Chapter 12
Basics of Dynamic
Model
0
10
20
30
40
90 91 92 93 94 95 96 97 98 99 00
Topics to be Discussed
?Basic principles of building
macroeconomic model
?Micro basis of macroeconomics
?Choices of households
?Choices of firms
?Introduction to labor market
12.1 Basic Principles of Building
Macroeconomic Model
? Static economics
? Static analysis,exogenous
variables+parameters==>endogenous variables
? Comparative static economics
? Comparative static analysis,exogenous
variables==>endogenous variables
? Dynamic economics
? Dynamic analysis,endogenous variables
?Dynamic model in microeconomics
?Consider variables’ time sequence and the time
and process needed for variables adjustment
?Cobweb theory
12.1 Basic Principles of Building
Macroeconomic Model
t
D
t paQ ???
1???? t
S
t pQ ??
D
t
S
t QQ ?
?Dynamic model in macroeconomics
?Income-expenditure model
12.1 Basic Principles of Building
Macroeconomic Model
yt=ct+It
ct=a+byt-1 yt -byt-1 =It+a
12.1 Basic Principles of Building
Macroeconomic Model
? Macroeconomic model is a highly abstract
description to the real economy,Throughout the
model-building process,it’s very important to
grasp the primary determinants (variables) and
ignore the secondary ones,
? As to the same economic phenomenon,there
can be different conclusions drawn from different
models,
? Is there a consistent standard to assess models?
12.1 Basic Principles of Building
Macroeconomic Model
? Basic principles of building macroeconomic
model
?Empirical data test
?Micro compatibility
12.1 Basic Principles of Building
Macroeconomic Model
? Basic principles of building macroeconomic
model
?Empirical data test
? Economic data are objective record for the real economic
operation
? Econometricians test theory models with varieties of
mathematical or statistical methods to show to what extent
these models are consistent with the real world,and predict
quantitatively economic growth in future,
12.1 Basic Principles of Building
Macroeconomic Model
? Example,
? GDP Time Series
? Implications, output of this year is influenced by
outputs of past years,How much is the influence?
How about the significance?
? There can be four different possibilities,
),,,( 21 itttt YYYfY ??? ????
12.1 Basic Principles of Building
Macroeconomic Model
? Autoregressive
? Moving Average,MA
? Autoregressive-Moving
Average,ARMA
? Integrated Autoregressive-
Moving Average,ARIMA
ttt eaYY ?? ? 1
???????? ?? 21 tttt eeeY ???
???????? ??? 211 ttttt eeeaYY ??
1
211
?
???
???
??????????
ttt
ttttt
YYY
eeeYaY ??
12.1 Basic Principles of Building
Macroeconomic Model
? Basic principles of building macroeconomic
model
?Researches indicate that many
macroeconomic variables,including GDP,all
have obvious features of time series,
?Meanwhile, the latest researches also
demonstrate macroeconomic variables have
another important feature,i.e,random walk
12.1 Basic Principles of Building
Macroeconomic Model
? Which is the most appropriate description？
? Blanchard & Fisher’s research
? Implications, from 1940s to 1970s,in short term，
shocks led to fluctuations in economy,however,from
the view of long term,economy will recover
automatically with the power of market,
? The result supports the view of Keynesian theory
2121 25.006.042.031.1 ???? ????? tttttt eeeYYY
12.1 Basic Principles of Building
Macroeconomic Model
? Let’s see Campbell and Mankiw’ s research
? Implications,shocks can have permanent influence
on economy,and it’s impossible for economy to
adjust automatically to the level before shocks,
? Real business-cycle theory emphasizes this point
211 024.008.02.0 ??? ??????? ttttt eeeYCY
12.1 Basic Principles of Building
Macroeconomic Model
? Conclusions,
? A model is a good model if it can pass the
empirical test,
? Even if a model can’t pass the empirical test,we
can’t come to the conclusion that the model is
wrong,
? We should consider whether the logic in the
model is reasonable,For a macroeconomic
model,we must check if it has a firm micro basis,
12.1 Basic Principles of Building
Macroeconomic Model
?Basic principles of building
macroeconomic model
?Micro basis
?The rules for macro economy should be consistent
with basic economic unit in the economy,
?Behavior rule of typical unit (households and firms)
in micro economy is the, micro basis”。
12.2 Micro Basis of Macroeconomics
? Basic unit in microeconomics of aggregate
demand,Households
? Basic unit in microeconomics of aggregate
supply,Firms
? Describing representative household and
firm’s motivations and behavior rules in
economic activities and their choices under
given constraints,
12.2 Micro Basis of Macroeconomics
? Representative household and firm in finance market
)( 1
1
ttt
ttt
VVq
KKI
??
