Advanced Political Economy

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Advanced Political Economy

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Title: Advanced Political Economy

1
Advanced Political Economy

New trends in Political Economy Econophysics

2
Why econophysics?

MANY reasons but
Two stand out
Because weve solved all the big problems in
physics
Remark by physicist Cheng Zhang at 1st
Econophysics Conference, Bali 2002, in response
to question from economist Paul Ormerod
Because one dominant concept in modern physics is
highly applicable to finance uncertainty
Pre-Einsteinian physics based on uniformity
certainty
Newtonian Laws of Motion circa 1700s
Supplemented by Maxwells equations for
electromagnetic phenomena circa 1800s
La Places conceit Give me the equations for
the universe I can predict not just the future
but also the past

3
A Quick Physics Primer

By late 19th century, just two anomalies
Speed of light
Light seen as wave
Waves presumed to move through medium
E.g., sound waves are cyclic compression/expansion
of air molecules
Light thought to move through aether
Unobserved substance thought to permeate all
space
Aether fixed, universe moves with respect to it
IF aether exists Earth moving through it, THEN
speed of light in one direction (forward into
aether) should be slower than other (backwards
with aether)
Michelson-Morley experiment speed of light
constant in all directions

4
A Quick Physics Primer

Black body radiation problem
Atom known to exist
Model of atom was positive nucleus orbited by
negative electrons
By Maxwells Newton equations, orbiting charge
should radiate energy
Electron should rapidly spiral into nucleus
Black bodies (i.e. any object, not just heated
ones) should radiate energy
Fitted to experimental data, model predicted
EITHER infinite energy at low frequency OR
infinite energy at high energy
Actual energy profile was a hump
Theory could fit one side or other but not both

5
A Quick Physics Primer

Einstein/Planck solutions to dual problems
light comes in small discrete packets called
quanta
Energy not continuous but discrete with minimum
unit Plancks constant
Probability uncertainty became essential
aspects of physics
Physics also accepted Boltzmanns Laws after
strong 19th century resistance
Progression of energy from highly ordered to
disordered state increase in entropy
All work involves generation of wasted energy
work (desired) necessitates heat undesired but
unavoidable)
Combination of ideas develops measure of
knowledge called Shannons entropy

6
A Quick Physics Primer

Later refinements of Einstein-Planck physics
Deterministic general theory of relativity
Highly successful model of universe on large
scale
Speed of light, relativistic mass effects,
gravity bending of light
Probabilistic quantum theory of matter
Bizarre experimental outcomes
Double slit experiment
Photons etc. interfere with each other even
when emitted singly
Dominant Copenhagen interpretationobserver
affects outcomebut many others
Essential some form of uncertain simultaneity
between quantum-entangled particles
Theorems/measurement derived from huge
experimental base

7
A Quick Physics Primer

Experiments involve massive particle
accelerators
Electro-magnetic cylinders pushing particles in
near vacuum to near light speed
Into collision with other particles
Massive sprays of fundamental particles
(leptons, muons, bosons, quarks) analysed by
sensitive detectors
Heavy-duty statistical apparatus developed to
cope with data (computer hardware software,
mathematical theorems)
Many other areas of analysis opened up with
computing (e.g., Josephson junction circuitry,
quantum tunnelling circuitry, quantum
computing) but no breakthroughs
Physicists also develop complexity theory as
explanation for large-scale phenomena (many
standard deviations events) regularly seen in
physical data (weather, earthquakes)

8
A Quick Physics Primer

Todays unresolved boundaries
Conflict between relativity quantum mechanics
on scale of very small very new
First microseconds of universe
Behavior of matter at black holes, etc.
Main theoretical development string theory
Matter as multi-dimensional vibrating strings
Standard models universe 10-11 dimensional
Only 4 dimensions (space time) visible to us
Tiny fraction of physicists now working on this
at highly abstract level (but still with
experimental-theoretical interplay
Experiments needed for string theory
controversies prohibitively expensive

9
Enter econophysics

Some physicists (e.g., Cheng Zhang, Joe McCauley,
Tsallis) had innate curiousity about economics
social phenomena
Large numbers physics graduate students with
little possibility of experimental
apprenticeship
Huge body of pure financial data available for
experimental analysis
Clear (and, to physicists, strange but not
unfamiliar) signs of discord in
economic/financial theory
Planck on acceptance of his ideas in physics An
important scientific innovation rarely makes its
way by gradually winning over and converting its
opponents it rarely happens that Saul becomes
Paul. What does happen is that its opponents
gradually die out, and that the growing
generation is familiarised with the ideas from
the beginning. (M. Planck, in G. Holton (Ed.),
Thematic Origins of Scientific Thought, Harvard
University Press, Cambridge, MA, 1973 in
Scientific Autobiography, New York Philosophical
Library, New York, 1949.)

