Post on 20-Jan-2016
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Reporter: Jing Huang2011.11.4
Monetary Circulation Model of A Local Economy in
Globalization
Outline
Basic concept1
Model2
Equilibrium analysis3
Simulation on dynamic process4
Basic concepts
A stock variable: measured at one specific time, and
represents a quantity existing at a point of time, which may have been accumulated in the past.
A flow variable: measured over an interval of time. Therefore
a flow would be measured per unit of time. Flow is roughly analogous to rate or speed in this sense. And the differences between two flows will result in the change in stock.
Model - Considering unemployment
( )uiu ou ui uo
dL tN N N N
dt
( )iiu ui
dL tN N
dt
( )oou uo
dL tN N
dt
( ) ( ) ( )o u iL t L t L t N
Lu
Lo Li
iuN ouN
uiN uoN
Model-Basic Variables and relation(1/6)the amount of money that flows into a
local economy :the amount of money that flows out of
the local economy at time t :the aggregate amount of money that
circulates in the local economy:The relationship among stock, in-flow
and out-flow:
( )iF t
( )oF t
( )lM t
( )( ) ( )li o
dM tF t F t
dt
iF
( )lM t
oF
Variables-Expenditures: Total expenditures of local people at time t:
The expenditures on global goods at time t:
This can be treated as out-flow of money.
The volume of local transactions at time t:
( )( ) ll
M tE t
( )( ) lo
M tE t
T
1 1( ) ( ) ( ) ( )*( )i l o lE t E t E t M t
T
Model-Basic Variables and relation(2/6)
relation between in-flow and wages earned outside
the total income obtained from local expenditures:
local wage
( ) ( )* ( )i o oF t L t W t
1 1( ) * ( ) * ( )*( )i i lY t b E t b M t
T
1 1* ( )*( )( )
( )( ) ( )
li
ii i
b M tY t TW tL t L t
Model-Basic Variables and relation(3/6)
Model - Basic Variables and relation (4/6)
The number of potential positions provided in local economy
where is the expected wage
obtained from inside.
*
0
( )ii
Y tL
kW
0kW
Model-Basic Variables and relation(5/6)
The changes of the number of people who work locally lose their job:
The changes of the number of unemployed people hired inside if the local economy :
* *[ *( ( ) ( )) ]* ( )iu i i i i iN L t L t L t if L L
* *( )( ( ) ( ))ui u i i i iN L t L t L t if L L
Model-Basic Variables and relation(6/6)
The changes of unemployed people hired outside
where is a time factor how long unemployed people would be hired outside.
The changes of unemployed people hired outside
where is turnover rate.
( )uo uN L t
( )ou oN L t
Equilibrium analysis
If
where
* ( ) ( )i iL t L t1 1
* * *( ) * * *( )
* * *
( ) ( ) ** * *
( ) 1( ) *
* * *
o
io
u oo
lo
o o
b N A k WTL tk W A
L t N t NT W A
M tL t N
T W T W A
1 1* *( ) * * 1
* * * * *
o
o o o
b k WTAk W T W T W
*
*
[ *( ( ) ( )) ]* ( ) ( ) ( ) 0
[ *( ( ) ( )) ]* ( ) 0
( ) ( ) 0
( ) ( )( )* 0
ui i i o u
ii i i
ou o
l lo o
dLL t L t L t L t L t
dtdL
L t L t L tdtdL
L t L tdtdM t M t
L t Wdt T
Equilibrium analysis
If
*( ) ( )i iN t N t
1 1 1 1* ( )*( ) * * *( )
( ) *1 1* * * *( ) * *
( ) *( ) *
1 1* * * *( ) * *
( ) *( ) *
1 1* * * *( ) * *
l
io
lu
o
lo
o
b M t T bT TL t N
k W T b k kT
M t kL t N
T W T b k kT
M t kL t N
T W T b k kT
*
*
*( ( ) ( ))* ( ) ( ) ( ) 0
*( ( ) ( )) ( ) 0
( ) ( ) 0
( ) ( )( )* 0
ui i u o u
ii i u
ou o
l lo o
dLL t L t L t L t L t
dtdL
L t L t L tdtdL
L t L tdtdM t M t
L t Wdt T
Simulation results ,
,
,,
,
,
，
* *[ *( ( ) ( )) ]* ( )iu i i i i iN L t L t L t if L L functions
* *( )( ( ) ( ))ui u i i i iN L t L t L t if L L ( )uo uN L t ( )ou oN L t
Parameters
0.2 1b
10
500oW 0.5k
0.05 ( 0) 100uL t ( 0) 200oL t ( 0) 700iL t
( 0) 2000000lM t 20T
0.8 Initial
2
Simulation results
Simulation results-shock 1 1.5b
Simulation results-shock 2 15T
Simulation results-shock 3 0.08
Simulation results-shock 4 0.8k
Simulation results-shock 5 0.3
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