macroeconomics
N,Gregory Mankiw
CHAPTER FOUR
Economic Growth,
Capital and Population
College of Management,HUST
CHAPTER 4 Economic Growth I
slide 1
9é ?
￥ù?
9é ?
￥ù?
???
? |??
ü6^?
D úe
?#
*"9é￥??
$ ?T
^￥?è
^
I
1$ ?T?
^?
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^
I
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c￥ | ?? ?￥?Y
^1ù |￥B? |
ì 7
S
± I
ìü
4
[1? 
e
Y fb
Robert E,Lucas
CHAPTER 4 Economic Growth I
slide 2
?S￥
L=
?S￥
L=
GDP 9é
9é
0
2
4
6
8
10
12
14
16
1979 1982 1985 1988 1991 1994 1997 2000
M
M

?
s
1
ü (9é
q
=9.8%
CHAPTER 4 Economic Growth I
slide 3
S￥
L=
S￥
L=
GDP 9é
9é
-4
-2
0
2
4
6
8
10
1960 1965 1970 1975 1980 1985 1990 1995 2000
Percent change
from 4 quarters
earlier
Average growth
rate = 3.5%
CHAPTER 4 Economic Growth I
slide 4
D1?
D1?
?D>ü6￥ Solow
?
?
3%1D | g9é ??YBS
￥
3
￡
ü
?D ??¨,á5,ùsKa
%1
q''i

CHAPTER 4 Economic Growth I
slide 5
"
c
"
c
1,'' ?
1.1 ?êy |￥
3áf
1.2 ''9é×?
1.3 tí×?
1.4 %1
q￥r?
2,''￥á5
￡
ü
2.1 ''￥á5
￡
ü
2.2 M?á5×
3, | g9é
4,'cl2
CHAPTER 4 Economic Growth I
slide 6
?ê ??
3áf
?ê ??
3áf
1.1
? 98 f ?,Y = F (K,L )
? ?l,y = Y/L = ?êy |á
k = K/L = ?êy |''
? L
!
?M,
zY = F (zK,zL ) ? ? z > 0
? ? z = 1/L,
*
1
Y/L = F (K/L,1)
y = F (k,1)
y = f(k) ? f(k) = F (k,1)
CHAPTER 4 Economic Growth I
slide 7
1.1
?ê ??
3áf
?ê ??
3áf
?ê ??
á,y
?êy |
￥'',k
f(k)
?,
3áf
A
U MPK?h,
?,
3áf
A
U MPK?h,
1
MPK =f(k +1) – f(k)
CHAPTER 4 Economic Growth I
slide 8
1.1
S
l ??
T
S
l ??
T
? Y = C + I (?i,? I
n G )
? ?,?ê ??,7y,
y = c + i
? c = C/L  i = I/L
Return
CHAPTER 4 Economic Growth I
slide 9
%1
qD?êhnf
%1
qD?êhnf
1.2
? s = %1
q
l ??¨?%1￥?s
(s
^B??
3?
)
?
?
,l￥
l￥
si??]?v￥
i??]?v￥
S
? hnf
,c = (1–s)y
(?ê ?? )
CHAPTER 4 Economic Growth I
slide 10
1.2
?ê%1g'
?ê%1g'
? %1 (?ê ?? ) = y – c
= y –(1–s)y
= sy
?S
l ??
T y = c + i
??a¤?,i = y – c = sy
(g' = %1 !)
? ?¨[
2
V?
i = sy = sf(k)
CHAPTER 4 Economic Growth I
slide 11
?êá
?êá
,hn
hn
,g'
g'
1.2
| (á,y
| ('',k
f(k)
sf(k)
k
1
y
1
i
1
c
1
CHAPTER 4 Economic Growth I
slide 12
1.2
| (''|?
| (''|?
| (|?,δk
| ('',k
δk
δ = |?
q
=
ù''
{￥?s
δ = |?
q
=
ù''
{￥?s
1
δ
CHAPTER 4 Economic Growth I
slide 13
''i
M?
''i
M?
1.2
? ''i
￥M? = g' – |?
k = i – δk
? ?? i = sf(k),[
 V?,
k = sf(k) – δk
CHAPTER 4 Economic Growth I
slide 14
K￥?Z?
1.2
￥?Z?
k = sf(k) – δk
? Solow
?￥?Z?
? %?''￥é
ù? …
? …?? %?
 
