Q7: An individual lives for only two periods and has preferences given by the follow- ing intertemporal utility function: U = lng + aln(1-h₁) + B[lno₂+ a ln(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= why and 0₂= 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 = lng + aln(1-h₁) + B[lno₂+ a ln(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= why and 0₂= 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: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Q7: An individual lives for only two periods and has preferences given by the follow-
ing intertemporal utility function:
U = lng + aln(1-h₁) + B[lno₂+ a ln(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= why and 0₂= 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%2F3d3c89ea-670d-41d2-a1e2-e3fa700a68d7%2Fddda030d-a3ad-4db9-af69-eba211965cbd%2F93j9rai_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 = lng + aln(1-h₁) + B[lno₂+ a ln(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= why and 0₂= 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.
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