4. A consumer maximises his/her intertemporal consumption, i [C₁+ i = & C²+i] - (1+ p)i subject to the following life-long budget constraint, max Ct+i i=0 (1+r)A, + T=0 ¹, a > 0, Ex[Yc+i] Et[Ct+i] (1+r)i (1+r)" Σ Σ t=0 where p is the time preference rate, the real interest rate, E[-] the expectation operator based on the information available at time=1, C, the consumption for period , Y, the labour income for period t, and A, is the wealth at the beginning of period 1. (a) Show and explain the Euler equation relating C, to expectations concerning Cr+1 (b) Show and explain the permanent income of C, if the time preference rate is equal to the real interest rate. (c) Continued with (b), show that C = rA +Y, if Y, follows a pure random walk. Explain the results
4. A consumer maximises his/her intertemporal consumption, i [C₁+ i = & C²+i] - (1+ p)i subject to the following life-long budget constraint, max Ct+i i=0 (1+r)A, + T=0 ¹, a > 0, Ex[Yc+i] Et[Ct+i] (1+r)i (1+r)" Σ Σ t=0 where p is the time preference rate, the real interest rate, E[-] the expectation operator based on the information available at time=1, C, the consumption for period , Y, the labour income for period t, and A, is the wealth at the beginning of period 1. (a) Show and explain the Euler equation relating C, to expectations concerning Cr+1 (b) Show and explain the permanent income of C, if the time preference rate is equal to the real interest rate. (c) Continued with (b), show that C = rA +Y, if Y, follows a pure random walk. Explain the results
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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Question
![4. A consumer maximises his/her intertemporal consumption,
E. [C++i - C]
,a > 0,
(1 + p)!
тах
Ce+i
subject to the following life-long budget constraint,
(1+r)A, + E[G+i]
(1+r)i
E[Ye+i]
(1 +r)A, +
(1+r)i"
t=0
i=0
where p is the time preference rate, r the real interest rate, E[.] the expectation operator
based on the information available at time =1, C, the consumption for period 1, Y, the labour
income for period t, and A, is the wealth at the beginning of period t.
(a) Show and explain the Euler equation relating G, to expectations concerning C+1.
(b) Show and explain the permanent income of C, if the time preference rate is equal to
the real interest rate.
(c) Continued with (b), show that C, = rA, + Y, if Y, follows a pure random walk. Explain
the results](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62b02545-3413-493c-8ddf-7a9affe3a8d1%2F48276912-d9d0-462b-bebc-145f51922393%2Fkbzruar_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. A consumer maximises his/her intertemporal consumption,
E. [C++i - C]
,a > 0,
(1 + p)!
тах
Ce+i
subject to the following life-long budget constraint,
(1+r)A, + E[G+i]
(1+r)i
E[Ye+i]
(1 +r)A, +
(1+r)i"
t=0
i=0
where p is the time preference rate, r the real interest rate, E[.] the expectation operator
based on the information available at time =1, C, the consumption for period 1, Y, the labour
income for period t, and A, is the wealth at the beginning of period t.
(a) Show and explain the Euler equation relating G, to expectations concerning C+1.
(b) Show and explain the permanent income of C, if the time preference rate is equal to
the real interest rate.
(c) Continued with (b), show that C, = rA, + Y, if Y, follows a pure random walk. Explain
the results
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