e
μ
=
3M
￥?
y1
ì? | %? k,1 ?
|￥
l ?,y = f(k)
|￥hn,c = (1–s) f(k)
CHAPTER 4 Economic Growth I
slide 15
×?
×?
1.2
k = sf(k) – δk
? ?Tg'Dz V[
?|?
[sf(k) = δk ],
*
1
?y |?μ￥''
 ??M,
k = 0,
N
H k
*
^B?è
?1 ×?
￥''i
,
CHAPTER 4 Economic Growth I
slide 16
×?
×?
1.2
g'D|?
| ('',k
sf(k)
δk
k
*
Return
CHAPTER 4 Economic Growth I
slide 17
_×?
M?
_×?
M?
1.3
k = sf(k)? δk
g'D|?
| ('',k
sf(k)
δk
k
*
|?
k
k
1
g'
CHAPTER 4 Economic Growth I
slide 18
_×?
M?
_×?
M?
1.3
k = sf(k)? δk
g'D|?
| ('',k
sf(k)
δk
k
*
k
1
k
k
2
CHAPTER 4 Economic Growth I
slide 19
_×?
M?
_×?
M?
1.3
k = sf(k)? δk
g'D|?
| ('',k
sf(k)
δk
k
*
k
2
g'
|?
k
CHAPTER 4 Economic Growth I
slide 20
_×?
M?
_×?
M?
1.3
k = sf(k)? δk
g'D|?
| ('',k
sf(k)
δk
k
*
k
2
k
k
3
CHAPTER 4 Economic Growth I
slide 21
_×?
M?
_×?
M?
1.3
k = sf(k)? δk
g'D|?
| ('',k
sf(k)
δk
k
*
k
3
l2,
?T k < k
*
,g'v?
|?,k |_ k
*
¤í
l2,
?T k < k
*
,g'v?
|?,k |_ k
*
¤í
CHAPTER 4 Economic Growth I
slide 22


:
1.3
 Solow
?mViS:×?
￥ k
*
,
à
ê |B?v? k
*
￥?T1
S
''i
iS:1 k
1
,
)
k |?
3
I
1M,
k ¤í×?

^ù ?×?

CHAPTER 4 Economic Growth I
slide 23
1.3
B?
3 è0
B?
3 è0
3áf
(98 ):
==×=
1/2 1/2
(,)Y FKL K L K L
1¤? | (
3áf

H?"[ L:

==


1/2
1/2 1/2
Y KL K
LL L
==
1/2
()y fk k
9D? ? y = Y/L  k = K/L  ¤?
CHAPTER 4 Economic Growth I
slide 24
1.3
B?
3 è0
B?
3 è0
L
!,
? s = 0.3
? δ = 0.1
? 
S′ k = 4.0
CHAPTER 4 Economic Growth I
slide 25
¤í×?
¤í×?
,B?
3 è01.3
B?
3 è0
Assumptions,; 0.3; 0.1; initial 4.0yks kδ=== =
Year kyci δk 'k
1 4.000 2.000 1.400 0.600 0.400 0.200
2 4.200 2.049 1.435 0.615 0.420 0.195
3 4.395 2.096 1.467 0.629 0.440 0.189
Year δk 'k
1 4.000 2.000 1.400 0.600 0.400 0.200
2 4.200 2.049 1.435 0.615 0.420 0.195
3 4.395 2.096 1.467 0.629 0.440 0.189
CHAPTER 4 Economic Growth I
slide 26
¤í×?
¤í×?
:B?
3 è01.3
B?
3 è0
Assumptions,; 0.3; 0.1; initial 4.0yks kδ=== =
Year kyci δk 'k
1 4.000 2.000 1.400 0.600 0.400 0.200
2 4.200 2.049 1.435 0.615 0.420 0.195
3 4.395 2.096 1.467 0.629 0.440 0.189
4 4.584 2.141 1.499 0.642 0.458 0.184
…
10 5.602 2.367 1.657 0.710 0.560 0.150
…
25 7.351 2.706 1.894 0.812 0.732 0.080
…
100 8.962 2.994 2.096 0.898 0.896 0.002
…
∞ 9.000 3.000 2.100 0.900 0.900 0.000
Year δk 'k
1 4.000 2.000 1.400 0.600 0.400 0.200
2 4.200 2.049 1.435 0.615 0.420 0.195
3 4.395 2.096 1.467 0.629 0.440 0.189
4 4.584 2.141 1.499 0.642 0.458 0.184
…
10 5.602 2.367 1.657 0.710 0.560 0.150
…
25 7.351 2.706 1.894 0.812 0.732 0.080
…
100 8.962 2.994 2.096 0.898 0.896 0.002
…
∞ 9.000 3.000 2.100 0.900 0.900 0.000
CHAPTER 4 Economic Growth I
slide 27