??
?
?
Firm,investment must be equal
to the change of capital
accumulation in this period
which is also equal to the change
of the market value of the firm,
Household,current disposable
income must be equal to
consumption plus saving while
saving is equal to the change of
financial assets in this period,
)( 1 ttt
ttd
AAC
SCY
???
??
?
12.2 Micro Basis of Macroeconomics
? Households’
Problem,HP
? Aim, Maximizing Utility
? Utility function,Maximizing
Present Value of
Consumption
{}
0
1
1
1
m a x m a x ( )
1
., ( ) ( )
1
( ), ho us e ho l d ' s t i m e p r e f e r e nce
1
( ), c hange o f t he ass e t s
( ), e xchange c os t o f cons um pt i on
,a s s e t i ncom e ra t i o
t
t
t
C
t
d t
t t t d
t
tt
t
d
t
d
PV C
A
s t C Y A A h
Y
AA
A
h
Y
A
Y
?
?
?
?
?
?
?
?
? ? ? ?
?
?
?
?
12.2 Micro Basis of Macroeconomics
? Exchange cost of consumption
? A fresh graduate may have great potential（ Yd）,but the
assets he possesses are little,Hence,his （ At/Yd） is low
and his h(At/Yd) is high,So,his consumption will be limited
to a great extent by this cost,
? When growing up,he will convert human capital or other
non-current assets into financial assets,which leads to At/Yd
rising and h(At/Yd) falling,
? Once assets have risen to some extent,exchange cost will
be little （ h’<0,h’’>0） and no longer be a important factor
influencing consumption,
Exchange Cost of Consumption
d
t
Y
A0
1
2
3
cost
6 8 10 12 14
4
5
6
7
)( dtYAh
12.2 Micro Basis of Macroeconomics
? Exchange cost of consumption
As a result of young’s high exchange cost,after
subtracting the exchange cost,consumption
couldn’t be very big,When the young are growing
older,exchange cost will fall down gradually,
Hence,given the deposable income,there will be
few fluctuations in consumption among each period
of life,
? Optimal consumption of households
（ 1） choose consumption in each period
objective function and constraint condition,
12.2 Micro Basis of Macroeconomics
{}
0
1
1
m a x m a x ( )
1
., ( ) ( )
t
t
t
C
t
d t
t t t d
P V C
A
s t C Y A A h
Y
?
?
?
?
?
?
? ? ? ?
?
? Put the constraints into objective function,
? First-order condition,
? ??? ??? ??????? 0 10 )]()([)1 1()1 1(t dtttdtttt YAhAAYCPV ??
12.2 Micro Basis of Macroeconomics
1
1
()
0
()
( ) ( ) ( )
[ ( )]
t
d
t t t
d
t t t t t
PV
C
Y C A A
PV PV PV
C Y A A A
?
?
?
?
?
? ? ?
? ? ?
? ? ?
? ? ? ? ?
