lecture 04 dynamic modelling 2006

8/6/2019 Lecture 04 Dynamic Modelling 2006

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Financial Economics Lecture Ten

Dynamic Modelling & the Circuit


2/54

Dynamic modellingan introduction

Dynamic systems necessarilyinvolve time

Simplest expression starts with definition of thepercentage rate of change of a variable:

Population grows at 1% a year

Percentage rate of change of a variable y is

Slope of function w.r.t. time (dy/dt) Divided by current value of variable (y)

So this is mathematically1

.01dy

y dt=

This can be rearranged to .01dy

ydt =

Looks very similar to differentiation, which you havedone but essential difference: rate of change of yis some function of value of y itself.


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Dependence of rate of change of variable on its current

value makes solution of equation much more difficult thansolution of standard differentiation problem

Differentiation also normally used by economists to findminima/maxima of some function

Profit is maximised where the rate of change of totalrevenue equals the rate of change of total cost (blahblah blah)

Take functions for TR, TC

Differentiate Equate

Easy! (also wrong, but thats another story)

However differential equations


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Simple model like this gives

Exponential growth if a>0 Exponential decay if a


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Simple example: relationship of fish and sharks.

In the absence of sharks, assume fish population growssmoothly:

The rate of growth of the fish population is a% p.a.1 dF

a

F dt

= dF a dtF

=

dFadt

F= ( ) 0ln F a F c= +

( ) 0 0a t c ca t a t F t e e e C e + = = =

Rearrange

Integrate

Solve

Expo

nential

s


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Simulating gives exponential growth if a>0

a .02:= F0 100:= F t( ) F0 ea t:=

0 20 40 60 80 1000

200

400

600

800Fish population as a function of t ime

Years

F t( )

t


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Same thing can be done for sharks in the absence of fish:

Rate of growth of shark population equals c% p.a. But here c is negative

Sbadt

dFF =1

( ) 2c tS t C e =

c .01:= S0 50:= S t( ) S0 ec t

:=

0 20 40 60 80 10010

20

30

40

50Shark population as a function of time

Years

S t( )

t

But we know fish andsharks interact:

The rate of change offish populations is alsosome (negative) functionof how many Sharks

there are

The rate of change ofshark population is alsosome (positive) function ofhow many Fish there are

1 dS

c d FS dt = +


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Now we have a model where the rate of change of each

variable (fish and sharks) depends on its own value andthe value of the other variable (sharks and fish):

Sbadt

dF

F=

1

1 dSc d F

S dt = +

dFa F b S F

dt=

dSc S d F S

dt= +

This can still be solved, with more effort (dont worryabout the maths of this!):


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But for technical reasons, this is

the last level of complexity thatcan be solved

Add an additional (nonlinearlyrelated) variablesay,seagrass levelsand modelcannot be solved

But there are other ways

Mathematicians have shownthat unstable processes canbe simulated

Engineers have built tools forsimulating dynamic processes

( )lnd

F a b S dt

=

( )lnd F a b S dt =

( )lnd F a b S dt = ( ) ( )ln F a b S t c = +

( )( )1

a b S t t F C e =

( )( )2

c d F t t S C e + =


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(1) Enter (preferably empirically derived!) parameters:

Equilibrium values

Fish Fec

d:= Fe 10000=

Sharks Se

a

b:= Se 10=

(2) Calculate equilibrium values:

(3) Rather than stopping there:

Given

t

F t( )d

d

F t( ) a b S t( )( ) F 0( ) 8000

tS t( )

d

dS t( ) c d F t( )+( ) S 0( ) 12

F

S

Odesolve

F

S

t, 10, 1000,

:=

Parameters

a 1:= Annual population growth rate of fish in absence of sharks

b .1:= Impact of each shark on fish population growth rate

c 1:= Death rate of sharks in absence of fish

d .0001:= Impact of each fish on survival of sharks


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Dynamic modellingan introduction System is never in equilibrium

Equilibrium unstablerepels as much as it attracts

Commonplace in dynamic systems Systems are always far from equilibrium

(What odds that the actual economy is inequilibrium?)

