Financial Economics Lecture Ten

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Financial Economics Lecture Ten

• Dynamic Modelling the Circuit

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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.

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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

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Dynamic modellingan introduction

• Have to be integrated to solve them

Rearrange
Integrate
Solve
Take exponentials

• Constant is value of y at time t0

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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

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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
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Dynamic modellingan introduction

• Simulating gives exponential growth if agt0

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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

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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!)

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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,
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Dynamic modellingan introduction

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

• (2) Calculate equilibrium values

Simulate!

• (3) Rather than stopping there

Graph the results
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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 in
  equilibrium?)

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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

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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)

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Dynamic modellingan introduction

• MUCH more complicated models than this can be
  built

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Dynamic modellingan introduction

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

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Dynamic modellingan introduction

• System dynamics block has these components

• And this block has the following components

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Dynamic modellingan introduction

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

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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

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Dynamic modellingan introduction

• Sharks just shown as constant here

• Sharks substract from fish growth rate

• Now add shark dynamics

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Dynamic modellingan introduction

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

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Dynamic modellingan introduction

• Model now gives same cycles as seen in
  mathematical simulation.

• Now to apply this to endogenous money!

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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 (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

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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

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Modelling endogenous money dynamically
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Modelling endogenous money dynamically

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

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Modelling endogenous money dynamically

• In flowchart format, equations

• Become

• Simulating this in real time

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Modelling endogenous money dynamically

• Tidied up using compound blocks

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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?

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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)

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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

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Modelling endogenous money dynamically
But first...
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• But being a capitalist still a losing
  proposition
• Because production isnt yet modelled
• Capitalists borrow to produce, sell, make a
  profit

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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

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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

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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

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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

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Modelling endogenous money dynamically

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

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Modelling endogenous money dynamically

• Almost obvious why capitalists go into debt

• Does it matter that capitalists are in net debt?

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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

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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

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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

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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
• Final 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

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Modelling endogenous money dynamically

• Final system is

• Initial loan L can now fund one investment after
  another, as Keynes argued

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Modelling endogenous money dynamically

• All accounts stabilise at constant level

• Flow of revolving fund through accounts
  generates sustained stream of income for all 3
  classes from single initial loan

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Modelling endogenous money dynamically

• With parameter values used, 100 initial loan can
  finance
• 61 of profit
• 143 of wages and
• 1 of bank income per year

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Modelling endogenous money dynamically

• How can capitalists borrow money make a
  profit? dilemma easily solved
• So long as income from production exceeds
  interest payments on borrowed money!

Interest on debt
Income from production

• Circuitist how can M become M? dilemma a case
  of confusing stocks (initial loan) and flows
  (incomes, including profits)

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Additional insights from model

• Endogenous money works
• Dont need deposits to make loans (exogenous
  money perspective)
• 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
  third parties

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Additional insights from model

• Deposits destroyed as Loans repaid, not
  Moneywhich is conserved
• Money a bank asset
• Money(t) KD(t) BP(t)
• Technically, Loans destroyed by returning
  Deposits to Banks

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Additional insights from model

• Form of money is either
• Debt by other parties to banks (loansdeposits)
  or
• Banks unencumbered asset in BP account
  (reserves)
• Reserves created by repayments of loans
• Reverse of exogenous money perspective (loans
  made possible by reserves)

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Conclusion

• Circuitists/Keynes/Schumpeter correct
• Loan in pure credit system initiates sustained
  economic 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
  excessive debt
• Next lecture
• The nonlinear disequilibrium dynamics of debt