? This result implies that exchange cost falls when capital-
income ratio rises and if given time preference and the
expectation of income in the whole life fixed,exchange cost
will become linear,This means,from the point of consumption,
change of current assets can’t make people feel better,
12.2 Micro Basis of Macroeconomics
1
()
0
'( )
11
( ) [ 1 ] ( ) ( 1 ) 0
11
()
t
t
d
tt
d
tdt
d
PV
A
A
h
Y
Y
A
hY
Y
??
?
?
?
?
?
? ? ? ? ?
??
? ? ?
? Hence,keeping current assets in each period constant is the best
choice,
? The constraint can be converted to,
? Because Yd and At are relatively stable,Ct is also relatively stable 。
? In other words,given constraint condition,households will keep the
consumption in each period as stable as possible to maximize the
present value of consumption,
)( dtdt
Y
A
hYC ??
12.2 Micro Basis of Macroeconomics
? Households’ optimal consumption
（ 2） how to arrange current assets?
concept of current assets,
12.2 Micro Basis of Macroeconomics
s to c k p r ic e s h a r e q u a n ti ty
m o n e y p r ic e
t
t t t
t
tt
tt
M
A q V
P
qV
MP
??
,；, ；
,；, 。
? Households’ optimal consumption
government’s budget constraint,
relationship between investment and capital,
t
tt
t P
MMG ?? ? 1
tttt KKKI ???? ? )( 1
12.2 Micro Basis of Macroeconomics
?Households’ optimal consumption
ignoring international trade,
12.2 Micro Basis of Macroeconomics
1
1
11
1
1
11
()
[ ( ) ( ) ]
()
sup pose 0 the n
t t t t
d
t t t t
tt
t t t t t
tt
d t
t t t t t t
t
d
d
Y C I G
Y C A A
MM
C q V q V
PP
M
Y Y K V q q
P
M
Y Y K
P
Y Y K
??
??
?
?
?
?
??
?
?
??
? ? ?
? ? ?
? ? ? ? ?
? ? ? ? ? ?
? ? ? ?
?
??
,：
? Suppose （ qV） * is the appropriate share value and（ M/P）
* is the appropriate real money,
? The left of the equation denotes excessive demand for
money while the right excessive supply of shares,The
equation implies that if keep money in a proper level the
stock market will clean automatically,
12.2 Micro Basis of Macroeconomics
**
**
()()
or
( ) ( ) ( ) ( )
M M
qV qV A
P P
MM
qV qV
PP
? ? ? ?
? ? ?
：
? Suppose money demand is positively related to
income,O is the nominal revenue for holding
money,i is the nominal revenue for holding
shares,then we have,
0)()( ???? ?? oi
12.2 Micro Basis of Macroeconomics
? Maximization problem of firm
? Similar to household’s problem,this is also a
optimizing problem with constraint conditions
given,Firms choose inputs to maximize profit
just as households maximize consumption
utility,
? We will analyze this process by diagrams,
12.2 Micro Basis of Macroeconomics
Fixing Cost of Firm
Fixing cost
Investment
Labor Quantity Needed
labor
Cost and output
L*
e
MPL
Cost
/output
12.3 Introduction to Labor Market
? Labor market is just like a bridge between
households and firms,Compared with
goods and financial market,labor market is
more complicated,
? Basic assumptions about labor market,
?Labor supply is fixed
LLt ?
? The two parties in labor
market interact through
negotiation on wage,
? When wage is higher than
equilibrium level,firms will
endeavor to renegotiate on the
wage,
? When wage is lower than
equilibrium level,workers will
require to renegotiate on the
wage,
? Hence,the process of wage
adjustment is the process of
reducing exchange cost,
0* ?? WW
0* ?? WW
12.3 Introduction to Labor Market
* n o m i n a l e q u i l i b r i u m w a g e
n o m i n a l w a g e
W
W
,；
：
? Condition for minimizing exchange cost,
??
?
?? ???????
0
2*
11
*2*
}{ })]()[(){()1
1(m i n)(m i n
t
ttttttt
t
rC t ???????? ?
12.3 Introduction to Labor Market
ln
01
W?
?
?
??
