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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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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