10
Enter econophysics

A research paradigm develops
Why not apply tools of theoretical physics to
large body of financial data see what we find?
Large number of regularities seen by physicists
with respect to advanced physics that, from
neoclassical economics point of view, were
anomalies
Distributions of financial data follow Power /
Zipf / Pareto Distributions
Standard characteristic of highly interacting
nonlinear nonequilibrium processes
Versus neoclassical belief data should follow
innately random distributions since markets
assumed to be rational, rational defined as
all knowing, system assumed stable
Huge baggage of a priori assumptions at conflict
with data

11
Enter econophysics

Main areas of research
Statistical patterns in finance
Also income distribution, firm sizes, extinction
patterns
Initially chaos (Mandlebrot etc.) but
subsequently Power Laws, Zipf Laws, Pareto,
Exponential, Levy Gamma distributions now
Tsalliss q nonextensive statistical
mechanics
Parsimonious models of financial market
behaviour
El Farol model Minority Game
Little work to date in alternative economic
foundations
May come with time, and will probably be
radically different to either neoclassical or
classical foundations

12
Statistical Patterns

Perspective of econophysicists very different to
neoclassical economists (and other victims of
equilibrium thinking)
Statistical physicists, myself included, are
extremely interested in fluctuations. In the
field of economics, we find ourselves surrounded
by fluctuationswere it not for economic
fluctuations, economists would have no work to
do. Gene Stanley, (editor Physica A journal of
inter-disciplinary physics) 2000, Exotic
statistical physics Applications to biology,
medicine, and economics, Physica A 285 1-17.
Versus mechanisms that achieve equilibrium
focus of standard economic paradigm

13
Statistical Patterns

What do we do when we carry out research on
economic fluctuations? Our approach has been to
use our experience in critical phenomena research
and assume that when we see fluctuations,
correlations may be present. (10)
A search for feedback effects between data rather
than assumption of independence
Main finding events that are rare by 8 orders
of magnitudeevents that occur once in every 100
million tradesfall on the same curve as everyday
events. (12)
Subsumes results with all distribution types
Inspiration for main theoretical development
nonextensive statistical mechanics
Commenced with Mandlebrots work on fractals in
1960s

14
Mandelbrot, fractals, chaos

Mandelbrot began research in economics into
income distribution
Vilfredo Pareto in late 1800s noticed Power Law
in income distribution
Number of people N earning more than x follows
formula
log N log A m log x (A, m constants)
In 1961 by chance saw graph of cotton prices that
mirrored data on income distribution
Noticed scale invariance as a feature of
economic data argued fundamental feature of
financial data
BUT ignored in favour of The New Finance of
Sharpe CAPM!
Shifted into geography geometry now insights
re-emerging as foundation of new approach to
finance

15
Power (and other) Laws

Power Laws, Zipf Laws, Pareto Laws all relate to
distributions in which elements in the system
affect each other very strongly and nonlinearly
Resulting patterns appear random but are not
Compared to truly random data, have many more
extreme events
But random processes can be generated by strongly
chaotic processes!
Difference appears to lie in mixing random
processes achieve strong mixing of elements
chaotic processes lead to patterns of
self-similarity, not uniformity
Area still very speculative but clearly on track
to much more successful theory of finance than
CAPM

16
Non-extensive statistical mechanics

The basics Entropy
Boltzmann-Gibbs statistical mechanics
Shannon information theory
Advanced non-extensive statistical mechanics
After the hairy stuff, a quick survey of major
trends in econophysics

17
Entropy
Warning!
Warning!

Entropy is

Mind-bending material approaching!

Best introduced by jokes
The 3 laws of thermodynamics are
1. You can't win.
2. You can't even break even.
3. You can't get out of the game.
A more informative version
1. You can't win, you can only break even.
2. You can only break even at absolute zero.
3. You can never reach absolute zero.

