Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter6: Consumer Choice And Demand
Section: Chapter Questions
Problem 6QFR
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Question
Using the utility function and wage constraint in the problem, please complete the utility maximization problem using the substituion and Lagrangian method. If you can not do both, I would prefer the substitution method.
![Problem 4.5. Consider the (utility) maximization problem
subject to the (budget) constraint
max ln c₁ + ß ln c₂
C1,C2
C1 +
1
1 + R
4
C₂ = W.
Here, c₁ and c₂ are variables, and ß, R, and W parameters. Assume that 0 < ß < 1, R > 0, and
W > 0.
Using your knowledge of (micro)economic theory, give an economic interpretation to all these
variables and parameters.
Using the substitution method and the Lagrangian method, solve for c₁ and c₂.
How do c₁ and c₂ change when W increases? When ß increases? When R increases? Can you
give an economic interpretation to these comparative static exercises?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a49b22d-c2e7-40c7-ba9f-f03570a2f6b8%2Fd908f502-d440-4065-977a-4a2c5d69bc08%2Fbodanpf_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 4.5. Consider the (utility) maximization problem
subject to the (budget) constraint
max ln c₁ + ß ln c₂
C1,C2
C1 +
1
1 + R
4
C₂ = W.
Here, c₁ and c₂ are variables, and ß, R, and W parameters. Assume that 0 < ß < 1, R > 0, and
W > 0.
Using your knowledge of (micro)economic theory, give an economic interpretation to all these
variables and parameters.
Using the substitution method and the Lagrangian method, solve for c₁ and c₂.
How do c₁ and c₂ change when W increases? When ß increases? When R increases? Can you
give an economic interpretation to these comparative static exercises?
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