3) Jack's Labor Demand Problem Jack hires craftswomen like Jane to help produce widgets. Jack acts like a price-taker in the widget (output) market. His production function is as follows Q = ZOL2 T-BQ - WL-rK ニらo-2-16 Q = F(K,L) = 4(KxL) – Ľ In the short-run, Jack's capital is fixed at 5 units (K = 5). In the long-run, he cán acquire more capital by paying r for each unit of additional capital. Given a price of p for his t widgets, Jack's short-run profit maximization problem can be written as レ max 7=PxF(K, L) –[wL + rK] (rentalvateof apilal) = P x [4 (5 x L) – L2 ] - [ wL + 5r] Assume for now that Jack is a price-taker in the labor market as well. The going wage is w = $10, price for widgets P = 5, and factor price for capitál r= 15 (3a) What is Jack's short-run marginal product of labor? What is Jack's short-run marginal revenue? (3b) What is Jack's short-run marginal revenue product of labor? (3c) Given that Jack is a price-taker in the labor market, how much labor would Jack buy given the prevailing prices. How much widgets does Jack make? What is Jack's profit? OPTIONAL: Although Jack acts as a price taker, is the widget market competitive for this example? Look at Jack's profit. At the going price of widgets, is P = MC?
3) Jack's Labor Demand Problem Jack hires craftswomen like Jane to help produce widgets. Jack acts like a price-taker in the widget (output) market. His production function is as follows Q = ZOL2 T-BQ - WL-rK ニらo-2-16 Q = F(K,L) = 4(KxL) – Ľ In the short-run, Jack's capital is fixed at 5 units (K = 5). In the long-run, he cán acquire more capital by paying r for each unit of additional capital. Given a price of p for his t widgets, Jack's short-run profit maximization problem can be written as レ max 7=PxF(K, L) –[wL + rK] (rentalvateof apilal) = P x [4 (5 x L) – L2 ] - [ wL + 5r] Assume for now that Jack is a price-taker in the labor market as well. The going wage is w = $10, price for widgets P = 5, and factor price for capitál r= 15 (3a) What is Jack's short-run marginal product of labor? What is Jack's short-run marginal revenue? (3b) What is Jack's short-run marginal revenue product of labor? (3c) Given that Jack is a price-taker in the labor market, how much labor would Jack buy given the prevailing prices. How much widgets does Jack make? What is Jack's profit? OPTIONAL: Although Jack acts as a price taker, is the widget market competitive for this example? Look at Jack's profit. At the going price of widgets, is P = MC?
Principles of Microeconomics (MindTap Course List)
8th Edition
ISBN:9781305971493
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter18: The Markets For The Factor Of Production
Section: Chapter Questions
Problem 3PA
Related questions
Question
B and c please
![3) Jack's Labor Demand Problem
Jack hires craftswomen like Jane to help produce widgets. Jack acts like a price-taker in
the widget (output) market. His production function is as follows
= ZOL-L?
Q = F(K,L)=4(KxL) – Ľ²
TT-BrQ-WL-VK
In the short-run, Jack's capital is fixed at 5 units (K = 5). In the long-run, he cán acquire
more capital by paying r for each unit of additionalcapital. Given a price of p for his ŏll=O
widgets, Jack's short-run profit maximization problem can be written as
max 7=PxF(K,L)-[wL+rK]
= P x [ 4 (5 × L) – L2 ] - [ wL + 5r]
Assume for now that Jack is a price-taker in the labor market as well. The going wage is
w= $10, price for widgets P = 5, and factor price for capitál r= 15
(3a) What is Jack's short-run marginal product of labor? What is Jack's short-run
marginal revenue?
(3b) What is Jack's short-run marginal revenue product of labor?
(3c) Given that Jack is a price-taker in the labor market, how much labor would Jack buy
given the prevailing prices. How much widgets does Jack make? What is Jack's profit?
OPTIONAL: Although Jack acts as a price taker, is the widget market competitive for
this example? Look at Jack's profit. At the going price of widgets, is P = MC?
