Financial Economics Lecture Ten

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Financial Economics Lecture Ten

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Aggregate income generated by initial loan L=$100 is stock: Integral of these over time: ... All money eventually accumulates in BP & activity ceases ... – PowerPoint PPT presentation

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Title: Financial Economics Lecture Ten

1
Financial Economics Lecture Ten

Dynamic Modelling the Circuit

2
Dynamic modellingan introduction

Dynamic systems necessarily involve time
Simplest expression starts with definition of the
percentage 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 mathematically

This can be rearranged to

Looks very similar to differentiation, which you
have done but essential difference rate of
change of y is some function of value of y itself.

3
Dynamic modellingan introduction

Dependence of rate of change of variable on its
current value makes solution of equation much
more difficult than solution of standard
differentiation problem
Differentiation also normally used by economists
to find minima/maxima of some function
Profit is maximised where the rate of change of
total revenue equals the rate of change of total
cost (blah blah blah)
Take functions for TR, TC
Differentiate
Equate
Easy! (also wrong, but thats another story)
However differential equations

4
Dynamic modellingan introduction

Have to be integrated to solve them

Rearrange
Integrate
Solve
Take exponentials

Constant is value of y at time t0

5
Dynamic modellingan introduction

Simple model like this gives
Exponential growth if agt0
Exponential decay if alt0
But unlike differentiation technique (most
functions can be differentiated)
Most functions cant be integrated no simple
solution can be found and also
Models can also be inter-related
Two variables x y (and more w z )
y can depend on itself and x
x can depend on itself and y
All variables are also functions of time
Models end up much more complicated

6
Dynamic modellingan introduction

Simple example relationship of fish and sharks.
In the absence of sharks, assume fish population
grows smoothly
The rate of growth of the fish population is a
p.a.

Rearrange
Integrate
Solve
Exponentials
7
Dynamic modellingan introduction

Simulating gives exponential growth if agt0

8
Dynamic modellingan introduction

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

But we know fish and sharks interact
The rate of change of fish populations is also
some (negative) function of how many Sharks there
are

The rate of change of shark population is also
some (positive) function of how many Fish there
are

9
Dynamic modellingan introduction

Now we have a model where the rate of change of
each variable (fish and sharks) depends on its
own value and the value of the other variable
(sharks and fish)

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

10
Dynamic modellingan introduction

But for technical reasons, this is the last level
of complexity that can be solved
Add an additional (nonlinearly related)
variablesay, seagrass levelsand model cannot be
solved
But there are other ways
Mathematicians have shown that unstable processes
can be simulated
Engineers have built tools for simulating dynamic
processes

similarly,
11
Dynamic modellingan introduction

(1) Enter (preferably empirically derived!)
parameters

(2) Calculate equilibrium values

Simulate!

(3) Rather than stopping there

Graph the results
12
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 in
equilibrium?)

13
Dynamic modellingan introduction

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

14
Dynamic modellingan introduction

Representing this as mathematics, we get

Next stage of a symbolic solution is

Symbolically you would continue, putting dt on
the RHS but instead, numerically, you integrate

As a flowchart, you get

Read it backwards, and its the same equation

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

15
Dynamic modellingan introduction

MUCH more complicated models than this can be
built

16
Dynamic modellingan introduction

Models can have multiple interacting variables,
multiple layers for example, a racing car
simulation

17
Dynamic modellingan introduction

System dynamics block has these components

And this block has the following components

18
Dynamic modellingan introduction

This is not toy software engineers use this
technology to design actual cars, planes,
rockets, power stations, electric circuits

19
Dynamic modellingan introduction

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 of

To add second half, have to alter part of model
to LHS of integrator

20
Dynamic modellingan introduction

Sharks just shown as constant here

Sharks substract from fish growth rate

Now add shark dynamics

21
Dynamic modellingan introduction

Shark population declines exponentially, just as
fish population rises
(numbers obviously unrealistic)
Now add interaction between two species

22
Dynamic modellingan introduction

Model now gives same cycles as seen in
mathematical simulation.

Now to apply this to endogenous money!

