Consider the following Cob-Douglas production function: f(k.1) = K°P°, where a 20 and > 0. 1. Show that the production function is homogeneous of degree n in inputs. What does n equal? 2. Using your answer from part (1), if a + 3 < 1, is the Cobb-Douglas production constant returns to scale, increasing returns to scale, or decreasing returns to scale? What if a+8 = 1? What if a+8 > 1? 3. Now suppose that a = 1/3 and = 1/3. What is the firm's marginal product of labor (MP)? What happens to the MP, when the firm's use of labor increases? Are labor and capital Edgeworth complements or substitutes?

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question
Question 1: Cobb-Douglas and returns to scale
Earlier in this class, you learned that the exponents in the Cobb-Douglas utility function had important
economic interpretations. In this question, we will learn about the exponents in the Cob-Douglas production
function.
Consider the following Cobb-Douglas production function:
f(k.1) = k*P°, where a > 0 and 8 > 0.
1. Show that the production function is homogeneous of degree n in inputs. What does n equal?
2. Using your answer from part (1), if a + 3 < 1, is the Cobb-Douglas production constant returns to
scale, increasing returns to scale, or decreasing returns to scale? What if a +8 = 1? What if a+§ > 1?
3. Now suppose that a = 1/3 and 8 = 1/3. What is the firm's marginal product of labor (MP)?
What happens to the MP when the firm's use of labor increases? Are labor and capital Edgeworth
complements or substitutes?
4. The firm's profit maximization problem is max 1&,3) pk3l3 – ul – rk, given market prices w, r, and p.
Solve for the firm's factor demand functions l* (w,r,p) and k' (w,r,p), and its output supply function
y'(u,r,p). Solve for the firm's proft function r1(u,r,p).
5. Now suppose that a = 1/2 and § = 1/2. Solve for the firm's factor demand functions l* (u,r,p) and
k(w, r,p), and its output supply function y*(u,r,p). Did you run into any problems? Why or why
not?
Transcribed Image Text:Question 1: Cobb-Douglas and returns to scale Earlier in this class, you learned that the exponents in the Cobb-Douglas utility function had important economic interpretations. In this question, we will learn about the exponents in the Cob-Douglas production function. Consider the following Cobb-Douglas production function: f(k.1) = k*P°, where a > 0 and 8 > 0. 1. Show that the production function is homogeneous of degree n in inputs. What does n equal? 2. Using your answer from part (1), if a + 3 < 1, is the Cobb-Douglas production constant returns to scale, increasing returns to scale, or decreasing returns to scale? What if a +8 = 1? What if a+§ > 1? 3. Now suppose that a = 1/3 and 8 = 1/3. What is the firm's marginal product of labor (MP)? What happens to the MP when the firm's use of labor increases? Are labor and capital Edgeworth complements or substitutes? 4. The firm's profit maximization problem is max 1&,3) pk3l3 – ul – rk, given market prices w, r, and p. Solve for the firm's factor demand functions l* (w,r,p) and k' (w,r,p), and its output supply function y'(u,r,p). Solve for the firm's proft function r1(u,r,p). 5. Now suppose that a = 1/2 and § = 1/2. Solve for the firm's factor demand functions l* (u,r,p) and k(w, r,p), and its output supply function y*(u,r,p). Did you run into any problems? Why or why not?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Returns to scale
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
  • SEE MORE 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