Principles of Economics, 7th Edition (MindTap Course List)
7th Edition
ISBN: 9781285165875
Author: N. Gregory Mankiw
Publisher: Cengage Learning
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Question
Chapter 18, Problem 1QR
To determine
To determine: How the production function is related to marginal productivity of labor.
Expert Solution & Answer
Explanation of Solution
The production function represents the relationship between the quantity of factors of production and the total quantity output produced. Labor is one of the important factors of production. If the marginal factors of production increase, the total quantity of production also increases. That is, the changes in marginal product of labor directly affect the production function. The value of marginal product of labor is equal to the wage rate. Thus, the relationship between the value of marginal product of labor and
Economics Concept Introduction
Concept introduction:
Production function: Aproduction function shows the relationship between quantity of input and quantity of output used during the production process.
Marginal product of labor: Marginal product of labor refers to an additional product to the total product due to a change in one unit of labor.
Value of marginal product of labor: Value of marginal product of labor is the monetary value of the marginal product of labor.
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A firm's production function is:
q = 20L1/2K1/2
where q is the firm's total product, L is the quantity of labor employed, and K is the quantity of capital employed. The price of labor is $25 per unit and the price of capital is $100 per unit.
a. What is the equation for the marginal product of labor?
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c. Given the price of labor is $25 per unit and the price of capital is $100 per unit, what is the cost-minimizing combination of capital and labor that can produce 800 units of output?
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Following is information on the production levels of three different firms. Firm A is currentlyproducing at a quantity where it is experiencing increasing returns. Firm B is currentlyproducing at a quantity where it is experiencing diminishing returns. Firm C is currentlyproducing at a quantity where it is experiencing negative returns.a. If each of the firms cut back on its labor force, what will happen to its marginalproduct of labor? And why?b. If each of the firms adds to its labor force, what will happen to its marginal product oflabor? And why?
Chapter 18 Solutions
Principles of Economics, 7th Edition (MindTap Course List)
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Similar questions
- What is the marginal product of labor? the average output of a unit of labor the total output obtained by using one more unit of labor the average output obtained by using one more unit of labor the extra output obtained by using one more unit of laborarrow_forwardSuppose that Tim runs his own lawn care service and that his firm is competitive in the lawn care industry. He has a fixed number of tools that can be used to maintain a yard, but he needs to determine the productivity gained from hiring various numbers of workers per week. Which of the following statements best represents the idea behind the marginal product of labor ( MPL )? When Tim hires more workers, he can mow more lawns per week, but at a decreasing rate. If Tim hires twice as many workers per week, he can mow twice as many lawns per week. If Tim buys one more lawn mower, he can mow 13 more lawns per week. If Tim hires an additional worker per week, he can mow 11 more lawns per week. The following graph portrays the weekly total product curve for lawn mowing given a fixed amount of capital and varying labor inputs. (Note: Each black point (plus symbol) represents a point on the total product curve.) 100 90 во 70 60 50 40 30 20 10 xxxx_ Total Product ° 0 1 2 4 5 7 8 10 LABOR…arrow_forwardGiven that the level of labour is 10, the total production is 1,200, and the marginal product of labour is 200, what is the average product of labour?arrow_forward
- If the marginal product of labor is 2 units of output per day per worker for the first five workers and 0 units of output for the sixth worker onward, draw the total product curve, the average product of labor curve, and the marginal product of labor curvearrow_forward“After the fifth worker is hired at the hourly wage $40, the output rate increases from 64 pairs of shoes per hour to 72 pairs per hour.” Given the statement, which of the following is correct after the fifth worker is hired? Group of answer choices The marginal cost (MC) becomes $8. The marginal physical product (MPP) per labor hour becomes 5. The marginal cost (MC) becomes $5. The marginal physical product (MPP) per labor hour becomes $40.arrow_forwardSuppose you are considering hiring another worker. Also assume that you are at a firm that is operating at a point where the marginal product of labor is 5 and the price of each unit of labor is $2, and the marginal product of capital is 20 and the price of each unit of capital is $10. Should you hire another worker? If you hire another worker, what will happen to the marginal product of labor and why?arrow_forward
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- Having a marginal product of labor that increases over low levels of employment is common in this situation. Why is that? a) The first workers a firm hires are just better workers than workers hired later on- they applied first and really want the job. B) often it has to do with specialization- workers are able to divide up tasks and be more productive. Is the answer a or b?arrow_forwardThe following table contains the relationship between a number of trainers working at a new gym and the number of clients they can train. These clients represent the output of trainers. Clients pay $40 per session. Number of Trainers Clients Trained 1 10 2 50 3 80 4 100 5 110 6 115 a. Find the marginal product of labor (MPL) and the value of the marginal product of labor (VMPL) for each additional trainer hired and record these numbers in columns in the table. b. Premier trainers earn $200 an hour. How many trainers will the gym hire?arrow_forwardSuppose Die Cast Aluminum Co. is a subcontractor for the auto industry and makes specialized auto parts. There is a bracket it manufactures that it sells for $1.50. The following table shows the number of brackets that can be produced from a given number of labor hours. Assume that the company cannot hire labor for a fraction of an hour. Hours of Labor Output 50 90 120 140 150 155 157 4. 6. The marginal product of labor for the third hour of labor is 30. (Enter your response as an integer.) The value of the marginal product of labor for the third hour of labor is 45. (Round your response to two decimal places.) If the wage paid to workers in Die Cast's plant is $25/hour, it should employ 4 worker(s). (Entor your response as an integer.) If the wage paid to workers in Die Cast's plant is $35/hour, it ahould employ 3 worker(s). (Enter your response as an integer.) If the wage is $25/hour, but the price of a bracket declines to $1.00, it should employ worker(s). (Enter your response as an…arrow_forward
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