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systems
Article
Taxation of Fiat Money Using Dynamic Control
Khalid Saeed
Social Science and Policy Studies Department, Worcester Polytechnic Institute, 100 Institute Rd.,
Worcester, MA 01609, USA; saeed@wpi.edu
Abstract: The treasury analogy is widely used in most countries in the execution of fiscal policies
striving to match taxation with public expenditure while, at the same time, the central banks tinker
with interest rates and reserve requirements and conduct open market operations for regulating
money supply. This paper investigates the relevance of those policy actions to the ubiquitous use of
fiat money tokens which in addition to meeting public expenditure and paying taxes also facilitate
transactions in the economy. A parsimonious model of the macroeconomic system subsuming
the prevalent fiscal and monetary interventions is developed and experimented with to explore
alternative policy levers for funding public expenditure and controlling money supply. A novel
dynamic control regimen to regulate taxation and open market operations for controlling inflation
is proposed. It is shown that while the public spending can be entirely met through new money
creation, taxation and open market operations must be used as inflation control instruments, whereas
expenditure instruments can be used to alleviate the regressivity of taxation regimen.
Keywords: public finance; taxation; tax reform; macroeconomics; fiat money; modern money theory;
economic growth; system dynamics; computer simulation
1. Introduction
Taxation for meeting public expenditure is an age-old norm that dates to the medieval
times when the sovereign took away a part of the crop from the farmers and relied on a
Citation: Saeed, K. Taxation of Fiat
feudal system to use serf labor in the name of the ruler. Treasuries and granaries were
Money Using Dynamic Control.
an integral part of the sovereign infrastructure to horde wealth and food grains collected
Systems 2022, 10, 84. https://
through revenue officials. Later, precious commodities became a way to exchange goods
doi.org/10.3390/systems10030084
and services and to pay taxes. It has also been reported in the history of taxation that
Academic Editor: Robert Y. Cavana some sovereigns issued base metal tokens and promissory notes in return for goods and
Received: 8 March 2022
services. These tokens and notes could be used later to pay taxes and they as well began
Accepted: 17 June 2022
to be traded in the everyday exchange of goods and services, which laid the foundation
Published: 19 June 2022
of the fiat currency system. The origins of money and its evolution into fiat currency are
eloquently discussed in literature [1,2] and are not further elaborated in this paper which is
Publisher’s Note: MDPI stays neutral
focused on the relevance of the present-day tax regimens to the fiat currency system and
with regard to jurisdictional claims in
exploring ways to reform them.
published maps and institutional affil-
Even though fiat currency has now become the norm and the modern money theory [3],
iations.
built on its premises is quite widely disseminated [4–6], the budgeting operations of the
governments continue to use the treasury analogy to run their tax collection and spending
functions. They implicitly assume money to be a commodity of value which must first be
Copyright: © 2022 by the author.
raised through taxation and stored in the treasury before it can be exchanged for goods
Licensee MDPI, Basel, Switzerland. and services. The collection of taxes continues to be an expensive and oppressive process
This article is an open access article that is a legacy of the origins of taxation for supporting autocratic rulers. Its burden
distributed under the terms and remains regressive in spite of advocacy of progressive taxation and the many complex
conditions of the Creative Commons proposals to implement it [7,8]. The tax collection process has created rampant corruption
Attribution (CC BY) license (https:// in the developing countries where recordkeeping is poor and collection calls for exercise
creativecommons.org/licenses/by/ of discretion by the state officials [9]. It has also created scams that extract ransoms
4.0/). from unknowing victims in the industrialized countries through phishing and fraud [10].
Systems 2022, 10, 84. https://doi.org/10.3390/systems10030084 https://www.mdpi.com/journal/systems
Systems 2022, 10, 84 2 of 19
These taxes are though collected in the form of fiat currency which the sovereign state is
empowered to create out of thin air anyways.