0 2 4 6 8 107000

8000

9000

1 .104

1.1 .104

1.2 .104

1.3 .104

1.4 .104

7

8

9

10

11

12

13

14

Fish (LHS)

Fish Equilibrium

Sharks (RHS)

Shark Equilibrium

Fish (LHS)

Fish Equilibrium

Sharks (RHS)

Shark Equilibrium

Fish & Shark populations over time

Years

Numb

er

7 8 9 10 11 12 13 146000

8000

1 .104

1.2 .104

1.4 .104

Time Path

Equilibrium

Time Path

Equilibrium

"Limit Cycle" of Fish & Sharks

Sharks

Fish


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Thats the hard way; now for the easy way

Differential equations can be simulated using flowcharts The basic idea Numerically integrate the rate of change of a

function to work out its current value Tie together numerous variables for a dynamic

system Consider simple population growth:

Population grows at 2% per annum


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Representing this as mathematics, we get1

.02dP

P dt

=

.02dP

Pdt

=

.02 . P P dt =

Next stage of a symbolic solution is

Symbolically you would continue,putting dt on the RHS; butinstead, numerically, you integrate:

As a flowchart, you get:

Read it backwards, andits the same equation:

Feed in an initial value (say, 18 million) and we cansimulate it (over, say, 100 years)

Population

* 1/S

0.02

Population


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MUCH more complicated models than this can be built

Population

* 1/S

0.02

Population

Plot

Time (sec)

0 10 20 30 40 50 60 70 80 90 1000

20000000

40000000

60000000

80000000

100000000

120000000

140000000

160000000

180000000

200000000


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Models can have multiple interacting variables, multiplelayers; for example, a racing car simulation:

Car Path and

Vital ParametersSystem Dynamics

LAPS

LAPS

LAPS

ENGINE TORQUE

LAPS

LAPS

TAU, MOD(Pi/2)

0

TAU, MOD(Pi)

0

1

2TAU, MOD(Pi)

ACCELERATION

-

-10

0

10

20ACCELERATION

ACCELR.

ENGINE RPM

LAPS

0 .2 .4 .6 .8 15000

6000

7000

8000ENGINE RPM

Fc

TORQUE AVA ILABLE

LAPS

0 .2 .4 .6 .8 1300

350

400

450

500ENGINE TORQUE, FT-#

ENGINE TORQUE

ENG.RPM

DELTA "S" (PER STEP)

LAPS

0 .2 .4 .6 .8 1.4

.5

.6

.7DELTA S

NORMAL FORCE

LATERAL FORCE LATERAL & NORM.FORCES

LAPS

0 .2 .4 .6 .8 10

1000

2000

3000LATERAL FORCE

TOT.TRACTION FORCE, Fc

LAPS

DELTA S

INPUT PARAMETERS

Automotive Dynamics:Simulation of Automobile RacingDynamics on a Race Track


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System dynamics block has these components:

TAU CONVERION.& DISPLAYS

Acceleration andBraking Logic

Normal andLateral Force

Conversions Computations

Rotating Mass

Dynamics

Car Mass

Radius of Curvature Minimum Veloc ity

LATERAL FORCE

NORMAL FORCE

MUACC-BRAKE FORCE & LOGIC

Fx,BRAKING

Fx, ACCEL.