? First-order condition,
12.3 Introduction to Labor Market
* * **
11 11
* * *
1 1 1 1
0
1
[ ( 1 ) ( ) ( ) ] [ ( ) ] 0()
1
( ) 2 ) ( ) ( 1 ) ( ) 0
t
t t t t t ttt
t t t t t t
C
r
r
rr
?
? ? ? ? ? ? ? ???
?
? ? ? ? ? ?
?
?? ??
? ? ? ?
?
?
?
?
? ? ? ? ? ? ? ? ??
?
? ? ? ? ? ? ? ? ? ?（
? If the interval between t and t+1,we get a
differential equation,
12.3 Introduction to Labor Market
'' '
12
*
11
*
*
11
12
0
''
''
1
2 ),( 1 )
tt
tt
tt
y y y
y
y
y
r
rr
??
??
??
??
??
?
??
??
? ? ?
??
??
??
?
? ? ? ? ? ?
，
，
（
?Solve the equation,
12.3 Introduction to Labor Market
12
2
1 1 2
1,2
12
4
2
tt
y e y e
??
? ? ?
?
? ? ?
?
?
??；
?Convergence problem of y,
?This implies that will gradually
decrease and finally be convergent to
*?? ?
12.3 Introduction to Labor Market
2
**
11
*
11
*
w h e n 1,y is c o n v e r g e n t
,',''
'' '
) ( )
o r 1
t t t
t t t t
tt
tt
y e y e y e
YY
? ? ?
?
??
?
? ? ? ? ?
??
?
??
??
??
?
? ? ?
??
? ? ? ?
?
??
?
（
：
*tt???
? Conclusions,
? Optimal decision of households and firms and
the equilibrium of labor market could all be
regarded as the maximization problems given
constraint conditions,
? If a macroeconomic model could justify itself,
then we can regard the model as a
consummate model from the aspect of
economic theory,
12.3 Introduction to Labor Market
Chapter 12
The End
0
10
20
30
40
90 91 92 93 94 95 96 97 98 99 00
Basics of Dynamic
Model
0
10
20
30
40
90 91 92 93 94 95 96 97 98 99 00
Topics to be Discussed
?Basic principles of building
macroeconomic model
?Micro basis of macroeconomics
?Choices of households
?Choices of firms
?Introduction to labor market
12.1 Basic Principles of Building
Macroeconomic Model
? Static economics
? Static analysis,exogenous
variables+parameters==>endogenous variables
? Comparative static economics
? Comparative static analysis,exogenous
variables==>endogenous variables
? Dynamic economics
? Dynamic analysis,endogenous variables
?Dynamic model in microeconomics
?Consider variables’ time sequence and the time
and process needed for variables adjustment
?Cobweb theory
12.1 Basic Principles of Building
Macroeconomic Model
t
D
t paQ ???
1???? t
S
t pQ ??
D
t
S
t QQ ?
?Dynamic model in macroeconomics
?Income-expenditure model
12.1 Basic Principles of Building
Macroeconomic Model
yt=ct+It
ct=a+byt-1 yt -byt-1 =It+a
12.1 Basic Principles of Building
Macroeconomic Model
? Macroeconomic model is a highly abstract
description to the real economy,Throughout the
model-building process,it’s very important to
grasp the primary determinants (variables) and
ignore the secondary ones,
? As to the same economic phenomenon,there
can be different conclusions drawn from different
models,
? Is there a consistent standard to assess models?
12.1 Basic Principles of Building
Macroeconomic Model
? Basic principles of building macroeconomic
model
?Empirical data test
?Micro compatibility
12.1 Basic Principles of Building
Macroeconomic Model
? Basic principles of building macroeconomic
model
?Empirical data test
? Economic data are objective record for the real economic
operation
? Econometricians test theory models with varieties of
mathematical or statistical methods to show to what extent
these models are consistent with the real world,and predict
quantitatively economic growth in future,
12.1 Basic Principles of Building
Macroeconomic Model
? Example,
? GDP Time Series
? Implications, output of this year is influenced by
outputs of past years,How much is the influence?