23
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 (BP)
Accepts repayment of debt by capitalist
Banker Income Account (BY)
Records incoming and outgoing interest payments
Starting at the very simplest level compound
interest

24
Modelling endogenous money dynamically

KD grows at rate of debt interest rd

KC grows at rate of credit interest rc

BY pockets the difference

As Circuitists feared, this is the road to ruin
for capitalists
With Loan L100, rd5, rc3, after one year
Simulating this with equations

25
Modelling endogenous money dynamically
26
Modelling endogenous money dynamically

Whod be a capitalist?
But model isnt complete yet no repayment
First, same model as a flowchart

27
Modelling endogenous money dynamically

In flowchart format, equations

Become

Simulating this in real time

28
Modelling endogenous money dynamically

Tidied up using compound blocks

29
Modelling endogenous money dynamically

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, ending
different times, some extended, others paid off
early
Aggregate outcome very different to each
individual loan
Fixed repayment commitment?
Like exponential decay

Debt would fall towards zero as t??
Sensible objective for capitalist borrowers
How to achieve it?

30
Modelling endogenous money dynamically

Currently debt has dynamics

To convert this to

Need to add
Repayment of interest

Repayment of principal

Both amounts have to come out of capitalist
credit account KC (capitalists only source of
funds)

Repayment of principal to banker principal
account BP

Interest to banker income account BY (already
shown)

31
Modelling endogenous money dynamically

So (still incomplete) system is

How does this behave?
Simulate and find out
Try R1

Picture looks a lot better for capitalists than
without repayment

32
Modelling endogenous money dynamically
But first...
a word from our sponsor...

But being a capitalist still a losing
proposition
Because production isnt yet modelled
Capitalists borrow to produce, sell, make a
profit

33
Modelling endogenous money dynamically

Observations on Circuitists vs Keynes
Graziani As soon as firms repay their debt to
the banks, the money initially created is
destroyed.
Keynes Credit, in the sense of finance, looks
after a flow of investment. It is a revolving
fund which can be used over and over again. It
does not absorb or exhaust any resources. The
same finance can tackle one investment after
another. (247)
Keynes is right the money created by the loan
continues to 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

34
Modelling endogenous money dynamically

Sum of capitalist debit account KD banker
principal account BP always equals value of
initial loan L

Debt destroyed by repayment money is conserved
as a revolving fund of finance

35
Modelling endogenous money dynamically

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 or wages
in proportions of flow of income from production,
wage share profit share 1

36
Modelling endogenous money dynamically

Call proportion of outflow that finances
production P

Fraction (1-p) of this flows to workers as wages

Fraction p flows back to capitalists as profits

Workers earn interest too

Paid by bankers from BY

Workers bankers consume

pay to KC account

37
Modelling endogenous money dynamically

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

38
Modelling endogenous money dynamically

Almost obvious why capitalists go into debt

Does it matter that capitalists are in net debt?

39
Modelling endogenous money dynamically

No
Capitalist entrepreneurs are the debtors par
excellence in capitalism
becoming a debtor arises from the necessity of
the case and is not something abnormal, an
accidental event to be explained by particular
circumstances. What he first wants is credit.
Before he requires any goods whatever, he
requires purchasing power. He is the typical
debtor in capitalist society. (Schumpeter,
Theory of Capitalist Development 102)
Net debt tapers to zero over time

40
Modelling endogenous money dynamically

After ten years
Capitalist net debt position negligible
Almost all net money in BP account

What about incomes?
KD, KC, WY, etc. record bank balances
Entries wWY, bBY, etc. record transactions
between accounts
Incomes are subset of transactions

41
Modelling endogenous money dynamically

Workers wages interest

Bankers net interest

Capitalists profit net interest

These are flows
Aggregate income generated by initial loan L100
is stock
Integral of these over time

42
Modelling endogenous money dynamically

So initial loan of 100 can generate
89 income to capitalists
2 to bankers and
215 to workers
(with example parameters)
Without relending
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 and over again. (Keynes)
Bankers re-lend proportion B of existing BP
Amount paid into KC recorded in KD

43
Modelling endogenous money dynamically