0

0

RADIUS OF CURVATURE

And this block has the following components


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Lets use it to build the Fish/Shark model

Start with population model, only Change Population to Fish Alter design to allow different initial numbers

This is equivalent to first half ofdF

a F b S F dt

=

To add second half, have toalter part of model to LHS ofintegrator

+

+

1/SFish

Fish

*0.02

Plot

Time sec

0 10 20 30 40 50 60 70 80 90 1000

5000

10000

15000

20000

25000

30000

1000

Initial Fish Population


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Sharks just shown

as constant here

Sharks substractfrom fish growth rate

Now add shark dynamics

Plot

0 20 40 60 80 1001000

2000

3000

4000

5000

6000

7000

8000

*

Sharks

1e-006

+

-

Initial Fish Population

1000

0.02*

Fish

Fish

1/S

+

+

Fish


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Shark population

declinesexponentially, justas fish populationrises

(numbersobviouslyunrealistic)

Now add interactionbetween two

species

Fish

Initial Shark Population

100

-0.1*

Sharks1/S

++

Sharks

Plot

Time (years)0 20 40 60 80 100

0

20

40

60

80

100


22/54


Model now gives same cycles as seen in mathematicalsimulation.

Now to apply this to endogenous money!

Fish

*

Sharks

2

+

-

10*

Fish

1/S 1/S*

1-

+

0.001Sharks

*

Fish

Sharks

Plot

0 2 4 6 8 100

1000

2000

3000

4000

50006000

7000

+

+

200010

+

+

Plot

0 2 4 6 8 100

5

10

15

20Plot

0 5 10 15 200

1000

2000

3000

4000

5000

6000

7000


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Modelling endogenous money dynamically

Remember our minimum 4 accounts?

Capitalist Credit (KC

) Money paid in here

Interest on balance

Repayments out of here to Banker

Capitalist Debt (KD) Repayment of debt recorded here

Interest on balance

Banker Principal Account (B

P)

Accepts repayment of debt by capitalist

Banker Income Account (BY)

Records incoming and outgoing interest payments

Starting at the very simplest level: compound interest


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KD grows at rate of debt interest rd: =D Ddd

K r Kdt

KC grows at rate of credit interest rc: = cC Cd K r Kdt

BY pockets the difference: = Y cD Cdd

B r K r K dt

As Circuitists feared, this is the road to ruin forcapitalists

With Loan L=$100, rd=5%, rc=3%, after one year

Simulating this with equations


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Modelling endogenous money dynamicallyGiven

KD 0( ) LCompound interest

on both accounts tKD t( )

d

drd KD t( )Initial Loan

recorded in bothdebt and creditaccount

KC 0( ) LtKC t( )

d

drc KC t( )

Bank comes outahead on the

interest

tBY t( )

d

drd KD t( ) rc KC t( ) BY 0( ) 0

Simulate themodel and seewhat happens

KD

KC

BY

Odesolve

KD

KC

BY

t, 10, 1000,

:=


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0 2 4 6 8 10100

120

140

160

180

0

10

20

30

Capitalist Debt

Capitalist Credit

Bank Income (RHS)

Capitalist Debt

Capitalist Credit

Bank Income (RHS)

Bank Balances over time: no repayment

Years

$

KD t( )

KC t( )BY t( )

t

KD 1( ) 105.127= KC 1( ) 103.045= KC 1( ) KD 1( ) 2.082= BY 1( ) 2 .082=

Whod be a capitalist?

But model isnt complete yet: no repayment

First, same model as a flowchart


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In flowchart format, equations

=D Ddd K r Kdt =cC C

dK r Kdt = Y cD Cd

dB r K r K dt

Become

KD1/S

Capitalist Debt

+

+

*rd

L

Bank Accounts

No repayment

Time (Years)0 2 4 6 8 10

0

20

40

60

80

100

120

140

160

180

200Capitalist Debt

Capitalist Credit

Bank Income

Parameters

rc *

++

1/S

Capitalist CreditKC

rd*

KD

KC

*rc

+-

1/SBank Income

BY

100

Initial Loan

KD

KC

Simulating this in realtime

01Norepayment.vsm


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Tidied up using compound blocks:

L

Bank AccountsNo repayment

Time (Years)

0 2 4 6 8 100

20

40

60

80

100

120

140

160

180

200Capitalist Debt

Bank IncomeCapitalist Credit

Parameters

BY100Initial Loan

KC

Capitalist

DebtKD

CapitalistCredit

BankIncome

01Norepayment02.vsm


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How to model repayment? Standard home loan styleregular payments over term

of loan? OK at micro level, but at macro:

Lots of loans, starting different times, endingdifferent times, some extended, others paid off

early Aggregate outcome very different to each

individual loan Fixed repayment commitment?