How about the significance?
? There can be four different possibilities,
),,,( 21 itttt YYYfY ??? ????
12.1 Basic Principles of Building
Macroeconomic Model
? Autoregressive
? Moving Average,MA
? Autoregressive-Moving
Average,ARMA
? Integrated Autoregressive-
Moving Average,ARIMA
ttt eaYY ?? ? 1
???????? ?? 21 tttt eeeY ???
???????? ??? 211 ttttt eeeaYY ??
1
211
?
???
???
??????????
ttt
ttttt
YYY
eeeYaY ??
12.1 Basic Principles of Building
Macroeconomic Model
? Basic principles of building macroeconomic
model
?Researches indicate that many
macroeconomic variables,including GDP,all
have obvious features of time series,
?Meanwhile, the latest researches also
demonstrate macroeconomic variables have
another important feature,i.e,random walk
12.1 Basic Principles of Building
Macroeconomic Model
? Which is the most appropriate description？
? Blanchard & Fisher’s research
? Implications, from 1940s to 1970s,in short term，
shocks led to fluctuations in economy,however,from
the view of long term,economy will recover
automatically with the power of market,
? The result supports the view of Keynesian theory
2121 25.006.042.031.1 ???? ????? tttttt eeeYYY
12.1 Basic Principles of Building
Macroeconomic Model
? Let’s see Campbell and Mankiw’ s research
? Implications,shocks can have permanent influence
on economy,and it’s impossible for economy to
adjust automatically to the level before shocks,
? Real business-cycle theory emphasizes this point
211 024.008.02.0 ??? ??????? ttttt eeeYCY
12.1 Basic Principles of Building
Macroeconomic Model
? Conclusions,
? A model is a good model if it can pass the
empirical test,
? Even if a model can’t pass the empirical test,we
can’t come to the conclusion that the model is
wrong,
? We should consider whether the logic in the
model is reasonable,For a macroeconomic
model,we must check if it has a firm micro basis,
12.1 Basic Principles of Building
Macroeconomic Model
?Basic principles of building
macroeconomic model
?Micro basis
?The rules for macro economy should be consistent
with basic economic unit in the economy,
?Behavior rule of typical unit (households and firms)
in micro economy is the, micro basis”。
12.2 Micro Basis of Macroeconomics
? Basic unit in microeconomics of aggregate
demand,Households
? Basic unit in microeconomics of aggregate
supply,Firms
? Describing representative household and
firm’s motivations and behavior rules in
economic activities and their choices under
given constraints,
12.2 Micro Basis of Macroeconomics
? Representative household and firm in finance market
)( 1
1
ttt
ttt
VVq
KKI
??
??
?
?
Firm,investment must be equal
to the change of capital
accumulation in this period
which is also equal to the change
of the market value of the firm,
Household,current disposable
income must be equal to
consumption plus saving while
saving is equal to the change of
financial assets in this period,
)( 1 ttt
ttd
AAC
SCY
???
??
?
12.2 Micro Basis of Macroeconomics
? Households’
Problem,HP
? Aim, Maximizing Utility
? Utility function,Maximizing
Present Value of
Consumption
{}
0
1
1
1
m a x m a x ( )
1
., ( ) ( )
1
( ), ho us e ho l d ' s t i m e p r e f e r e nce
1
( ), c hange o f t he ass e t s
( ), e xchange c os t o f cons um pt i on
,a s s e t i ncom e ra t i o
t
t
t
C
t
d t
t t t d
t
tt
t
d
t
d
PV C
A
s t C Y A A h
Y
AA
A
h
Y
A
Y
?
?
?
?
?
?
?
?
? ? ? ?
?
?
?
?
