sitier the production model studied in Chapter 4. Final output in the economy is pro- duced using capital K and labor L. The production function is: Y = ĀK'/³L^/5 Assume that the supply of all inputs are exogenous and equal to L and K. Perfectly compet- itive firms are price-takers and choose how much capital and labor to demand by maximizing profits. Let w and r denote the wage and rental rate of one unit of labor and capital respec- tively. (a) What are the 5 endogenous variables in this model? Also list the exogenous variables and the parameters and provide a brief explanation of each. (b) Show the first order conditions for labor and capital. Explain the intuition for why these conditions are optimal for a firm. Are there diminishing returns to these inputs in this model? ( (c) Show that the solution for output per capita can be written as y = Ak/5. Observed GDP per capita is 3 in this economy. Capital per person is 32. If Ā = 1, what does this model predict for GDP per person? Does this model over-predict or under-predict GDP? Show your working. (i ". o! (d) If the model is to explain the observed value of y, what must TFP (A) be equal to?

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question
sitier the production model studied in Chapter 4. Final output in the economy is pro-
duced using capital K and labor L. The production function is:
Y = ĀK'/³L^/5
Assume that the supply of all inputs are exogenous and equal to L and K. Perfectly compet-
itive firms are price-takers and choose how much capital and labor to demand by maximizing
profits. Let w and r denote the wage and rental rate of one unit of labor and capital respec-
tively.
(a) What are the 5 endogenous variables in this model? Also list the exogenous variables
and the parameters and provide a brief explanation of each.
(b) Show the first order conditions for labor and capital. Explain the intuition for why
these conditions are optimal for a firm. Are there diminishing returns to these inputs
in this model? (
(c) Show that the solution for output per capita can be written as y = Ak/5. Observed
GDP per capita is 3 in this economy. Capital per person is 32. If Ā = 1, what does
this model predict for GDP per person? Does this model over-predict or under-predict
GDP? Show your working. (i ". o!
(d) If the model is to explain the observed value of y, what must TFP (A) be equal to?
Transcribed Image Text:sitier the production model studied in Chapter 4. Final output in the economy is pro- duced using capital K and labor L. The production function is: Y = ĀK'/³L^/5 Assume that the supply of all inputs are exogenous and equal to L and K. Perfectly compet- itive firms are price-takers and choose how much capital and labor to demand by maximizing profits. Let w and r denote the wage and rental rate of one unit of labor and capital respec- tively. (a) What are the 5 endogenous variables in this model? Also list the exogenous variables and the parameters and provide a brief explanation of each. (b) Show the first order conditions for labor and capital. Explain the intuition for why these conditions are optimal for a firm. Are there diminishing returns to these inputs in this model? ( (c) Show that the solution for output per capita can be written as y = Ak/5. Observed GDP per capita is 3 in this economy. Capital per person is 32. If Ā = 1, what does this model predict for GDP per person? Does this model over-predict or under-predict GDP? Show your working. (i ". o! (d) If the model is to explain the observed value of y, what must TFP (A) be equal to?
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Demand Shock
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.
Similar questions
Recommended textbooks for you
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
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)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
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-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education