Like exponential decay: = 1

PDD

dK RK dt

Debt would fall towards zero as t Sensible objective for capitalist borrowers;

How to achieve it?


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Currently debt has dynamics: =D Ddd

K r Kdt

To convert this to = 1 PDD

d K RK dt Need to add:

Repayment of interest( )= D D Dd d

dK r K r K

dt

& Repayment of principal ( )= + pD D D D d dd

K r K r K R K dt Both amounts have to come out of

capitalist credit account KC(capitalists only source of funds)

( )= +c pC C D D dd

K r K r K R K dt

Interest to banker income account BY(already shown)

Repayment of principal to bankerprincipal account BP

=P P Dd

B R Kdt

ll


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So (still incomplete) system is: ( )= + pD D D D d dd

K r K r K R K dt

( )= +c pC C D D dd K r K r K R K dt

=P P Dd

B R Kdt

= Y cD Cdd B r K r K dt

How does this behave? Simulate and find out

Try R=1Given

t

KD t( )d

d

rd KD t( ) rd KD t( ) RP KD t( )+( ) KD 0( ) L

KC 0( ) L

tKC t( )

d

drc KC t( ) rd KD t( ) RP KD t( )+( )

BY 0( ) 0

tBY t( )

d

drd KD t( ) rc KC t( )

BP 0( ) 0

t

B

P

t( )d

d

R

P

K

D

t( )

KD

KC

BY

BP

Odesolve

KD

KC

BY

BP

t, 10, 1000,

:=

Picture looks a lot better forcapitalists than withoutrepayment

d ll d d ll


32/54


0 2 4 6 8 1050

0

50

100

0

1

2

3

Capitalist Debt

Capitalist CreditBank Income (RHS)

Capitalist Debt

Capitalist CreditBank Income (RHS)

Bank Balances over time: repayment

Years

$

KD t( )

KC t( )BY t( )

t

KD 1( ) 36.788= KC 1( ) 35.501= KC 1( ) KD 1( ) 1.287= BY 1( ) 1.287=

But being a capitalist still a losing proposition

Because production isnt yet modelled

Capitalists borrow to produce, sell, & make a profit

M d ll d d ll


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Observations on Circuitists vs Keynes

Graziani: As soon as firms repay their debt to thebanks, the money initially created is destroyed.

Keynes: Credit, in the sense of finance, looks after aflow of investment. It is a revolving fund which can beused over and over again. It does not absorb orexhaust any resources. The same finance can tackleone investment after another. (247)

Keynes is right: the money created by the loan continuesto exist & circulate as an asset of the banks. It is either

The outstanding debt of capitalists to banks; or

The balance in bankers principal account:

M d lli d d i ll


34/54

Modelling endogenous money dynamically Sum of capitalist debit account KD + banker principal account

BP always equals value of initial loan L:

0 2 4 6 8 100

50

100

150

Bankers Principal

Capitalist Debt

Sum

Bankers Principal

Capitalist Debt

Sum

Money, Credit & Debt

Years

$

Debt destroyed by repayment; money is conserved as a revolving

fund of finance

M d lli d d i ll


35/54


Final step to close (simple) model: production How to model?

