You need to hire some new employees to staff your startup venture. You know that potential employees are distributed throughout the population as follows, but you can't distinguish among them: Employee Value $30,000 $49,000 $68,000 $87,000 Probability 0.25 0.25 0.25 0.25 The expected value of hiring one employee is $ Suppose you set the salary of the position equal to the expected value of an employee. Assume that employees will not work for a salary below their employee value. The expected value of an employee who would apply for the position, at this salary, is $ Given this adverse selection, your most reasonable salary offer (that ensures you do not lose money) is

You need to hire some new employees to staff your startup venture. You know that potential employees are distributed throughout the population as follows, but you can't distinguish among them: Employee Value $30,000 $49,000 $68,000 $87,000 Probability 0.25 0.25 0.25 0.25 The expected value of hiring one employee is $ Suppose you set the salary of the position equal to the expected value of an employee. Assume that employees will not work for a salary below their employee value. The expected value of an employee who would apply for the position, at this salary, is $ Given this adverse selection, your most reasonable salary offer (that ensures you do not lose money) is

Brief Principles of Macroeconomics (MindTap Course List)

8th Edition

ISBN:9781337091985

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter9: The Basic Tools Of Finance

Section: Chapter Questions

Problem 9PA

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Consider an insurance contract with the premium r=$200 and payout q=$800. a.) John has healthy-state income IH = $900 and sick-state income IS = $100. He has probability of illness p = 0.2. Is the contract fair and/or full for John? What is John’s expected income WITHOUT this insurance contract? What is John’s expected income WITH this insurance contract?
Suppose there are two types of people, high ability and low ability. A high-ability person's productivity is valued at wH = $100,000, while a low-ability person's productivity is valued at wL = $50,000. Assume that the employer does not know the ability of a job applicant, but knows that the probability of an applicant being high ability is 50%. Assume next that only high ability applicants can send a signal, i.e., obtain a degree. The employer pays the expected wage. i. What is the wage oer in a pooling equilibrium (no applicant attains a degree)? ii. What is the wage oer in a separating equilibrium (only high-ability applicants attain a degree)? iii. Suppose now both types can attain a degree, but it is costlier to attain for low-ability people and costs them cL = $60,000, while it costs high-ability people cH = $40,000. Is a separating equilibrium where only high-ability people send education as a signal possible? Explain.
An individual has 40,000 in income per year. The person will get sick with probability 0.1. If he does get sick, the medical bills will total 30,000. The following tables shows the utility derived from certain amounts of income: Income Utility40,000 20037,000 19535,000 19030,000 17020,000 14010,000 100Considering the probability of illness, what is the expected utility of income without insurance? Show your work.
The Healthcare Managers Team Challenge Question: Considering the same graph above, and assume that the probability of a hurricane in Springfield is 23% this coming summer: a) calculate the expected wealth and utility of the Simpson's residence; b) explain why Homer Simpson is likely to buy insurance, or why he might not be wanting to buy insurance. Note that if the hurricane takes place the value of the Simpsons' wealth will be $10,000. but if there is no hurricane, their wealth will remain at $20,000.
Wanda works as a waitress and consequently has the opportunity to earn cash tips that are not reported by her employer to the Internal Revenue Service. Her tip income is rather variable. In a good year (G), she earns a high income, so her tax liability to the IRS is $5000. In a bad year (B), she earns a low income, and her tax liability to the IRS is $0. The IRS knows that the probability of her having a good year is 0.6, and the probability of her having a bad year is 0.4, but it doesn’t know for sure which outcome has resulted for her this tax year. In this game, first Wanda decides how much income to report to the IRS. If she reports high income (H), she pays the IRS $5000. If she reports low income (L), she pays the IRS $0. Then the IRS has to decide whether to audit Wanda. If she reports high income, they do not audit, because they automatically know they’re already receiving the tax payment Wanda owes. If she reports low income, then the IRS can either audit (A) or not audit…
Consider the model of competitive insurance. Peter is a risk averse individual with the utility function u(w) = w0.5. His current wealth is $300 and with probability 1/2 he will incur a loss of D = $240, but with probability 1/2 he will incur no loss. Ann has the same utility u(w) = w0.5 and current wealth $300 as Peter, but a different probability of loss: she will incur a loss of D = $240 with probability 0.3, and no loss with probability 0.7. In the separating equilibrium Peter is offered actuarially fair full insurance contract, so his wealth is equal to $180, whether loss happens or not. What amount of insurance (approximately) will Ann be offered an insurance contract with?
Suppose that Mira has a utility function given by U=2I+10√I. She is considering two job opportunities. The first job pays a salary of $40,000 for sure. The second job pays a base salary of $20,000 but offers the possibility of a $40,000 bonus on top of your base salary. She believes that there is a probability of p=0.50 that she will earn the bonus. What is the expected salary of the second job? Which offer gives Mira a higher expected utility? Based on this information, is Mira risk adverse, risk neutral, or risk-loving?
Natasha has utility function u(I) = (10*I)0.5, where I is her annual income (in thousands). (a) Is she a risk loving, risk averse or risk neutral individual? She is [risk loving, risk adverse, risk neutral] , as her utility function is [concave, convex, linear] (b) Suppose that she is currently earning an income of $40,000 (I = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000. She should [take, not take] the new job because her expected utility of (approximately) [18.27,19.82,20,20.95,21.14] is [greater than, less than, equal to] her current utility of [18.27,19.85,20,20.95,21.14] .
Question 4 Suppose a prosecutor expects to convict a defendant with probability 0.5 and that the sentence on conviction is 10 years in prison. Assume the prosecutor values prison time at $1,000 per year (its value as a deterrent of crime), and incurs a cost of trial equal to $2,000. a. What is the minimum prison sentence the prosecutor will o er as part of a plea bargain if her objective is to maximize the expected value of the sentence imposed, less the cost of trial (ignore the information provided in b. below to answer this question a.)? b. Suppose the defendant believes his chances of being convicted are 0.3, his cost of prison time is $5,000 per year, and his cost of a trial is $1,000. Will he accept the plea bargain in a.?
Khalid has a utility function U = W1/2, where W is his wealth in millions of dollarsand U is the utility he obtains from the wealth. In a game show, the host offershim a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with probability 0.6 and $9 million with probability 0.4.i. Graph Khalid’s utility function with the help of above utility function. Ishe risk lover? Explain. ii. Does A or B choice offer Khalid a higher expected prize? Explain yourreasoning with appropriate calculations. iii. Does A or B offer Khalid a higher expected utility? Again, show yourcalculations. iv. Should Jamal pick A or B choice? Why?
Leora has a monthly income of $20,736. Unfortunately, there is a chance that she will have an accident that will result in costs of $10,736. Thus leaving her an income of only $10,000. The probability of an accident is 0.5. Finally assume that her preferences over income can be represented by the utility function u(x) = 2ln(x).a) What is the expected income? What is Leora’s expected utility (you may leave in log form)? b) What is the certainty equivalent to her situation? What is the risk premium associated with her situation?c) What is the maximum that Leora would be willing to pay for a full insurance policy?d) Illustrate her expected utility, expected wealth, certainty equivalent, the risk premium and her willingness to pay for a full insurance policy in a diagram.
Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.