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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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