1. Labor Market = Consider an economy with production function given by Y AK0.5 L0.5 where A is the total factor productivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is fixed and equal to 1. Assume A=100. a. Write the firm's problem of choosing labor demand. Derive the demand for labor as a function of the real wage. b. Assume labor supply is inelastic and fixed at Ī = 100. Find the equilibrium values of the wage and the employment level for this economy. Display graphically the labor supply and the labor demand curves. Carefully label your graph. c. Suppose the economy faces a positive productivity shock and TFP is now A=150. Display graphically the new labor demand function. What are the equilibrium values of employment and the real wage? d. Compute the total output when A=100 and when A=200. What is the output's growth rate? Compare that growth rate with the growth rate in A. How does the growth rate of output per capita compares to the growth rate in A? Explain carefully. e. Now, suppose that Congress, concerned about the welfare of the working class, passes a law setting the minimum wage that is 10 percent above the equilibrium wage you just derived (in the case where A 100). Assuming that Congress cannot dictate how many workers are hired at the mandated wage, what are the effects of this law? Specifically, calculate what happens to the real wage, the employment, the output, and the total amount earned by workers. f. Does Congress succeed in its goal of helping the working class? Explain. g. Do you think the analysis provides a good way of thinking about a minimum-wage law? Why or why not?
1. Labor Market = Consider an economy with production function given by Y AK0.5 L0.5 where A is the total factor productivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is fixed and equal to 1. Assume A=100. a. Write the firm's problem of choosing labor demand. Derive the demand for labor as a function of the real wage. b. Assume labor supply is inelastic and fixed at Ī = 100. Find the equilibrium values of the wage and the employment level for this economy. Display graphically the labor supply and the labor demand curves. Carefully label your graph. c. Suppose the economy faces a positive productivity shock and TFP is now A=150. Display graphically the new labor demand function. What are the equilibrium values of employment and the real wage? d. Compute the total output when A=100 and when A=200. What is the output's growth rate? Compare that growth rate with the growth rate in A. How does the growth rate of output per capita compares to the growth rate in A? Explain carefully. e. Now, suppose that Congress, concerned about the welfare of the working class, passes a law setting the minimum wage that is 10 percent above the equilibrium wage you just derived (in the case where A 100). Assuming that Congress cannot dictate how many workers are hired at the mandated wage, what are the effects of this law? Specifically, calculate what happens to the real wage, the employment, the output, and the total amount earned by workers. f. Does Congress succeed in its goal of helping the working class? Explain. g. Do you think the analysis provides a good way of thinking about a minimum-wage law? Why or why not?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Please don't use
Transcribed Image Text:1. Labor Market
=
Consider an economy with production function given by Y AK0.5 L0.5 where A is the total factor
productivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is
fixed and equal to 1. Assume A=100.
a. Write the firm's problem of choosing labor demand. Derive the demand for labor as a function
of the real wage.
b. Assume labor supply is inelastic and fixed at Ī = 100. Find the equilibrium values of the wage
and the employment level for this economy. Display graphically the labor supply and the labor
demand curves. Carefully label your graph.
c. Suppose the economy faces a positive productivity shock and TFP is now A=150. Display
graphically the new labor demand function. What are the equilibrium values of employment and
the real wage?
d. Compute the total output when A=100 and when A=200. What is the output's growth rate?
Compare that growth rate with the growth rate in A. How does the growth rate of output per
capita compares to the growth rate in A? Explain carefully.
e. Now, suppose that Congress, concerned about the welfare of the working class, passes a law
setting the minimum wage that is 10 percent above the equilibrium wage you just derived (in
the case where A 100). Assuming that Congress cannot dictate how many workers are hired
at the mandated wage, what are the effects of this law? Specifically, calculate what happens to
the real wage, the employment, the output, and the total amount earned by workers.
f. Does Congress succeed in its goal of helping the working class? Explain.
g. Do you think the analysis provides a good way of thinking about a minimum-wage law? Why or
why not?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: State the given information
VIEWStep 2: Derive the labor demand
VIEWStep 3: Find equilibrium level of wage and employment when L=100
VIEWStep 4: When A=150, Derive the labor demand, equilibrium level of real wage and employment
VIEWStep 5: Compute and compare total output when A=100 and A=150
VIEWStep 6: Analyze the concern of minimum wage law
VIEWSolution
VIEW
Step by step
Solved in 7 steps with 21 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 Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education