It should be recognized that when taxpayers write checks to the treasury, they are
reducing the money supply. Since money tokens they are foregoing also reduce their ability
to buy goods and services, the tax payments simultaneously reduce the household demand
for goods and services. Writing a check to pay for goods and services purchased from a
private vendor is different from writing a check to pay taxes. When used for purchases,
writing a check reduces the payer’s bank balance, but the money stays in the system since
it is transferred to another account. On the other hand, government expenditure funded
by fiat money increases money supply in addition to augmenting the demand for goods
and services [11]. Thus, the taxes collected at the outset sponge away excess money in
the financial system of the economy, which increases the velocity of money thus slowing
down transactions [12]. Since money also entitles households to buy goods and services,
taxes additionally reduce this entitlement, thus limiting economic growth potential [13].
The statistical evidence for this progression of events, however, varies since a multitude of
processes are at work in the economy and causality between two variables can often not
be established through association using statistical analysis [14,15]. For example, while
taxation may exert a downward pressure on prices by limiting household demand, it might
simultaneously push prices up by increasing money velocity that also drives up interest
rates—increasing capital costs on the supply side.
This paper constructs a parsimonious and aggregate model of the financial system of
a sovereign state subsuming both fiscal and monetary interventions. This model is then
linked to a one-sector one-factor macroeconomic system adapted from [16]. The larger
model so created is applied to understanding the role of taxation in a fiat currency system.
The model is programmed in Stella Architect 1 using system dynamics modeling framework
briefly described in Section 2 and elaborated at length in [15]. The impact of unlinking
public spending from taxation and completely meeting it through deficits is tested using
computer simulation. Also, the impact of using taxation and open-market operations
for regulating money supply using dynamic feedback control [17] is investigated. It is
demonstrated that taxation must not be seen only as a purely fiscal instrument, but should
be tied also to monetary policy [18]. A market-determined interest rate is proposed as a
controller for driving both taxation and open-market operations. Based on the results of
computer simulations of the model, a public finance regimen that unlinks taxation from
public expenditure and is dynamically controlled by market-determined interest rate is
proposed. Limitations of the analysis and further research agendas are outlined.
2. System Dynamics Modeling
System dynamics modeling, originally introduced by Jay Forrester in the1950s to
address problems of industrial management [19], came in limelight with the publication of
the Limits to Growth study [20] which drew many criticisms [21,22]. However, since then,
system dynamics has become one of the most popular simulation techniques [23], and it has
been applied to many topics spanning such fields as management [24], economics [25,26],
and health [27].
The underlying computational process in a model representing the microstructure of
a theory can be expressed as a set of ordinary nonlinear integral equations, but models
are constructed using icons and connections that can be easily assembled using dedicated
software such as ithink, Stella, Vensim, and Powersim 2 . Table 1 shows the icons and the
processes they represent in a typical system dynamics model. A rectangle denotes a
stock that integrates the flows connected to it. A flow is a rate of change associated with
a stock, which may conserve more than one flows. These two types of variables are
the basic components of an abstract system implicit in a theory. Information links from
stocks to flows define decision rules or policies that drive flows. Intermediate computations
transforming information in stocks into policy components are represented by the converter
symbol. A converter is an algebraic function of stocks, other converters, and constant
Systems 2022, 10, 84 3 of 20
Systems 2022, 10, 84 3 of 20
Systems 2022, 10, 84 3 of 20
Systems 2022, 10, 84 3 of 20
converter is an algebraic function of stocks, other converters, and constant parameters
Systems 2022, 10, 84 converter 3 of 20
When an is an algebraic
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Systems 2022, 10, 84 3 of 19
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3. A Parsimonious System Dynamics Model of the Public Finance System
3. A Parsimonious System Dynamics Model of the Public Finance System
The model of this paper portrays an aggregate, homogenous and closed economy.
Figure 1 gives a summary view of the model, which includes the macroeconomic pro-
Systems 2022, 10, 84 4 of 19
cesses as well as the financial policy interventions typically exercised by the state institu-
tions.
