Q1. Consider the adverse selection model, where the ability of each worker, 0, can be 1, 2 or 5. Workers observe their own abilities, but firms only observe the overall distribution of probabilities (1/3, 1/6, 1/2). Suppose that the reservation value is r(0) = 0.5+0.50. (a) What is the range of wages, for which all workers accept the competitive wage? What is expected productivity in this case? What is the range of possible wages for which a firm hires a random worker? Will there be a functioning labor market in this case? (b) What is the range of wages, for which no workers accept the competitive wage? (c) What is the range of wages, for which only lowest type workers accept the competitive wage? What is expected productivity in this case? What is the range of possible wages for which a firm hires a random worker in this case? Will there be functioning labor market? 2140
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- Give typing answer with explanation and conclusion 1. If wH=100 and wL=36 and U(w)=w^1/2. Further, let the reservation utility be 7. (a) What is the minimum probability for which the wage earner accepts the contract? (b)Let p=3/4. What is the maximum cost of effort for which the tenant accepts the contract?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?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…
- Suppose there are two types of workers. Type 1 workers have a marginal product of labor (MPL) = 1. That is, if a firm hires an extra Type I worker, that worker will produce 1 extra unit of output. Type II workers have a MPL = 2. The firm can sell each extra unit of output for P = $12,000. Firms are unable to identify whether or not a worker is Type I or Type Il unless the worker sends a signal of what type they are. The signal that workers can send is a level of education, e. The firm adopts the following hiring strategy: If e >e* then offer the worker a wage rate equal to $24,000. If e < e* then offer the worker a wage rate equal to $12,000. The cost to Type I workers of getting education level e is $4000*e. The cost to Type II workers of getting education level e is $2000*e. If the firm sets e* = 8, which of the following statements is true? O Type I workers will not get e*, but Type II workers will get e*, which means there is a separating equilibrium. O Neither type of workers will…A firm's revenue R is stochastically related to the effort exerted by its employee. Effort is a continuous variable. The employee can choose any level of effort e e [0, c0). The choice of effort affects revenue so that: E(R|e) = e and Var(R|e) = 1 where E(R|e) and V ar(R|e) denote the expected value and variance, respectively, of rev- enue when the employee exerts effort level e. The employer cannot observe the level of effort exerted by the employee. The employer wants to design a wage contract w based on the revenue and considers only contracts of the form: w = a + BR, and so the employee is guaranteed a payment a and then a bonus payment ßR which de- pends on revenue. The employee is a risk-averse expected utility maximiser. A contract w gives expected utility: Eu(w\e) = E(w\e) – oV ar(w\e) – c(e) where E(w|e) and V ar(w|e) denote the expected value and variance of the contract, re- spectively, conditional on effort e, p is a parameter of risk aversion, and c(e) denotes the…A firm's revenue R is stochastically related to the effort exerted by its employee. Effort is a continuous variable. The employee can choose any level of effort e e [0, 0). The choice of effort affects revenue so that: E(R|e) = e and Var(R|e) = 1 where E(R|e) and Var(R|e) denote the expected value and variance, respectively, of rev- enue when the employee exerts effort level e. The employer cannot observe the level of effort exerted by the employee. The employer wants to design a wage contract w based on the revenue and considers only contracts of the form: W-α + βR, and so the employee is guaranteed a payment a and then a bonus payment BR which de- pends on revenue. The employee is a risk-averse expected utility maximiser. A contract w gives expected utility: 1 Eu(w\e) = E(w\e) - jeV ar(w\e) – c(e) pV. where E(wle) and Var(w|e) denote the expected value and variance of the contract, re- spectively, conditional on effort e, p is a parameter of risk aversion, and c(e) denotes the…
- 1) Consider observable effort. Assume that if the Agent does not accept the wage the Principal offers his outside option gives him a net utility of v =2. The probability of high profit under e=1 is %, the probability of high profit under low effort is 1/4. Calculate the minimum wage that the agent will accept to work and supply the asked effort when the Principal asks him to supply e=0, and e=1. Let us call these wages wo and wi. Now, assume that instead of offering him a flat wage, the Principal is offering the agent a wage schedule (, w) where the agent receives when the (gross) profit is High and w when the (gross) profit is low. Calculate all the lowest cost wage schedules the agent will accept to supply e=1, and e=D0. Does the principal's expected net profit change when he pays the minimum cost wage schedule instead of the flat wage minimum cost wage? Explain the intuition for your answer.QUESTION 12 Suppose that a worker value jobs by both the wage rate and the workplace collegiality. The woker's utility is strictly increasing in the wage rate but strictly decreasing in the chance of being bullied in the workplace. The utility function of the worker is U = wa (1- ), where a = 0.5, w is the wage rate and b is the probability that a worker is bullied in a workplace. Suppose for a typical job A, the chance of getting bullied is 0.01, and the wage rate is 100. Which of the following statements is correct? If job B offer w = 121 and b = 0.04, the worker would prefer job B to job A %3D If job B offer w = 144 and b = 0.09, the worker would prefer job B to job A %3D If job B offer w = 80 and b = 0, the worker would prefer job B to job A If job B has bullying probablity b = 0.04, the worker is indifferent between job A and job B. Then, the compensating wage differential of job B is at least 25. %3D If job B offer w = 80 and b = 0, the worker would be indifferent between job A…For Group A the cost of attaining an educational level y is CA(y) = $6,000y and for Group B the cost of attaining that level is CB(y) = $10,000y. Employees will be offered $50,000 if they have where y* is an education threshold determined by the employer. They will be offered $130,000 if they have An employer who only wants to hire individuals who find learning less costly can do so by choosing y* to be anywhere between:
- 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? Solve it early I upvote.Suppose workers can be divided into two groups: high and low skill workers. Let y be the number of years of college education of a worker. For workers in Group A (high skill workers) the cost of attaining an educational level y is CA(Y)=$25y; for workers in Group B (low skill workers) the cost of attaining an educational level y is CB(y)=$65y. Employees will be offered $350 if they have y ≥ y*, where y* is an educational threshold determined by the employer. They will be offered $50 if they have y y* zQ) 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 early