For Questions 31 and 32, use the following information: Consider a firm minimising the cost of production under the following Cobb-Douglas production technology constraint: q = KªL²-a where q is the output level, K is the quantity of capital used and L is the quantity of labour used. Let w be the wage rate and r be the rental rate of capital. 31. The Lagrangean for this optimisation problem is: a) wL + rK + µ[q = KªL²=«] b) KªL²-a – [wL +rK] c) wL +rK + µ[K«L-«] d) wL + rK + µ[q – K«L²-«] 32. The demand function for capital is: a) K = q[-²_"1-a b) K = q[ c) K = q[-a d) K = q[ 1-a w1-a 1-a e a w 1-a
For Questions 31 and 32, use the following information: Consider a firm minimising the cost of production under the following Cobb-Douglas production technology constraint: q = KªL²-a where q is the output level, K is the quantity of capital used and L is the quantity of labour used. Let w be the wage rate and r be the rental rate of capital. 31. The Lagrangean for this optimisation problem is: a) wL + rK + µ[q = KªL²=«] b) KªL²-a – [wL +rK] c) wL +rK + µ[K«L-«] d) wL + rK + µ[q – K«L²-«] 32. The demand function for capital is: a) K = q[-²_"1-a b) K = q[ c) K = q[-a d) K = q[ 1-a w1-a 1-a e a w 1-a
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
please answer the both questions
![For Questions 31 and 32, use the following information:
Consider a firm minimising the cost of production under the following Cobb-Douglas
production technology constraint:
q = KªL!-a
where q is the output level, K is the quantity of capital used and L is the quantity of labour
used. Let w be the wage rate and r be the rental rate of capital.
31. The Lagrangean for this optimisation problem is:
a) wL + rK + µ[q = K«L²-«]
b) KªL²-a – [wL +rK]
c) wL + rK + µ[KªL!-«]
d) wL + rK + µ[q – KªL!-«]
32. The demand function for capital is:
a w11-a
a) K = ql,-a
b) K = q[
c) K = q
d) K = ql
1-a r
1-a w1-a
a r
a r.
1-a
1-a e
1-a
1-a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe72ae499-6521-46bb-b012-744f262625bc%2F815b616b-3a7f-4056-9921-7befd02f0171%2Fam2dqf_processed.png&w=3840&q=75)
Transcribed Image Text:For Questions 31 and 32, use the following information:
Consider a firm minimising the cost of production under the following Cobb-Douglas
production technology constraint:
q = KªL!-a
where q is the output level, K is the quantity of capital used and L is the quantity of labour
used. Let w be the wage rate and r be the rental rate of capital.
31. The Lagrangean for this optimisation problem is:
a) wL + rK + µ[q = K«L²-«]
b) KªL²-a – [wL +rK]
c) wL + rK + µ[KªL!-«]
d) wL + rK + µ[q – KªL!-«]
32. The demand function for capital is:
a w11-a
a) K = ql,-a
b) K = q[
c) K = q
d) K = ql
1-a r
1-a w1-a
a r
a r.
1-a
1-a e
1-a
1-a
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 4 steps
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