12.2 Micro Basis of Macroeconomics
? Exchange cost of consumption
? A fresh graduate may have great potential（ Yd）,but the
assets he possesses are little,Hence,his （ At/Yd） is low
and his h(At/Yd) is high,So,his consumption will be limited
to a great extent by this cost,
? When growing up,he will convert human capital or other
non-current assets into financial assets,which leads to At/Yd
rising and h(At/Yd) falling,
? Once assets have risen to some extent,exchange cost will
be little （ h’<0,h’’>0） and no longer be a important factor
influencing consumption,
Exchange Cost of Consumption
d
t
Y
A0
1
2
3
cost
6 8 10 12 14
4
5
6
7
)( dtYAh
12.2 Micro Basis of Macroeconomics
? Exchange cost of consumption
As a result of young’s high exchange cost,after
subtracting the exchange cost,consumption
couldn’t be very big,When the young are growing
older,exchange cost will fall down gradually,
Hence,given the deposable income,there will be
few fluctuations in consumption among each period
of life,
? Optimal consumption of households
（ 1） choose consumption in each period
objective function and constraint condition,
12.2 Micro Basis of Macroeconomics
{}
0
1
1
m a x m a x ( )
1
., ( ) ( )
t
t
t
C
t
d t
t t t d
P V C
A
s t C Y A A h
Y
?
?
?
?
?
?
? ? ? ?
?
? Put the constraints into objective function,
? First-order condition,
? ??? ??? ??????? 0 10 )]()([)1 1()1 1(t dtttdtttt YAhAAYCPV ??
12.2 Micro Basis of Macroeconomics
1
1
()
0
()
( ) ( ) ( )
[ ( )]
t
d
t t t
d
t t t t t
PV
C
Y C A A
PV PV PV
C Y A A A
?
?
?
?
?
? ? ?
? ? ?
? ? ?
? ? ? ? ?
? This result implies that exchange cost falls when capital-
income ratio rises and if given time preference and the
expectation of income in the whole life fixed,exchange cost
will become linear,This means,from the point of consumption,
change of current assets can’t make people feel better,
12.2 Micro Basis of Macroeconomics
1
()
0
'( )
11
( ) [ 1 ] ( ) ( 1 ) 0
11
()
t
t
d
tt
d
tdt
d
PV
A
A
h
Y
Y
A
hY
Y
??
?
?
?
?
?
? ? ? ? ?
??
? ? ?
? Hence,keeping current assets in each period constant is the best
choice,
? The constraint can be converted to,
? Because Yd and At are relatively stable,Ct is also relatively stable 。
? In other words,given constraint condition,households will keep the
consumption in each period as stable as possible to maximize the
present value of consumption,
)( dtdt
Y
A
hYC ??
12.2 Micro Basis of Macroeconomics
? Households’ optimal consumption
（ 2） how to arrange current assets?
concept of current assets,
12.2 Micro Basis of Macroeconomics
s to c k p r ic e s h a r e q u a n ti ty
m o n e y p r ic e
t
t t t
t
tt
tt
M
A q V
P
qV
MP
??
,；, ；
,；, 。
? Households’ optimal consumption
government’s budget constraint,
relationship between investment and capital,
t
tt
t P
MMG ?? ? 1
tttt KKKI ???? ? )( 1
12.2 Micro Basis of Macroeconomics
?Households’ optimal consumption
ignoring international trade,
12.2 Micro Basis of Macroeconomics
1
1
11
1
1
11
()
[ ( ) ( ) ]
()
sup pose 0 the n
t t t t
d
t t t t
tt
t t t t t
tt
d t
t t t t t t
t
d
d
Y C I G
Y C A A
MM
C q V q V
PP
M
Y Y K V q q
P
M
Y Y K
P
Y Y K
??
??
?
?
?
?
??
?
?
??
? ? ?
? ? ?
? ? ? ? ?
? ? ? ? ? ?
? ? ? ?
?
??