18
Entropy the 2nd law

Starting at the beginning
Key concept in science in general is conservation
law some key entity is conserved through a
series of transformations
In physics, its energy
1st law is Law of Conservation of Energy
Energy can change form but cannot be created or
destroyed
Hence You cant win
Not a priori belief (like economics law of one
price or other empirically false propositions)
but expression of observed regularity
Form of energy can change but amount of energy in
a system remains constant
Define overall energy as U and two
transformations of it as Q (heat) W (work)

19
Entropy

Then DUQW0
Rule first developed in experiments with steam
engines where focus was on inputting heat
(burning coal) and getting out work (turning a
shaft), so expressed as
DUQ-W
Just a convention reflecting heat in, work out
Objective of engineers was to achieve maximum
conversion of heat (Q) into work (W), but found
waste heat always generated.
Puzzle became why?
Solved by imagining ideal device that converted
all energy of system U into work W and then
extending analysis to non-ideal systems (compare
this to economics)

20
Entropy

Basic model piston moving weight

If weight removed from piston, then gas would
move piston to new location where pressure in gas
balanced weight of piston

Weightat height H
CylinderVolume V

What if weight consisted of many fine grains of
sand one was removed at a time?
How far could piston itself raise the sand?
How much work could the piston do on the sand?

PistonArea A
GasPressure P
21
Entropy

Upwards force from compressed gas equals Pressure
P times area of piston A
At start of process, weight stationary gas at
pressure P
Forces must then be in balance
Force of gas (P.A) just equals downwards force of
gravity on weight
If weight moves small dh distance then change in
volume dV equals A times dh
Work done is integral of force over distance it
operates

where
so that
22
Entropy

In ideal cylinder (all energy converted into
work), work equals integral of pressure with
respect to volume
In 0 efficiency cylinder (all energy converted
into heat), heat equals integral of temperature
with respect to something well label S for
now.
In between, the rule applies that

Change in energy equals heat plus work becomes
Change in energy Temperature times change in
Entropy Pressure times change in Volume
(change in volume is workuseful expenditure of
energy)
So how efficient can a working engine be?

23
Entropy

Basic cycle of internal combustion engine is
Piston at top of cylinder pressure temperature
low
Call Volume V1, Pressure P1, Temperature T1
Piston pushed by crankshaft pressure increased
Temperature necessarily rises
Volume V2, Pressure P2, Temperature T2
Gas ignited
Temperature rises dramatically
Volume V3V2, Pressure P3P2, Temperature T3
Piston pushed back to starting position
Temperature falls, volume rises, pressure drops
Volume V4V1, Pressure P4, Temperature T4
Hot gases expelled
Return to V1, P1, T1

24
Entropy

Perfect efficiency engine now assumed no
friction losses etc., all processes involve only
changes in pressure or temperature, not both at
once
Change in energy of perfect gas given by heat
capacity times change in temperature e.g. heat
capacity 5 units
Example temperatures of
T1300K (Kelvin or temperature above absolute
zero)
T2400
T31600
T4600
Can now apply

where at each stage either dS0 or dV0 (perfect
efficiency)

25
Entropy

Stage 1 all compression, dS0. So

(work in so negative work output)

Stage 2 all temperature change, dV0. So

Stage 3 all expansion, dS0. So

Stage 4 all temperature change, dV0. So

Work sum is -50050004500
Energy input is 6000
Ratio is efficiency of perfect engine
4500/600075

26
Entropy

Actual engine has lower efficiency
Conversion of some compression into temperature,
some rise in temperature into rise in volume
As well as the usual suspects friction, etc.
Typically achieve only half ideal ratio.
Whats the problem?
Truly ideal engine design reveals part of cause
Carnot (1824) imagined perfect heat-exchange
engine
Found engine had to discharge heat to perform
work
Efficiency function of discharge temperature
level
Only if discharge temperature was absolute zero
could engine be 100 efficient

27
Entropy Carnot engine

During initial expansion phase, gas in cylinder
kept at constant temperature TH heat QH must be
added

During work expansion phase, temperature drops
because volume expands W extracted

During initial contraction phase, gas in cylinder
kept at constant temperature TC heat QC must be
extracted

During final contraction phase, temperature rises
because volume contracts

28
Entropy Carnot engine

Since engine repeats cycle, energy change over
whole cycle zero so Work extracted must equal
sum of heat input extraction

