Suppose the hourly wage is $20 and the price of each unit of capital is $2. The price of output is constant at $20/unit. The production function and marginal product function, respectively, are shown below. If the current capital stock is fixed at 2,500 units, how much labor should the firm employ in the short run? Show your work
Suppose the hourly wage is $20 and the price of each unit of capital is $2. The price of output is constant at $20/unit. The production function and marginal product function, respectively, are shown below. If the current capital stock is fixed at 2,500 units, how much labor should the firm employ in the short run? Show your work
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
ChapterB: Differential Calculus Techniques In Management
Section: Chapter Questions
Problem 7E
Related questions
Question
100%
Suppose the hourly wage is $20 and the price of each unit of capital is $2. The price of output is constant at $20/unit. The production function and marginal product function, respectively, are shown below.
If the current capital stock is fixed at 2,500 units, how much labor should the firm employ in the short run? Show your work.
![The equation presented is:
\[ MP_E = \frac{1}{2} \left( \frac{K}{E} \right)^{\frac{1}{2}} \]
This formula seems to describe a mathematical relationship where:
- \( MP_E \) could represent a particular measure or index in a specific context, such as marginal productivity or another economic or scientific variable.
- \( K \) and \( E \) are variables or parameters involved in this relationship.
The expression \(\left( \frac{K}{E} \right)^{\frac{1}{2}}\) indicates taking the square root of the ratio of \( K \) to \( E \).
Understanding the specific context or field in which this equation applies is crucial for its practical interpretation and application.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5a04c38-ce16-4925-9fe7-6fc0bcb8cf36%2F318c5a35-540f-4646-a050-dfa1db878da0%2F3nwp00r_processed.gif&w=3840&q=75)
Transcribed Image Text:The equation presented is:
\[ MP_E = \frac{1}{2} \left( \frac{K}{E} \right)^{\frac{1}{2}} \]
This formula seems to describe a mathematical relationship where:
- \( MP_E \) could represent a particular measure or index in a specific context, such as marginal productivity or another economic or scientific variable.
- \( K \) and \( E \) are variables or parameters involved in this relationship.
The expression \(\left( \frac{K}{E} \right)^{\frac{1}{2}}\) indicates taking the square root of the ratio of \( K \) to \( E \).
Understanding the specific context or field in which this equation applies is crucial for its practical interpretation and application.
![The equation displayed is:
\[ f(E, K) = \frac{1}{E^{\frac{1}{2}} K^{\frac{1}{2}}} \]
This mathematical expression represents a function \( f(E, K) \) that depends on two variables, \( E \) and \( K \). The function is defined as the reciprocal of the square root of the product of \( E \) and \( K \). This could describe a variety of scientific or mathematical relationships, often related to rates or efficiencies involving these two variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5a04c38-ce16-4925-9fe7-6fc0bcb8cf36%2F318c5a35-540f-4646-a050-dfa1db878da0%2Fa6eb8jr_processed.gif&w=3840&q=75)
Transcribed Image Text:The equation displayed is:
\[ f(E, K) = \frac{1}{E^{\frac{1}{2}} K^{\frac{1}{2}}} \]
This mathematical expression represents a function \( f(E, K) \) that depends on two variables, \( E \) and \( K \). The function is defined as the reciprocal of the square root of the product of \( E \) and \( K \). This could describe a variety of scientific or mathematical relationships, often related to rates or efficiencies involving these two variables.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
Managerial Economics: Applications, Strategies an…
Economics
ISBN:
9781305506381
Author:
James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:
Cengage Learning
Economics (MindTap Course List)
Economics
ISBN:
9781337617383
Author:
Roger A. Arnold
Publisher:
Cengage Learning
Managerial Economics: Applications, Strategies an…
Economics
ISBN:
9781305506381
Author:
James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:
Cengage Learning
Economics (MindTap Course List)
Economics
ISBN:
9781337617383
Author:
Roger A. Arnold
Publisher:
Cengage Learning
