LABOR ECONOMICS
8th Edition
ISBN: 9781260004724
Author: BORJAS
Publisher: RENT MCG
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Question
Chapter 5, Problem 6P
To determine
Determine where the worker choose to work.
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Emma (the agent) works for Rachel (the principal). Emma's utility function is given by U=C0.5 if she doesn't work hard, and U=C0.5-3.0 if she works hard. If Emma works hard, the expected profit for Rachel increases from $1000 to $1500. Rachel cannot directly tell whether Emma works hard or not.
Rachel wants Emma to work hard. Rachel is willing to pay Emma a flat salary of $144 plus a bonus. Since the expected profit increases from $1000 to $1500, Rachel is willing to pay some percentage of this excess $500 to Emma if the profit turns out to be $1500. That is, a bonus to Emma is in the form of $500*x, where x is a fraction between 0 and 1. To induce Emma to work hard, x must be greater than or equal to some percentage. Answer this number as % and up to 2 decimal places. (That is, your answer should be between 0 and 100.)
A firm wants to hire a worker. The worker can choose two effort levels: "work" or "shirk". The result of the workers effort is
an output for the firm, which may take two levels: YL = 50 USD or YH = 100 USD (YL = low output, YH = high output).
The actual output depends both workers effort and pure luck. Either level of output can occur if the worker works or
shirks, but the lower output is more likely if the worker shirks. Below are the probabilities of the output levels as a
function of the workers effort: shirk: probability of output 100 USD = 1/5shirk: probability of output 50 USD = 4/5work:
probability of output 50 USD = 1/5work: probability of output 100 USD = 4/5The firm cannot observe the effort, hence
it cannot specify the desired effort in the contract. It may only specify the wage as a function of the observed output.The
workers expected utility is given by V = h krát odmocnina z (Wh C) + I krát odmocnina z (WI- C), where h, I and Wh
and WI denote the probabilities and wages…
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?
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- Assume, in producing one unit of a good X, an agent can exert either the good effort (G) or the bad effort (L), which cause production defects with probability 0.25 or 0.75 respectively. His utility function in effort e and wage w is U(w, e) = 100 (10/w) - c(e) where c(G) = 2 for the good effort and c(L) = () for the bad effort. Production defects are contractible and so can be included in the agent's contract, but effort is not contractible. Good X sells for $20 if there are no defects and $0 otherwise. The principal is risk-neutral and likes profit. Assume the agent has a reservation utility/outside option of U=0. Assume for this question that the principal wants to achieve the good effort and that effort is not contractible. Assume the principal offers an optimal 2 part contract {ws, Wf}, where we is paid if there are no defects and Wf is paid if there are any defects. What is the principal's expected profit under the optimal contract in this case? Answer to at most 2 decimal places…arrow_forwardSuppose 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…arrow_forwardConsider an overtime rule that requires that workers get paid double for any weekly hours over 40. Draw a picture that shows how a worker decides how much to work. Label everything in your picture and explain what is happening. Consider an investment that costs $100 and pays back $10 each year as long as the person making the investment is alive. Construct an equation for the net present value of the investment. An individual has a utility function, U = AX1 X2 where X1 and X2 are consumption of goods 1 and 2. The individual also faces a budget constraint. Show mathematically how an increase in Aa§ects the individualís decisions about consumption of each good.arrow_forward
- Assume, in producing one unit of a good X, an agent can exert either the good effort (G) or the bad effort (L), which cause production defects with probability 0.25 or 0.75 respectively. His utility function in effort e and wage w is U(w, e) = 100 (10/w) c(e) where c(G) = 2 for the good effort and c(L) = () for the bad effort. Production defects are contractible and so can be included in the agent's contract, but effort is not contractible. Good X sells for $20 if there are no defects and $0 otherwise. The principal is risk-neutral and likes profit. Assume the agent has a reservation utility/outside option of U=0. If effort is not contractible then:: Select one: O a. There is insufficient information to know the principal's choice of contract because we do not know the agent's level of absolute risk aversion. O b. the principal will be indifferent between writing a contract to achieve the good effort level and writing a contract to achieve the bad effort level O c. the principal will…arrow_forwardTen workers work jointly on a project. All 10 workers are equally skilled. The total value of the output produced is $100 times the sum of the number of hours worked by all 10 workers. Each worker's utility is equal to his income minus the square of the number of hours he works. Each worker is selfish. The employers have no way of keeping track of any individual's work effort, so they decide to let each person work as long as he wants to and they divide the total value of the output equally among the workers. How much income will each worker get?arrow_forwardSuppose 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…arrow_forward
- This problem considers the decisions of a consumer whose preferences are given by u(C, 1) = C + y log 1, in which is the quantity of consumption and I is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N = 1 with N³ as the time spent working (or the labor supply). Assume that 0 < x < 1. The main advantage of working is the wages consumers receive. Consumers take wages as given (outside of their control) and obtain wage income equal to w Nº. The budget constraint is C = wN+T-T, with as real dividend income and T as the real lump-sum taxes paid to government. Assume that an interior solution always exists in the optimal consumption-leisure choice.arrow_forwardLet the demand and supply function for a commodity be Qa= D(p,Y) Dp 0 Qs = S(p, w) Sp>0, Sw<0 where p is the price, Y in exogenous income, and w is the exogenous wage rate. a. Find dp and dp using the implicit-function theorem. dw dp dy b. Find and dp by totally differentiating the equilibrium condition. dwarrow_forwardSome economists maintain that the returns to additional years of education is actually quite small but that there is a substantial “sheepskin” effect whereby one receives a higher salary with the successful completion of degrees or the earning of diplomas (i.e., sheepskins).Explain how the sheepskin effect is analogous to a signaling model.arrow_forward
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