Engine efficiency is ratio of work output to
energy input

There is a simple relationship between Q and T

So energy efficiency can only be 100 of TC0
Kelvin

Also explains why high temperature engines are
more efficient

29
Entropy

So something in nature means that no work
process can occur without generating waste heat.
That something is 2nd law of thermodynamics
entropy increases where entropy is the S in

General statement For any process by which a
thermodynamic system is in interaction with the
environment, the total change of entropy of
system and environment can almost never be
negative. If only reversible processes occur, the
total change of entropy is zero if irreversible
processes occur as well, then it is positive.
S taken as measure of disorder of system since
related by Boltzmann Gibbs to the number of
distinguishable states W that a system can be in
by

30
Entropy

Boltzmanns formula linked to structure of matter
by concept of microstates
Overall state (temperature, pressure, etc) of
given system reflects ensemble of states of
constituents (atoms, molecules, etc.)
State of constituents reflects
How many ways constituents can be organised
Number of constituents having each possible state
E.g., consider placing colour squares on 4x4 grid

Say 1st square is red can be placed in any of 16
locations

Next e.g. blue placed in any of 15
16!20,920,000,000,000,000 possible combinations!

31
Entropy

But say there is 1 red, 3 green, 5 blue, 7 orange
squares in ensemble. Then

are different combinations but cant be
distinguished from each other

and

Ditto for other arrangements of other colours
(numbers there just to show difference)
To compensate, have to divide 16! by product of
all possible ways of achieving identical
microstates
Divide by 1! x 3! x 5! x 7!3,628,800, leaving
5,765,760 distinct arrangements
General formula is

32
Entropy

Can also be put as

Where W is number of discrete microstates system
can be in and pi is probability of the ith such
state
Entropy as defined here applies to ergodic
systems
dynamics whose time averages coincide with
ensemble averages (Tsallis et al. 2003,
Nonextensive statistical mechanics and
economics, Physica A 324 89-100)
Colloquially, systems that converge to or orbit
long run equilibrium values that over time fill
the entire phase space

33
Entropy

Consider our 4x4 grid
Imagine these represent entities in a dynamic
system
E.g., gas molecules in a tiny container
Odds of squares being in highly ordered initial
state (all similar colours next to each other)
very low

Many more ways for squares to be in more
disordered arrangement than one where all
colours are mixed up
Over time, each square will spend 1/16th of its
time in each of 16 possible positions (time
averages coincide with ensemble averages)

But far from all (physical or social) systems
have this characteristic

34
Entropy

For example, Lorenzs model

Complex dynamics means time average very
different to average over phase space because
system never goes near equilibria

35
Entropy

Problem of failure of deep, established concept
like Boltzmann-Gibbs entropy to characterise many
real world systems troubled physicists,
statisticians
Ironically, CAPM analysis of derivatives
(Black-Scholes) related to this area
Many alternative characterisations proposed
Power Laws
Hurst exponents
Best to date is revised version of
Boltzmann-Gibbs entropy suggested by Tsallis in
1985
Sheer intuitionnot derived but guessed at.
Interesting example of how scientific advance can
occur. In his words

36
Nonextensive Statistical Mechanics

A MexicanFrenchBrazilian workshop entitled
First Workshop in Statistical Mechanics was
held in Mexico City, during 213 September 1985
That was the time of fashionable multifractals
and related matters. During one of the coffee
breaks, everybody went out from the lecture room,
excepting Brezin, a Mexican student , and
myself Brezin was explaining something to the
student. At a certain moment, he addressed some
point presumably related to multifractalsfrom my
seat I could not hear their conversation, but I
could see the equations Brezin was writing. He
was using pq, and it suddenly came to my
mindlike a flash and without further
intentionthat, with powers of probabilities, one
could generalize standard statistical mechanics,
by generalizing the BG entropy itself and then
following Gibbs path. Back to Rio de Janeiro, I
wrote on a single shot the expression for the
generalized entropy, namely

Tsallis 2004 727
37
Nonextensive Statistical Mechanics

Why does it matter?
q 1 returns standard distributions
q gt 1 privileges common events
Common (near mean events) occur more frequently
than for Gaussian/standard entropy distributions
and
rare events will lead to large fluctuations,
whereas more common events will result in more
moderate fluctuations.
A concrete consequence of this is that the BG
formalism yields exponential equilibrium
distributions (and time behavior of typical
relaxation functions), whereas nonextensive
statistics yields (asymptotic) power-law
distributions (Tsallis et al. 2003 91)
Tsalliss q may capture interactive instability
of finance markets. Tsallis distributions fit
finance data accurately with q1.4