(3d) Suppose that Jack is a monopolist in the widget market and faces the following
inverse demand for widgets: P(Q) = 30 – 0.25 Q. What is Jack’s marginal revenue now?
marginal revenue product for labor?
(3e) Sketch Jack’s labor demand curve as a price-taker and as a monopolist in the widget
market.
(3f) As a monopolist, does Jack buy more or less labor? Briefly explain why. No need to
solve for the profit maximizing quantity of labor. But you can if you want (algebraically
tedious).
(3g) Re-do (3c) assuming that K=4 and K = 6.
(3h) Based on (3c) and (3g) and the prevailing prices, would Jack rather use more or less
capital given the choice? In the medium/long run, what would we expect to happen to the
factor price of capital (r), assuming w and p remain unchanged?
(3i) Suppose Jack is a monopsonist in the labor market and faced a labor supply curve
similar to the labor supply curve you derived for Jane (Question 2). Would Jack buy more
or less labor as a monopsonist ? Briefly explain why.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e99b076-d7ba-4bd3-9136-e67d6db3098b%2Fad4898c9-e022-4b69-a3f7-2367dc26ab33%2Ftm36orm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3) Jack's Labor Demand Problem
Jack hires craftswomen like Jane to help produce widgets. Jack acts like a price-taker in
the widget (output) market. His production function is as follows
= ZOL-L?
Q = F(K,L)=4(KxL) – Ľ²
TT-BrQ-WL-VK
In the short-run, Jack's capital is fixed at 5 units (K = 5). In the long-run, he cán acquire
more capital by paying r for each unit of additionalcapital. Given a price of p for his ŏll=O
widgets, Jack's short-run profit maximization problem can be written as
max 7=PxF(K,L)-[wL+rK]
= P x [ 4 (5 × L) – L2 ] - [ wL + 5r]
Assume for now that Jack is a price-taker in the labor market as well. The going wage is
w= $10, price for widgets P = 5, and factor price for capitál r= 15
(3a) What is Jack's short-run marginal product of labor? What is Jack's short-run
marginal revenue?
(3b) What is Jack's short-run marginal revenue product of labor?
(3c) Given that Jack is a price-taker in the labor market, how much labor would Jack buy
given the prevailing prices. How much widgets does Jack make? What is Jack's profit?
OPTIONAL: Although Jack acts as a price taker, is the widget market competitive for
this example? Look at Jack's profit. At the going price of widgets, is P = MC?
(3d) Suppose that Jack is a monopolist in the widget market and faces the following
inverse demand for widgets: P(Q) = 30 – 0.25 Q. What is Jack’s marginal revenue now?
marginal revenue product for labor?
(3e) Sketch Jack’s labor demand curve as a price-taker and as a monopolist in the widget
market.
(3f) As a monopolist, does Jack buy more or less labor? Briefly explain why. No need to
solve for the profit maximizing quantity of labor. But you can if you want (algebraically
tedious).
(3g) Re-do (3c) assuming that K=4 and K = 6.
(3h) Based on (3c) and (3g) and the prevailing prices, would Jack rather use more or less
capital given the choice? In the medium/long run, what would we expect to happen to the
factor price of capital (r), assuming w and p remain unchanged?
(3i) Suppose Jack is a monopsonist in the labor market and faced a labor supply curve
similar to the labor supply curve you derived for Jane (Question 2). Would Jack buy more
or less labor as a monopsonist ? Briefly explain why.
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 4 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Microeconomics (MindTap Course List)
Economics
ISBN:
9781305971493
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Exploring Economics
Economics
ISBN:
9781544336329
Author:
Robert L. Sexton
Publisher:
SAGE Publications, Inc
Principles of Microeconomics (MindTap Course List)
Economics
ISBN:
9781305971493
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Exploring Economics
Economics
ISBN:
9781544336329
Author:
Robert L. Sexton
Publisher:
SAGE Publications, Inc
Principles of Economics, 7th Edition (MindTap Cou…
Economics
ISBN:
9781285165875
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning