you want the worker to work hard? What payments would you offer and for what effort?