38
Nonextensive Statistical Mechanics

E.g., Stock market returns for top ten stocks on
NYSE

Dotted line is the Gaussian distribution 2-
and 3-min curves are moved vertically for display
purposes Far better fit to data than CAPM
models

Many other areas where Tsalliss q enables
accurate fit to data whereas standard extensive
statistics models (Black-Scholes, CAPM, EMH etc.)
do not

39
Econophysics

Tsalliss analysis may become foundation of all
other statistical analysis by econophysicists
In meantime, many other areas where skills
technologies of physicists are being applied.
E.g.
Sornettes analysis of asset bubbles and bursts
Minority Game parsimonious model of finance
markets
Scarfettas analysis of income distribution
Ponzis model of multi-sectoral dynamics
Many others can be found at
http//www.unifr.ch/econophysics/

40
Why Stock Markets Crash

Sornette geophysicist
Study of earths dynamics
Developed theory of earthquakes as extension of
Per Baks theory of self-organised criticality
Classic model the sand pile
Pour sand onto surface one grain at a time
For a while, pyramidal shape forms
Slope of pyramid gets steeper
Slope then collapses in avalanche
One grain of sand causes more than one to fall in
a chain reaction
Collapse of pyramid reduces slope below critical
level
Pyramid reforms process repeats

41
Why Stock Markets Crash

Sornettes earthquake model similar with tectonic
plates as the grains of sand, motion of earths
core as pouring force
Movement of molten core causes plates to move on
surface
Increasing tension between plates causing
vibrations that increased over time
Release in large scale earthquake
Decreasing tension between plates over time
process repeats
Pattern captured by log periodic function
Applied to stock market where collective
interactions between agents leading to a cascade
of amplifications replace movement of plates

42
Why Stock Markets Crash

Basic function for change of index is of the form

Predicts increasing frequency of fluctuations as
critical time approaches
Problem is to identify critical time!

43
Why Stock Markets Crash

On other side of crash, critical time known
Curiosity now is does crash fit log-periodic
form?
Graph fits US SP500 to function

Problems develop when extended further in time
Tectonic plate dynamics dont change on human
time scale finance markets economies do
But clear relevance of log periodic form to
short-term market movements before/after crash

44
The Minority Game

Minority Game development begun by economist
Brian Arthur
Model was El Farol Irish (yes, Irish!) pub in
Santa Fe
Popular after-hours venue but only pleasant when
neither empty nor full
Problem how to predict whether worth attending a
given night?
Arthurs model 100 Irish music fans in Santa Fe
bar only enjoyable when less than 40 attend a
night
Fans decide whether or not to attend based on
various strategies
A minority game you win by being in the
minority
Therefore no equilibrium any winning strategy
will break down as other agents adopt it

45
The Minority Game

Extended by Yi-Cheng Zhang others to Minority
Game
Artificial stock market in which winning strategy
is to sell when majority is buying, buy when
majority selling
Realisation that MG isnt a complete model
In financial trading, often it is convenient to
join the majority trend, not to fight against the
trend. During the Internet stock follies, it was
possible to reap considerable profits by going
along with the explosive boom, provided one got
off the trend in time. There are many other
situations where success is associated with
conforming with the majority.
But proposition that might still be on the
money because

46
The Minority Game

majority situations may actually have minority
elements embedded in them. The real financial
trading probably requires a mixed
minority-majority strategy, in which timing is
essential. The minority situations seem to
prevail in the long run because speculators
cannot all be winners. Indeed no boom is without
end, being different from the crowd at the right
time is the key to success. In a booming trend,
it is the minority of those who get off first who
win, the others lose. (Damien Challet, Matteo
Marsili, Yi-cheng Zhang 2003, Minority Games,
Oxford University Press, Oxford, 12-13)

47
A two-part income distribution model

Basic Econophysics model a Power Law
Implies increasing concentration all the way up
Actual empirics of US data suggested a tail (low
income) that didnt fit Power Law
An empirical distribution of wealth shows an
abrupt change between the lowmedium range, that
may be fitted by a non-monotonic function with an
exponential-like tail such as a gamma
distribution, and the high wealth range, that is
well fitted by a Pareto or inverse power-law
function. (Nicola Scafetta, Sergio Picozzi and
Bruce J West, 2004, An out-of-equilibrium model
of the distributions of wealth, Quantitative
Finance 4 353)

48
A two-part income distribution model

Scarfetta et al suggest
Top end (rich) due to investment
Power Law wealth distribution generates matching
income one
Bottom end (poor) due to trade which is biased in
favour of poor
Hard to explain from neoclassical foundation
Neoclassic economists do not expect trade to
involve a transfer of wealth, but rather an
increase in utility for both parties with a zero
net transfer of wealth.