Complicated! Input-output issues, pricing, stocks Leave till later & take essence:

Whole purpose of production to make $ profit Must spend $ to make $: outflow from KC Production requires workers

Must be paid wages (into new account WY)

Products sold to capitalists, workers, bankers Transactions from sale flow to capitalist credit

account (out of BY, WY) Net revenue generated resolves into either

profits orwages in proportions of flow of income from

production, wage share + profit share = 1

M d lli d d i ll


36/54


Call proportion of outflowthat finances production P:

( )= + c pC C D D Cdd

K r K r K R K PK dt

Fraction (1 ) of this flows toworkers as wages:

( )= 1Y Cd

W PKdt

Workers earn interest too: ( )= +1Y c YCdW PK rW dt

Paid by bankers from BY: = Y c c Y D Cdd

B r K r K rW dt

Fraction flows back to

capitalists as profits:

( ) = + +c pC C D D C Cdd

K r K r K R K PK PK dt

Workers & bankers consume:( ) = + 1Y c Y Y C

dW PK rW W

dt= Y c c Y Y D Cd

dB r K r K rW B

dt

( ) = + + + +c p Y Y C C D D C C dd

K r K r K R K PK PK W B

dt

& pay $ to KC account

M d lli d d i ll


37/54

L


Time (Years)

0 2 4 6 8 10-100

-50

0

50

100Capitalist Debt

Bank PrincipalCapitalist Credit

Parameters

BY

100Initial Loan

KC

CapitalistDebt

KD

CapitalistCredit

BankIncome

KD

Bank Accounts

No repayment

Time (Years)0 2 4 6 8 10

0

5

10

15

20Bank Income

Workers Income

KC

BankPrincipal

BP

WY

WYBY

WorkerIncome


So the first complete (but still simple!) system is:

( )= + pD D D D d dd

K r K r K R K dt

( ) = + + + +c p Y Y C C D D C C dd

K r K r K R K PK PK W B dt

=P P Dd

B R Kdt

( ) = + 1Y c Y Y CdW PK rW W dt

= Y c c Y Y D Cdd

B r K r K rW B dt 06Production02.vsm

M d lli d d i ll


38/54


Almostobvious why capitalists go into debt:

0 2 4 6 8 100

5

10

15

0

5

10

15

20

Capitalist Debt

Capitalist Credit

Bank Income (RHS)

Worker Credit

Capitalist Debt

Capitalist Credit

Bank Income (RHS)

Worker Credit

Bank Account Balances over time: production

Years

$

KD t( )

KC t( )

BY t( )

WY t( )

t

KD 1( ) 36.788= KC 1( ) 27.452= KC 1( ) KD 1( ) 9.336= BY 1( ) 0 .747= WY 1( ) 8.589=

Does it matter that capitalists are in net debt?

M d lli d d i ll


39/54


No:

Capitalist entrepreneurs are the debtors parexcellence in capitalism:

becoming a debtor arises from the necessity ofthe case and is not something abnormal, anaccidental event to be explained by particularcircumstances. What he first wants is credit.Before he requires any goods whatever, herequires purchasing power. He is the typicaldebtor in capitalist society. (Schumpeter, Theory

of Capitalist Development: 102) Net debt tapers to zero over time:

M d lli d d i ll


40/54


After ten years

Capitalist net debt position negligible Almost all net money in BP account:

0 2 4 6 8 100

50

100

150

Bankers Principal

Capitalist Debt

Sum

Bankers Principal

Capitalist Debt

Sum

Money, Credit & Debt

Years

$

KD 10( ) 4.54 103

= KC 10( ) KD 10( ) 1.89 103

= WY 10( ) 8.306 104

=

KC 10( ) 2.65 103

= BY 10( ) 1.059 103

= BP 10( ) 99.995=

What about incomes?

