4. Complete the steps in the derivation of the Fisher equation discussed on slide 17 of lecture 3 by showing that if we 1+i (a) Begin with = 1+r. 1+ 7 (b) Replace 1 with the Taylor-series expansion 1+ 7° 1 = 1- 7° + (7°)² - (7*)³ + (m*)ª – .. in the expression in part 4(a) above. (c) Assume that we can ignore any terms involving in“ or (7*)" for n > 2 because 7 is small. that we are left with the Fisher equation r = i – ".

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.7P
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4. Complete the steps in the derivation of the Fisher equation discussed on slide 17 of
lecture 3 by showing that if we
1+i
(a) Begin with
= 1+r.
1+ 7
(b) Replace
1
with the Taylor-series expansion
1+ 7°
1
= 1- 7° + (7°)² - (7*)³ + (m*)ª – ..
in the expression in part 4(a) above.
(c) Assume that we can ignore any terms involving in“ or (7*)" for n > 2 because 7
is small.
that we are left with the Fisher equation r = i – ".
Transcribed Image Text:4. Complete the steps in the derivation of the Fisher equation discussed on slide 17 of lecture 3 by showing that if we 1+i (a) Begin with = 1+r. 1+ 7 (b) Replace 1 with the Taylor-series expansion 1+ 7° 1 = 1- 7° + (7°)² - (7*)³ + (m*)ª – .. in the expression in part 4(a) above. (c) Assume that we can ignore any terms involving in“ or (7*)" for n > 2 because 7 is small. that we are left with the Fisher equation r = i – ".
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