49
A two-part income distribution model

Scarfetta et al. propose
in trades there may be a transfer of wealth from
one agent to the other because the price paid
fluctuates around an equilibrium price ( value)
and, therefore, the price may differ from the
value of the commodity transferred
(b) in a trade transaction the amount of wealth
that may move from one agent to the other is
bounded because the price and the value of a
commodity cannot (usually) exceed the wealth of
the poorer of the two traders
(c) the price is socially determined in such a
way that the trade is statistically biased in
favour of the poorer trader.

50
A two-part income distribution model

In fact results validate my interpretation of
Marx on value
Marx spoke of the relationship between the wage
and the value of labour-power, he used the term
minimum wage, that is, a subsistence payment
1315, thus emphasizing that in practice he
expected the wage to exceed this minimum and
hence there to be a price-value divergence in
favour of the working class at the expense of
capitalists. These effects can be incorporated
into the social equality index f of equation (14)
that measures the statistical bias of the trade
in favour of the poor.

51
Multi-sectoral instability

Physicists perception of economic cycles
Economic dynamics is easily observed to be far
from equilibrium where periodic recessions,
unemployment and unstable prices occur
persistently. An understanding of the origins of
this behaviour from the viewpoint of complex
dynamical systems theory would be very valuable.
(Adam Ponzi, Ayumu Yasutomi, and Kunihiko Kaneko
2003, Multiple Timescale Dynamics in Economic
Production Networks, APS/123-QED
Starting point is standard von Neumann
equilibrium growth path

52
Multi-sectoral instability

The VNM is defined as a static equilibrium model
describing relationships between the variables
which must hold at equilibrium. Equilibrium is a
state of balanced growth where prices are
constant. There are no dynamics defined by the
model which might describe out of equilibrium or
approach to equilibrium behaviour. (1)
However it is rarely the case that economic
processes are in equilibrium
Their approach actual output depends on the
quantity of the minimum of its input supplies and
not on the quantities of its other supplies. (1)

53
Multi-sectoral instability

Basic picture of economy reflects physics
backgroundprocesses described as catalytic
play important role

A production process is the operation which
converts one bundle of goods, including capital
equipment, into another bundle of goods,
including the capital equipment.

Capital goods therefore function approximately
like catalysts in chemical reactions, reformed at
the end of the reaction in amounts conserved in
the reaction. (1)

54
Multi-sectoral instability

Model implemented as computer simulation and
generates obvious cycles in output, prices, etc.

Not necessarily correct model of market economy
Constraint normally effective demand, not supply
(stocks provide buffer)

But useful example of dynamic multisectoral
modelling

55
Conclusion?

Econophysics still in infancy, but
Unencumbered by equilibrium obsession
Equipped with advanced mathematical computing
data analysis tools designed to cope with
uncertainty nonlinearity
For first time ever, a coherent group of rivals
to neoclassicism who totally outgun it in
technical terms
At time of great weakness of neoclassical
paradigm in finance
Best chance yet for break in neoclassical
hegemony
However, some problems

56
Worrying Trends in Econophysics

Paper in Physica A by Mauro Gallegati, Steve
Keen, Thomas Lux, Paul Ormerod
First, a lack of awareness of work that has been
done within economics itself.
Second, resistance to more rigorous and robust
statistical methodology.
Third, the belief that universal empirical
regularities can be found in many areas of
economic activity.
Fourth, the theoretical models which are being
used to explain empirical phenomena.
My beef use of conservation laws where they
dont apply
Energy is conserved nothing in economics (like
utility, income, etc.) is conserved

57
Spurious conservation

The criticism by some economists that the model
is not valid because money is conserved and other
levels of money such as credit are not accounted
for seems to these authors to be ill founded. It
is certainly possible to develop any model to
include, for example, debt. This could be simply
a matter of allowing the money held by an
individual to take negative values...20, p. 145
No it cantremember Circuit model
Money not conserved but endogenously created
Debt not simply negative money

58
Conclusion