KD, KC, WY, etc. record

bank balances

Entries WY, BY,

etc. recordtransactionsbetweenaccounts

Incomes are subset oftransactions

M d lli d s d mi ll


41/54


Workers: wages + interest =

+ cC C DdPK r K r K

( ) +1 c YCPK rW

c c YD Cdr K r K rW Bankers: net interest =

Capitalists: profit + net interest =

These are flows

Aggregateincomegenerated byinitial loanL=$100 is stock:

Integral of theseover time:

Profit t( )

0

t

t P KC t( ) rd KD t( )

d:= Profit 10( ) 86.754=

CapInc t( )

0

t

t P KC t( ) rc KC t( ) rd KD t( )( )+

d:= CapInc 10( ) 89.048=

BankInc t( )

0

t

trd KD t( ) rc KC t( ) rc WY t( )

d:= BankInc 10( ) 2.062=

WorkInc t( )

0

t

t1 ( ) P KC t( ) rc WY t( )+

d:= WorkInc 10( ) 214.736=

M d llin nd n us m n d n mic ll


42/54


So initial loan of $100 can generate:

$89 income to capitalists; $2 to bankers; and

$215 to workers

(with example parameters)

Withoutrelending All money eventually accumulates in BP & activity

ceases

Next extension: with re-lending so that we model

credit as a revolving fund which can be used over andover again. (Keynes)

Bankers re-lend proportion B of existing BP

Amount paid into KC; recorded in KD:



43/54


Final system is:

( )= + +p PD D D D d dd

K r K r K R K BB dt

( ) = + + + + +c p Y Y P C C D D C C dd

K r K r K R K PK PK W B BB dt

= P P PDd

B R K BB dt


= Y c c Y Y D Cdd

B r K r K rW B dt

Initial loan L can now fund oneinvestment after another, as

Keynes argued:

L

Bank Accounts

No repayment

Time (Years)

0 2 4 6 8 100

20

40

60

80

100Capitalist Debt

Bank PrincipalCapitalist Credit

Parameters

BY

100Initial Loan

KC

CapitalistDebt KD

CapitalistCredit

BankIncome

KD


Time (Years)

0 2 4 6 8 100

5

10

15

20

25

30Bank Income

Workers Income

KC

BankPrincipal

BP

WY

WYBY

WorkerIncome

BP

BP

07Relending02.vsm



44/54


All accounts stabilise at constant level:

0 2 4 6 8 10

20

40

60

80

100 Capitalist DebtCapitalist Credit

Bank Principal

BP+KD

Capitalist DebtCapitalist Credit

Bank Principal

BP+KD

Bank Account Balances over time: relending

Years

$

KD t( )

KC t( )

BP t( )

BP t( ) KD t( )+

t

0 2 4 6 8 100

5

10

15

20

Workers Account

Bankers Income Account

Workers Account

Bankers Income Account

Bank Account Balances over time: relending

Years

$

WY t( )

BY t( )

t

Flow of revolving fund

through accountsgenerates sustainedstream of income for all 3classes from single initial

loan:



45/54


With parameter values used, $100 initial loan can finance:

$61 of profit $143 of wages; and

$1 of bank income per year

CapInc t( )t 1

t

t P KC t( ) rc KC t( ) rd KD t( )( )+

d:= CapInc 10( ) 59.367=

BankInc t( )

t 1

t

trd KD t( ) rc KC t( ) rc WY t( )

d:= BankInc 10( ) 1.375=

WorkInc t( )

t 1

t

t1 ( ) P KC t( ) rc WY t( )+

d:= WorkInc 10( ) 143.162=

TotalInc t( ) CapInc t( ) BankInc t( )+ WorkInc t( )+:= TotalInc 10( ) 203.904=



46/54

InterestInterest

on debton debt


How can capitalists borrow money & make a profit?dilemma easily solved:

So long as income from production exceeds interestpayments on borrowed money!:

IncomeIncomefromfrom

productionproduction

Profits t( )

t 1

t

t P KC t( ) rd KD t( )( )

d:= Profits 10( ) 57.838=

Circuitist how can Mbecome M`? dilemma a case ofconfusing stocks(initial loan) and flows(incomes,including profits)

Additional insights from model


47/54


Endogenous money works

Dont need deposits to make loans (exogenous moneyperspective)

instead loans create deposits

Loans(t) = KD(t)

