Q7: An individual lives for only two periods and has preferences given by the follow- ing intertemporal utility function: U = Ing₁ +aln(1 -h₁) + [Inc₂+aln(1 - h₂)] (1) where, c₁, c₂ denotes consumption in period 1 and period 2 respectively h₁, h₂ denote the labour supply in period 1 and 2 respectively. Therefore 1-h is the amount of leisure time in period 1. The term 3 is the discount factor. The problem of the individual at period 1 is to choose consumption in both periods and labour supply in both periods subject to the following budget constraints: +8= wh and c₂= w₂h₂ + (1+r)s where s denote the saving, w denotes the wates and r denotes the real interest rate. (a) Provide an economic interpretation of the two budget constraints written above. (b) Combine the two budget constraints written above and prove the economic interpretation of of life time budget constraint. (c) Set the Lagrangean function and find the first order conditions with respect to C₁ C₂, hi and h₂. (d) Find the Euler equation of consumption and explain what happens to the relative consumption when there is an increase in interest rate.
Q7: An individual lives for only two periods and has preferences given by the follow- ing intertemporal utility function: U = Ing₁ +aln(1 -h₁) + [Inc₂+aln(1 - h₂)] (1) where, c₁, c₂ denotes consumption in period 1 and period 2 respectively h₁, h₂ denote the labour supply in period 1 and 2 respectively. Therefore 1-h is the amount of leisure time in period 1. The term 3 is the discount factor. The problem of the individual at period 1 is to choose consumption in both periods and labour supply in both periods subject to the following budget constraints: +8= wh and c₂= w₂h₂ + (1+r)s where s denote the saving, w denotes the wates and r denotes the real interest rate. (a) Provide an economic interpretation of the two budget constraints written above. (b) Combine the two budget constraints written above and prove the economic interpretation of of life time budget constraint. (c) Set the Lagrangean function and find the first order conditions with respect to C₁ C₂, hi and h₂. (d) Find the Euler equation of consumption and explain what happens to the relative consumption when there is an increase in interest rate.
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
Related questions
Question
![Q7: An individual lives for only two periods and has preferences given by the follow-
ing intertemporal utility function:
U = Ing₁ +aln(1 -h₁) + [Inc₂+aln(1 - h₂)]
(1)
where, c₁, c₂ denotes consumption in period 1 and period 2 respectively h₁, h₂ denote
the labour supply in period 1 and 2 respectively. Therefore 1-h is the amount of
leisure time in period 1.
The term 3 is the discount factor. The problem of the individual at period 1 is to
choose consumption in both periods and labour supply in both periods subject to
the following budget constraints:
+8= wh and c₂= w₂h₂ + (1+r)s
where s denote the saving, w denotes the wates and r denotes the real interest rate.
(a) Provide an economic interpretation of the two budget constraints written above.
(b) Combine the two budget constraints written above and prove the economic
interpretation of of life time budget constraint.
(c) Set the Lagrangean function and find the first order conditions with respect to
C₁ C₂, hi and h₂.
(d) Find the Euler equation of consumption and explain what happens to the
relative consumption when there is an increase in interest rate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49498a46-0cfd-4d83-b48d-102bb84a08fc%2Fd88b16cb-3c2d-4e04-acd4-3910b25e4d09%2F5q7rfo4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q7: An individual lives for only two periods and has preferences given by the follow-
ing intertemporal utility function:
U = Ing₁ +aln(1 -h₁) + [Inc₂+aln(1 - h₂)]
(1)
where, c₁, c₂ denotes consumption in period 1 and period 2 respectively h₁, h₂ denote
the labour supply in period 1 and 2 respectively. Therefore 1-h is the amount of
leisure time in period 1.
The term 3 is the discount factor. The problem of the individual at period 1 is to
choose consumption in both periods and labour supply in both periods subject to
the following budget constraints:
+8= wh and c₂= w₂h₂ + (1+r)s
where s denote the saving, w denotes the wates and r denotes the real interest rate.
(a) Provide an economic interpretation of the two budget constraints written above.
(b) Combine the two budget constraints written above and prove the economic
interpretation of of life time budget constraint.
(c) Set the Lagrangean function and find the first order conditions with respect to
C₁ C₂, hi and h₂.
(d) Find the Euler equation of consumption and explain what happens to the
relative consumption when there is an increase in interest rate.
AI-Generated Solution
AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.
Unlock instant AI solutions
Tap the button
to generate a solution
Recommended textbooks for you
Accounting
Accounting
ISBN:
9781337272094
Author:
WARREN, Carl S., Reeve, James M., Duchac, Jonathan E.
Publisher:
Cengage Learning,
Accounting Information Systems
Accounting
ISBN:
9781337619202
Author:
Hall, James A.
Publisher:
Cengage Learning,
Accounting
Accounting
ISBN:
9781337272094
Author:
WARREN, Carl S., Reeve, James M., Duchac, Jonathan E.
Publisher:
Cengage Learning,
Accounting Information Systems
Accounting
ISBN:
9781337619202
Author:
Hall, James A.
Publisher:
Cengage Learning,
Horngren's Cost Accounting: A Managerial Emphasis…
Accounting
ISBN:
9780134475585
Author:
Srikant M. Datar, Madhav V. Rajan
Publisher:
PEARSON
Intermediate Accounting
Accounting
ISBN:
9781259722660
Author:
J. David Spiceland, Mark W. Nelson, Wayne M Thomas
Publisher:
McGraw-Hill Education
Financial and Managerial Accounting
Accounting
ISBN:
9781259726705
Author:
John J Wild, Ken W. Shaw, Barbara Chiappetta Fundamental Accounting Principles
Publisher:
McGraw-Hill Education