Problem 1: Properties of Production Functions Consider the following production functions: a) Y a In K + (1 – a) In N, for 0 0 c) Y K N, for a > 0, 3 > 0 and a +B<1 where K stands for capital and N stands for labor. For simplicity, I have omitted the time index t. For each function, check whether it satisfies the two main assumptions of the Solow Growth Model (SGM), namely: • constant returns to scale • decreasing marginal productivities for both capital K and labor N
Problem 1: Properties of Production Functions Consider the following production functions: a) Y a In K + (1 – a) In N, for 0 0 c) Y K N, for a > 0, 3 > 0 and a +B<1 where K stands for capital and N stands for labor. For simplicity, I have omitted the time index t. For each function, check whether it satisfies the two main assumptions of the Solow Growth Model (SGM), namely: • constant returns to scale • decreasing marginal productivities for both capital K and labor N
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Problem 1 - Macroeconomics - please help.
Transcribed Image Text:Problem 1: Properties of Production Functions
Consider the following production functions:
a) Y
a In K + (1 – a) In N, for 0 <a <1
b) Y
ak+ (1- a) N ", for 0 < a < 1 and e > 0
c) Y
K*N, for a> 0, 8 > 0 and a +B<1
where K stands for capital and N stands for labor. For simplicity, I have omitted the time index t. For each
function, check whether it satisfies the two main assumptions of the Solow Growth Model (SGM), namely:
• constant returns to scale
• decreasing marginal productivities for both capital K and labor N
Problem 2: The Golden Rule
Consider the SGM studied in class. We found an explicit expression for its steady state
sA
k = k* =
(1)
Let e = denote consumption per capita. As shown on the slides, the steady state level of ct, call it
c* = y* - i*, is given by
sA
c* (1– s) A
(2)
Find an expression for the saving rate smax that maximizes c". This is often referred to as the golden rule
saving rate. Plot c as a fuunction of s. Can you provide a brief intuition for why it is bell-shaped? Namely,
whu ot tho borinning a highor saving rate increases c but nassed a certain threshold c* starts to decline?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 6 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