Deposits(t) = KC(t)+WY(t)+BY(t) Amounts identically equal over time

Bank creates money ab initio

No need for it to have any assets

Just need acceptance of its IOUs as money by thirdparties



48/54


0 2 4 6 8 100

20

40

60

80

100

5 .104

0

5 .104

Deposits

Loans

Loans-Deposits (RHS)

Deposits

Loans


Loans & Deposits: No relending

Years

$

0 2 4 6 8 1060

70

80

90

100

5 .104

0

5 .104

Deposits

Loans


Deposits

Loans


Loans & Deposits: Relending

Years

$

Deposits destroyed as Loans repaid, not Moneywhich isconserved

Money a bank asset: Money(t) = KD(t) + BP(t)

Technically, Loans destroyed by returning Deposits to Banks



49/54


Form of money is either

Debt by other parties to banks (loans=deposits); or Banks unencumbered asset in BP account (reserves)

Reserves created byrepayments of loans

Reverse of exogenous money perspective

(loans made possible by reserves)

0 2 4 6 8 100

50

100

150

Bankers Principal

Capitalist Debt

Sum (=Money)

Bankers Principal

Capitalist Debt

Sum (=Money)

Money: no relending

Years

$

0 2 4 6 8 100

50

100

Bankers Principal

Capitalist Debt

Sum (=Money)

Bankers Principal

Capitalist Debt

Sum (=Money)

Money: relending

Years

$

Next extension: creation of new money


50/54

Next extension: creation of new money

Model so far has single injection of money KD(0)

In actual economy, new money created endogenously allthe time

How to model here?

Simplest step: banks create new money at rate nm%

p.a. New money generated in Bank Principal account1

P m P m P P

d dB n B n B

B dt dt = =

New money then loaned to firms

Recorded as positive entry in credit (money) and debtaccount

Subtracted from Bankers Principal account once paidto capitalists

Creation of new money


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Final model is:

( )p PD D D m PDd dd

K r K r K R K BB dt n B= + + +

( )c p Y Y P C C D D C C m Pdd

K r K r K R K PK PK W B B nt

BBd

= + + ++ + +

( )mD mP P P Pd

B R K B dt n n BB + =


= Y c c Y Y D Cdd

B r K r K rW B dt

Model now has growing levels of income over time



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All account balances grow over time

0 20 40 60 80 1000

1 106

?

2 106

?

3 106

?

0

5 104

?

1 105

?

1.5 105

?

Capitalist DebtBankers Principal

Bankers Income (RHS)

Workers Income (RHS)

Transaction account balances

Year

$

As do incomes, etc.

0 10 20 30 40 500

2 106

?

4 106?

6 106

?

0

1 108

?

2 108

?

3 108

?

4 108

?

Flow of net profit

Flow of wages

Aggregate profit (RHS)

Aggregate wages (RHS)

Profit & wage flows and aggregates

$

But things arentquite this stable inthe real world



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Creation of new money Components of US Money Supply 1959-2006:

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

0

1000

2000

3000

4000

5000

6000

7000

Money Stock

M2-M1

M1-Currency

Currency

US Money Stock & Components

Year (Source: US Federal Reserve H6Hist1,2,5)

US

$

Billions

Latest data confirms Kydland-Prescott stats, endogenousmoney theory: credit drives Base Money

But system very cyclical

Conclusion


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Conclusion

Circuitists/Keynes/Schumpeter correct:

Loan in pure credit system initiates sustainedeconomic activity

Money in economy endogenously determined

Debt an essential aspect of capitalist economy

This simple linear model reaches equilibrium But with endogenous money, debt an essential aspect

of capitalism

Behavioural dynamics of capitalism can lead to cycles &

excessive debt levels Next lecture

The nonlinear, disequilibriumdynamics of debt

lecture 04 dynamic modelling 2006

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