Problem #3: Labor Unions (20 points)Sarah is thinking if she should join the labor union in their company. Her utility function isU (c, 1) = (cl)05, where c denotes consumption, and I denotes leisure. She has 16 hours eachday to allocate between work and leisure.1. Given her non-labor income is zero, how many hours will Sarah work at $7 wage/hour?In addition, how much consumption and leisure can she afford, and how much utilitycan she achieve from this?2. If the labor unioh bargains for a $10.5 overtime pay rate for work hours beyond 8hours, will Sarah benefit from this proposal?3. If, instead, the labor union proposes an 8-hour workday, will Sarah benefit from it?

Detailed explanation:Question 1: Work and Utility Calculation Sarah has to decide how many hours to…

Answered: Problem #3: Labor Unions (20 points)…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Calculate the Marginal Product (MP) at each input level. If the price of printer is $100 each, calculate the Value of the Marginal of labor (VMPL). If the wage rate (per week) is $1800 , how many workers will be employed? If the firm decides to hire 14 workers, what is the maximum wage the firm would be willing to pay?
The following are correct descriptions about the concept of Marginal Productivity of Labor (MPL), EXCEPT: Question 1 options: MPL measures the extra production generated by adding one extra unit of labor. MPL initially increases and eventually declines as more units of Labor are added. From the producer's perspective, The optimal level of labor is the one when MPL = Market Wage and MPL is still Increasing. If MPL increases for any given amount of labor, it will lead to a shift up of the Demand for Labor.
All individuals have the same utility function over consumption, C, and leisure, L, given by U = C1/3L2/3, Denote the wage rate by w. The total time available for labour and leisure is equal to 12. The price of consumption is PC=1. Denote the amount of labour supplied as N. Find the Labour supply function.
A carpenter quits his job at a furniture factory to open his own cabinetmaking business. In his first two years of operation, his sales average $100 000 per year and his operating costs for wood, workshop and tool rental, utilities, and miscellaneous expenses average $70 000 per year. Now his old job at the furniture factory is again available. What is the lowest wage at which he should decide to return to his old job? Why?
1. Consider a static labour supply model for an individual. Assume that the person works a positive number of hours. Assume that the utility function is of the following form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a parameter of the utility function. The person is paid a wage of w for each hour worked. The person has no other source of income other than employment earnings. Assume that the price of x equals 1. a) Specify the utility maximization problem, write down the Lagrange function, and solve for the first order conditions. b) Solve for the MRS condition between consumption and hours of work. c) Assume that 8=2 if the person has a child living at home, and 8=1 otherwise. Explain (and either show mathematically or graphically) how this will affect the optimal number of hours of work of the person.
3
Consider the following production function: q=100L0.8K0.4 Currently the wage rate (w) is $2.00 and the price of capital (r) is $4.00. If the firm is using 100 units of capital in production, how much labor should be employed to minimize costs? Labor input = units. (Enter a numeric response using a real number rounded to two decimal places.)
1. Julie needs to hire a plumber. She is told that the cost of hiring the plumber, C, is determined by the amount of time spent on the job, t, in hours. The plumber charges a one-time fee of $30 and an hourly rate of $40. How many hours did the plumber work if Julie paid him $190? Find the value for C (total cost) when time, t =0. Write a sentence describing its meaning.
assume the following labor supply curves: 1. N = C + .64 W -2.33 I + 0.08 K 2. N = C + 1.33 W - .59 I - .28 K 3. N = C - 1.11 W - .59I - .28K a. Determine whether leisure is inferior in the 2nd labor supply curve. b. which if any of the above three equations represent back-bending labor supply curves? justify your answer. c. which if any of the above three labor supply curves is inconsistent with theory? justify your answer.
Consider an economy with 20 workers. If the marginal product of labor (MPL) is 13 and the market price (P) is $6, what isthe value of the marginal product of labor (VMPL)? Provide your answer below:
4. Winona has 80 hours to divide between leisure and labor. Her utility function is u(r,c) = f(r) + c, when r represents hours of leisure, c represents dollars of consumption, and fis strictly concave. Winona's wage is wo = $15/hr. initially, then it rises to wi = $20/hr. (i) Explain what happens to Winona's labor supply when the wage rises, and why. (ii) Explain how the answer to (i) would change if Winona were to win a lottery.
Consider the Labor Economics Question. This will provide insight into the idea of the optimal number of workers and the value of the marginal product of labor. If wages in the restaurant is $16.80 per hour and the price of a Hamburger is $8.30 and the production function for the workers is: Q = 11L – 0.25L2 How many workers should Your Restaurant employ during the lunch hour to maximize profits? 1 Point (note—the value of the marginal product of labor and the marginal revenue product are the same) We maximize profits which are total revenues less total costs:

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