STUDY NOTES & REFERENCE GUIDE
SOLUTIONS MANUAL TO ROMER'S
ADVANCED MACROECONOMICS 4TH
EDITION. COMPLETE SOLUTION
MANUAL DAVID ROMER.
SOLUTIONS TO CHAPTER 1
Problem 1.1
(a) Since the growth rate of a variable equals the time derivative of its log, as shown by
equation (1.10) in the text, we can write
Z(t) d ln Z(t) d ln X(t)Y(t)
(1) .
Z(t) dt dt
Since the log of the product of two variables equals the sum of their logs,
we have Z(t) d ln X(t) ln Y(t) d ln X(t) d ln
Y(t)
(2) ,
Z(t) dt dt dt
or simply
Z(t) X(t) Y(t)
(3)
. Z(t) X(t)
Y(t)
(b) Again, since the growth rate of a variable equals the time derivative of its log, we can write
Z(t) d ln Z(t) d ln X(t) Y(t)
(4) .
Z(t) dt dt
Since the log of the ratio of two variables equals the difference in their logs,
we have Z(t) d ln X(t) ln Y(t) d ln X(t) d ln
Y(t)
(5) ,
Z(t) dt dt dt
or simply
Z(t) X(t) Y(t)
(6)
. Z(t) X(t)
Y(t)
(c) We have
Z(t) d ln Z(t) d ln[X(t) ]
(7) .
Z(t) dt
dt
Using the fact that ln[X(t) ] = lnX(t), we have
Z(t) d ln X(t) d ln X(t) X(t)
(8) ,
Z(t) dt X(t)
dt
where we have used the fact that is a question, the path of the growth rate of X,
constant. X(t) X(t), is depicted in the figure at right.
Problem 1.2
(a) Using the information provided in the
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X(t)
X(t)
From time 0 to time t1 , the growth rate of X is
constant and equal to a > 0. At time t1 , the
growth
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any
© 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
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website, in whole or part.
, STUDY NOTES & REFERENCE GUIDE
rate of X drops to 0. From time t1 to time t2 , the
growth rate of X rises gradually from 0 to a. Note
that we have made the assumption that X(t)
X(t) rises at a constant rate from t1 to t2 . Finally,
after time t2 , the growth rate of X is constant and
equal to a again.
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whole or part.
, STUDY NOTES & REFERENCE GUIDE
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SOLUTIONS MANUAL TO ROMER'S
ADVANCED MACROECONOMICS 4TH
EDITION. COMPLETE SOLUTION
MANUAL DAVID ROMER.
SOLUTIONS TO CHAPTER 1
Problem 1.1
(a) Since the growth rate of a variable equals the time derivative of its log, as shown by
equation (1.10) in the text, we can write
Z(t) d ln Z(t) d ln X(t)Y(t)
(1) .
Z(t) dt dt
Since the log of the product of two variables equals the sum of their logs,
we have Z(t) d ln X(t) ln Y(t) d ln X(t) d ln
Y(t)
(2) ,
Z(t) dt dt dt
or simply
Z(t) X(t) Y(t)
(3)
. Z(t) X(t)
Y(t)
(b) Again, since the growth rate of a variable equals the time derivative of its log, we can write
Z(t) d ln Z(t) d ln X(t) Y(t)
(4) .
Z(t) dt dt
Since the log of the ratio of two variables equals the difference in their logs,
we have Z(t) d ln X(t) ln Y(t) d ln X(t) d ln
Y(t)
(5) ,
Z(t) dt dt dt
or simply
Z(t) X(t) Y(t)
(6)
. Z(t) X(t)
Y(t)
(c) We have
Z(t) d ln Z(t) d ln[X(t) ]
(7) .
Z(t) dt
dt
Using the fact that ln[X(t) ] = lnX(t), we have
Z(t) d ln X(t) d ln X(t) X(t)
(8) ,
Z(t) dt X(t)
dt
where we have used the fact that is a question, the path of the growth rate of X,
constant. X(t) X(t), is depicted in the figure at right.
Problem 1.2
(a) Using the information provided in the
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whole or part.
, STUDY NOTES & REFERENCE GUIDE
X(t)
X(t)
From time 0 to time t1 , the growth rate of X is
constant and equal to a > 0. At time t1 , the
growth
© 2012 by McGraw-Hill Education. This is proprietary material solely for authorizedainstructor use. Not authorized for sale or distribution in
any
© 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
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distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a
website, in whole or part.
, STUDY NOTES & REFERENCE GUIDE
rate of X drops to 0. From time t1 to time t2 , the
growth rate of X rises gradually from 0 to a. Note
that we have made the assumption that X(t)
X(t) rises at a constant rate from t1 to t2 . Finally,
after time t2 , the growth rate of X is constant and
equal to a again.
Acadexas Stuvia | Page 3 of 450
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
, STUDY NOTES & REFERENCE GUIDE
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