,：
? Suppose （ qV） * is the appropriate share value and（ M/P）
* is the appropriate real money,
? The left of the equation denotes excessive demand for
money while the right excessive supply of shares,The
equation implies that if keep money in a proper level the
stock market will clean automatically,
12.2 Micro Basis of Macroeconomics
**
**
()()
or
( ) ( ) ( ) ( )
M M
qV qV A
P P
MM
qV qV
PP
? ? ? ?
? ? ?
：
? Suppose money demand is positively related to
income,O is the nominal revenue for holding
money,i is the nominal revenue for holding
shares,then we have,
0)()( ???? ?? oi
12.2 Micro Basis of Macroeconomics
? Maximization problem of firm
? Similar to household’s problem,this is also a
optimizing problem with constraint conditions
given,Firms choose inputs to maximize profit
just as households maximize consumption
utility,
? We will analyze this process by diagrams,
12.2 Micro Basis of Macroeconomics
Fixing Cost of Firm
Fixing cost
Investment
Labor Quantity Needed
labor
Cost and output
L*
e
MPL
Cost
/output
12.3 Introduction to Labor Market
? Labor market is just like a bridge between
households and firms,Compared with
goods and financial market,labor market is
more complicated,
? Basic assumptions about labor market,
?Labor supply is fixed
LLt ?
? The two parties in labor
market interact through
negotiation on wage,
? When wage is higher than
equilibrium level,firms will
endeavor to renegotiate on the
wage,
? When wage is lower than
equilibrium level,workers will
require to renegotiate on the
wage,
? Hence,the process of wage
adjustment is the process of
reducing exchange cost,
0* ?? WW
0* ?? WW
12.3 Introduction to Labor Market
* n o m i n a l e q u i l i b r i u m w a g e
n o m i n a l w a g e
W
W
,；
：
? Condition for minimizing exchange cost,
??
?
?? ???????
0
2*
11
*2*
}{ })]()[(){()1
1(m i n)(m i n
t
ttttttt
t
rC t ???????? ?
12.3 Introduction to Labor Market
ln
01
W?
?
?
??
? First-order condition,
12.3 Introduction to Labor Market
* * **
11 11
* * *
1 1 1 1
0
1
[ ( 1 ) ( ) ( ) ] [ ( ) ] 0()
1
( ) 2 ) ( ) ( 1 ) ( ) 0
t
t t t t t ttt
t t t t t t
C
r
r
rr
?
? ? ? ? ? ? ? ???
?
? ? ? ? ? ?
?
?? ??
? ? ? ?
?
?
?
?
? ? ? ? ? ? ? ? ??
?
? ? ? ? ? ? ? ? ? ?（
? If the interval between t and t+1,we get a
differential equation,
12.3 Introduction to Labor Market
'' '
12
*
11
*
*
11
12
0
''
''
1
2 ),( 1 )
tt
tt
tt
y y y
y
y
y
r
rr
??
??
??
??
??
?
??
??
? ? ?
??
??
??
?
? ? ? ? ? ?
，
，
（
?Solve the equation,
12.3 Introduction to Labor Market
12
2
1 1 2
1,2
12
4
2
tt
y e y e
??
? ? ?
?
? ? ?
?
?
??；
?Convergence problem of y,
?This implies that will gradually
decrease and finally be convergent to
*?? ?
12.3 Introduction to Labor Market
2
**
11
*
11
*
w h e n 1,y is c o n v e r g e n t
,',''
'' '
) ( )
o r 1
t t t
t t t t
tt
tt
y e y e y e
YY
? ? ?
?
??
?
? ? ? ? ?
??
?
??
??
??
?
? ? ?
??
? ? ? ?
?
??
?
（
：
*tt???
? Conclusions,
? Optimal decision of households and firms and
the equilibrium of labor market could all be
regarded as the maximization problems given
constraint conditions,
? If a macroeconomic model could justify itself,
then we can regard the model as a
consummate model from the aspect of
economic theory,
12.3 Introduction to Labor Market
Chapter 12
The End
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