Solutions Manual to Romer's Advanced Macroeconomics 5th Edition. Complete Solution Manual David Romer All Chapters Complete Newest Edition Instant Pdf Download.

Solutions Manual to Romer's Advanced Macroeconomics 5th
Edition. Complete Solution Manual David Romer All Chapters
Complete Newest Edition Instant Pdf Download.
SOLUTIONS TO CHAPTER 1 re re re




Problem 1.1 re


(a) Since the growth rate of a variable equals the time derivative of its log, as shown by equation
re re re re re re re re re re re re re re re re re


(1.10) in the text, we can write
Ż(t) d ln Z(t) d lnX(t)Y(t)
re re re re re re re

re
re re re

(1)   .
re re re

Z(t) dt dt
Since the log of the product of two variables equals the sum of their logs, we have
Ż(t) dln X(t)  ln Y(t) d ln X(t) d ln Y(t)
re re re re re re re re re re re re re re re re

re
re re re re re re re re

(2)   re  , re re re re

Z(t) dt dt dt
or simply
re

Ż(t) Ẋ (t) Ẏ (t)
re re re


(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
re re re re re re re re re re re re re re re re re



Ż(t) d ln Z(t) d lnX(t)
re
re

 
re re re re
(4) .
dt
re

Z(t) dt
Since the log of the ratio of two variables equals the difference in their logs, we have
Ż(t) dln X(t)  ln Y(t) d ln X(t) d ln Y(t)
re re re re re re re re re re re re re re re re

re
re re re re re re re re

(5)   re  , re re re

Z(t) dt dt dt
or simply
re

Ż(t) Ẋ (t) Ẏ (t)
re re re


(6)   .
Z(t) X(t) Y(t)

(c) We have re


Ż(t) d ln Z(t) d ln[X(t)
re re


re re

(7) ] re re



re
Z(t) .
dt dt
Using the fact that ln[X(t) ] = lnX(t), we have
re re re re re re re re re



Ż(t) d ln X(t)
re
d ln X(t) Ẋ (t) re re re

  
re re re

(8) , re re re

Z(t) dt dt X(t) re


where we have used the fact that  is a constant.
re re re re re re re re re re




Problem 1.2 re


(a) Using the information provided in the question,
re re re re re re


the path of the growth rate of X, Ẋ X(t), is
re re re re re re re re re
Ẋ (t) re




(t)
re X(t)
depicted in the figure at right. re re re re re




From time 0 to time t1 , the growth rate of X is
re re re re re re re re re re re re


constant and equal to a > 0. At time t1 , the
re re re re re re re r e re re re re
a
growth rate of X drops to 0. From time t1 to
re r e re re re re re r e re re re


time t2 , the growth rate of X rises gradually from
re re re re re re re re re re re



© re2012 reby reMcGraw-Hill reEducation. reThis reis reproprietary rematerial resolely refor reauthorized reinstructor reuse. reNot reauthorized refor resale reor
redistribution rein reany r e manner. reThis redocument remay renot rebe recopied, rescanned, reduplicated, reforwarded, redistributed, reor reposted reon rea

website, in whole or part. 0 t1 t2 time

, 0 to a. Note that
re re re r e re


we have made the assumption that Ẋ X(t) rises at
re re re re re re re re


(t)
re



a constant rate from t1 to t2 . Finally, after time t2
re re re re re re re r e re re re


, the growth rate of X is constant and equal to a
re re re re re re re re re re re re


again.
re




© re2012 reby reMcGraw-Hill reEducation. reThis reis reproprietary rematerial resolely refor reauthorized reinstructor reuse. reNot reauthorized refor resale reor
redistribution rein reany r e manner. reThis redocument remay renot rebe recopied, rescanned, reduplicated, reforwarded, redistributed, reor reposted reon rea

website, in whole or part.

,
, 1-2 Solutions to Chapter re re


1

(b) Note that the slope of lnX(t) plotted againstre re re re re re re


time is equal to the growth rate of X(t). That
re re re re re re re re re r e
lnX(t)
is, we know
re re re
slope = re

d ln X(t) Ẋ (t) re
a

re re re

re

dt X(t)
slope =
re
(See equation (1.10) in the text.)
re re re re re
a

From time 0 to time t1 the slope of lnX(t) equals
re re re re re re re re re re


a > 0. The lnX(t) locus has an inflection point at
re re r e re re re re re re re lnX(0)
t1 , when the growth rate of X(t) changes
re re re re re re re re re


discontinuously from a to 0. Between t1 and t2 ,
re re re re re r e re re re re


the slope of lnX(t) rises gradually from 0 to a.
re re re re re re re re re re
0 t1 t2 time
After time t2 the slope of lnX(t) is constant and
r e re re re re re re re re re


equal to a > 0 again.
re re re re re re




Problem 1.3 re


(a) The slope of the break-even investment line
re re re re re re

Inv/ (n + g +
is given by (n + g + ) and thus a fall in the
re re re


)k
re re re re re re re re re re re re re re
reeff

rate of depreciation, , decreases the slope of
re re re re re re re re
lab
the break- even investment line.
re re re re re (n + g +
re re re


NEW)k
The actual investment curve, sf(k) is unaffected.
re re re re re re

sf(k)
From the figure at right we can see that the
re re re re re re re re re


balanced- growth-path level of capital per unit of
re re re re re re re re


effective labor rises from k* to k*NEW .
re r e re re re re re re




k* k*NEW k


(b) Since the slope of the break-even re re re re re


investment line is given by (n + g + ), a rise
re re re re re re re re re re re re Inv/ (n + gNEW +
re re re


in the rate of technological progress, g, makes
re re re re re re re re reeff )k
the break-even investment line steeper.
re re re re re
lab
(n + g +
re re re



The actual investment curve, sf(k), is unaffected.
re re re re re re
)k

sf(k)
From the figure at right we can see that the
re re re re re re re re re


balanced-growth-path level of capital per unit
re re re re re re


of effective labor falls from k* to k*NEW .
re re re re re re re re re




k*NEW k* k




© re2012 reby reMcGraw-Hill reEducation. reThis reis reproprietary rematerial resolely refor reauthorized reinstructor reuse. reNot reauthorized refor resale reor
redistribution rein reany r e manner. reThis redocument remay renot rebe recopied, rescanned, reduplicated, reforwarded, redistributed, reor reposted reon rea

website, in whole or part.