, p3×?
1.3
p3×?
L
!
s = 0.3,δ = 0.1,and y = k
1/2
?¨
k = sf(k)? δk
? p3×?
/￥ k,y,c,
CHAPTER 4 Economic Growth I
slide 28
s?
s?
:
1.3
0 def,of steady statek? =
( *) * eq'n of motion with 0sf k k k= =δ?
0.3 * 0.1 * using assumed valueskk=
*
3 *
*
k
k
k
==
Solve to get,* 9k = and * * 3yk= =
Finaly,*(1 )*0.732.1csy=?=×=
Return
CHAPTER 4 Economic Growth I
slide 29
%1
q4ú
%1
q4ú1.4
%1
q4ú|9Fg' …
…\
P''i
r?B??￥ú,
g'|?
k
Kk
s
1
f(k)
*
k
1
s
2
f(k)
*
k
2
CHAPTER 4 Economic Growth I
slide 30
??
??
:
1.4
? ÷ú￥ s? ÷ú￥ k
*
,
? y1 y = f(k),
÷ú￥ k
*
÷ú￥ y
*
,
? yN Solow
??yVé
ù A ?
TBSμ÷ú￥%1
qg'5|μ
÷ú￥ | (''i

￡
ü
l ?
￡
ü,
CHAPTER 4 Economic Growth I
slide 31
Egypt
Chad
Pakistan
Indonesia
Zimbabwe
Kenya
India
Cameroon
Uganda
Mexico
Ivory
Coast
Brazil
Peru
U.K.
U.S.
Canada
France
Israel
Germany
Denmark
Italy
Singapore
Japan
Finland
100,000
10,000
1,000
100
Income per
person in 1992
(logarithmic scale)
0510
15
Investment as percentage of output
(average 1960 –1992)
20
25 30 35 40
g'
qD | (
l ?￥S=￡
g'
qD | (
l ?￥S=￡
1.4
Return
CHAPTER 4 Economic Growth I
slide 32
á5
á5
,eo
2.1
eo
? ?]￥ s ′μ?]￥×?
,
'?
^,Ka,￥×?;?
? ü6? ?
￡
ü | %?hn
￡
üyN,Ka,×?
μKú￥ | (hn
￡
ü,c
*
= (1–s) f(k
*
)
? s ￥4ú
?á÷ú￥ k
*
 y
*
 c
*
V
-
6ú
hn]
l ?￥1 è (1–s)??5 V
?á c
*
?
?
? yN31ê4 s k
*
[
P c
*
Kvb
CHAPTER 4 Economic Growth I
slide 33
2.1
''￥á5
￡
ü
''￥á5
￡
ü
*
gold
k =
''￥á5
￡
ü
Kvhn
￡
ü￥×?
￥ k ′,
n5[ k
*
?V
U c
*
:
c
*
= y
*
i
*
= f(k
*
)? i
*
= f(k
*
)? δk
*
B?￥,
i =?k + δk
×?
/,
i
*
= δk
*
y1?k = 0.
CHAPTER 4 Economic Growth I
slide 34
2.1
''￥á5
￡
ü
''￥á5
￡
ü
mV?T
f(k
*
) δk
*
i
ùs
?-WM
μKv￥?,
×?
￥
áD|?
×?
￥
| ('',k
*
f(k
*
)
δk
*
*
gold
k
*
gold
c
**
gold gold
ikδ=
**
()
gold gold
yfk=
CHAPTER 4 Economic Growth I
slide 35
2.1
''￥á5
￡
ü
''￥á5
￡
ü
?
3áf
￥|
q
D|? wL￥|
q
M?
H'
c
*
= f(k
*
)? δk
*
Kvb
k
*
f(k
*
)
δk
*
*
gold
k
*
gold
c
MPK = δ
Return
CHAPTER 4 Economic Growth I
slide 36
_á5×?
￥V
_á5×?
￥V
2.2
? ü68"
àμ _á5×?
M?￥1
? t
],
? 1r?á51 p?|?????%1
q s.
? ?????á÷úhn
￡
ü￥?￥×?
,
? ???V?| ??Yhn
￡
ü;?
CHAPTER 4 Economic Growth I
slide 37
2.2
?''
t 7
S
?''
t 7
S
hn c
*
9F1
p%1 s ??,
_á5
￥VV??
hn
￡
ü?1
e ?ú,
**
If
gold
kk>
time
t
0
c
i
y
CHAPTER 4 Economic Growth I
slide 38
2.2
V''
t
 7
S
V''
t
 7
S
1
P c
*
9FA
?9F s,
| ?μ?ú￥h
n
￡
ü?K
1h
hn?
r?
"￥,
**
If
gold
kk<
t
0 time
c
i
y
Return
CHAPTER 4 Economic Growth I
slide 39
3
| g9é
| g9é
? L
! | gg' ?? ?9é
q1 n,(n
^
?
3￥ )
L
n
L
=
? è,L
!? 1
M L = 1000 | g9é
q1 2%/
M (n = 0.02),
*
1?L = n L = 0.02 × 1000 = 20,
yN? 2
M L = 1020,
CHAPTER 4 Economic Growth I
slide 40
3
?êg'
?êg'
?(δ +n)k = break-even investment,
 ? | (''?M￥g'
|??êg',
??êg' ?,
– δ k
?''|?
– n k 1?y |4 | (''
(?5, | g￥9é7''i
?M
9é?
¤ k |Ml )
CHAPTER 4 Economic Growth I
slide 41
K￥?Z?
3
￥?Z?
?
" | g9é k ￥?Z?
^
k = sf(k)? (δ +n)k
L=g'
?êg'
CHAPTER 4 Economic Growth I
slide 42
Solow
?
?3
g',?êg'
| ('',k
sf(k)
(δ+ n )k
k
*
k = s f(k)? (δ +n)k
CHAPTER 4 Economic Growth I
slide 43
| g9é￥?Y
| g9é￥?Y
3
g'
| ('',k
sf(k)
(δ+n
1
)k
k
1
*
(δ+n
2
)k
k
2
*
| g9é
q n
￥9F?á?
êg'9F
éB??á
×?
k
￥??
CHAPTER 4 Economic Growth I
slide 44
?y
?y
:
3
??ú￥ n? ??￥ k
*
,
?y1 y = f(k),
??￥ k
*
??￥ y
*
,
?yN Solow
??yVé
ù A | g
9é
q?ú￥SE | (''
l ?
￡
ü
??,
CHAPTER 4 Economic Growth I
slide 45
Chad
Kenya
Zimbabwe
Cameroon
Pakistan
Uganda
India
Indonesia
Israel
Mexico
Brazil
Peru
Egypt
Singapore
U.S.
U.K.
Canada
France
Finland
Japan
Denmark
Ivory
Coast
Germany
Italy
100,000
10,000
1,000
100
12340
Income per
person in 1992
(logarithmic scale)
Population growth (percent per year)
(average 1960 –1992)
| g9é
qD | (
l ?￥S=￡
| g9é
qD | (
l ?￥S=￡
3
CHAPTER 4 Economic Growth I
slide 46
3
| g9é/￥á5
| g9é/￥á5
?1
9
á5''i
[
k
*
?V
U c
*
:
c
*
= y
*
i
*
= f (k
*
)? (δ +n)k
*
c
*
r?Kv￥Hq
MPK = δ + n
?
MPK? δ = n
r?á5×?

''H=á
h ?''|?
q
?? | g9é
qb
r?á5×?
r?á5×?

''H=á

''H=á
h ?''|?
q
h ?''|?
q
?? | g9é
q
?? | g9é
q
b
Return
CHAPTER 4 Economic Growth I
slide 47
4
'cl2
'cl2
1,Solow 9é
?V
üé
ù ? ABS
￥
3
￡
ü ——
? ?M1?%1
q,
? μM1? | g9é
q,
2,%1
q￥9F?á
? é
ù￥á9F
? 
H￥9é
q4ú
? ??
4úr?×?
a￥9é
q
CHAPTER 4 Economic Growth I
slide 48
4
'cl2
'cl2
3, ?Tü6?μú?á5
￡
ü￥''i

h
%1|9F
μ
H?
￥hn
￡
ü
P
B} |?
sm,
?Tü6?￥''
￡
ü??á5
￡
ü
9F%1|4ú| ?
W}￥hn
￡
ü?|
h
C?B} |￥hn
￡
ü,
End