Performance
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financial
economy
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tions.
The module on the left represents an aggregate macroeconomic system while the one
on theTheright is a sub-model
module of the financial
on the left represents operations
an aggregate manifest in fiscal
macroeconomic system and monetary
while the one
interventions.
on the right isThe model behavior
a sub-model of theover time isoperations
financial described in terms ofinseveral
manifest fiscal representative
and monetary
variables designated
interventions. as performance
The model measures
behavior over time placed in a separate
is described module
in terms to avoid
of several clutter
representa-
in thevariables
tive model organization.
designated as The logic of the
performance three components
measures of the model
placed in a separate module shown in
to avoid
Figure 1 is described below.
clutter in the model organization. The logic of the three components of the model shown
in Figure 1 is described below.
3.1. Financial Operations
Figure 2 shows
3.1. Financial the stock and flow structure of the financial operations module. It cap-
Operations
tures the determination of interest rate based on income velocity of money by a competitive
Figure 2 shows the stock and flow structure of the financial operations module. It
financial market. It also subsumes the government budgetary actions such as taxation and
captures the determination of interest rate based on income velocity of money by a com-
spending, and open market operations such as bond issue and redemption, and how they
petitive financial market. It also subsumes the government budgetary actions such as tax-
all affect money supply.
ation and spending, and open market operations such as bond issue and redemption, and
The financial system is represented by three stocks: market interest rate, money
how they all affect money supply.
supply and public debt. Additionally, indicated deficit consisting of the difference between
The financial system is represented by three stocks: market interest rate, money sup-
budgeted government spending and taxation is averaged into a fourth stock of “perceived
ply and public debt. Additionally, indicated deficit consisting of the difference between
deficit” to create actionable information.
budgeted government spending and taxation is averaged into a fourth stock of “perceived
The central bank actions affect the money supply through buying and selling of
deficit” to create
government bonds actionable information.
and securities and payment of dividends on public debt. The treasury
The central bank actions affect the of
collects taxes and processes payments money supply
budgeted through
public buyingwhich
spending, and selling of gov-
also impact
ernment bonds and securities and payment of dividends on public debt.
money supply. The bonds issued by the government are viewed as public debt, but they The treasury col-
lects taxes and processes payments of budgeted public spending, which
also serve as a secure investment portfolio for the public where it can park surplus cash also impact
money
for supply.
future use asThe
wellbonds issued
as get by the government
guaranteed returns on it.areThese
viewed as public
stocks debt,
and the but they
regulatory
also serve as a secure investment portfolio for the public where
operations controlling them are described below as integral equations. it can park surplus cash
for future use as well as get guaranteed returns on it. These stocks and the regulatory
operations
3.1.1. controlling
Interest Rate them are described below as integral equations.
The interest rate adjusts towards an indicated value determined by the relative money
velocity that represents the imbalance between money demand created by average income
and money supply held in bank accounts and currency notes in circulation.
Z
Interest rate(t) = (indicated interest rate − Interest rate)/interest rate adjustment time) × dt (1)
indicated interest rate = (INIT(Interest rate)) × relative money velocity
relative money velocity = Av income/Money supply
Systems 2022, 10,
Systems 2022, 10, 84
84 5 5of
of 20
19
market
interest
Rate
interest rate change in
adjustment time interest rate
economy.Av
income
normal indicated
interest rate interest rate
interest dividend
parity relative money
dividend
velocity money reduction
rate money issued from
from taxes
govt payments
and bond issue
Money
supply
economy.government
spending economy.taxes
indicated collected
deficit
deficit
perceived
perception
deficit
time
dividends change in
paid perceived
deficit
deficit
finance
bonds bonds
redeemed issued
public
debt
av life of bond fr deficit met from
bond issue
normal fr deficit
net cash flow met from bond issue
from bond trade
and dividends
market
dynamic control SW dynamic
interest
on bond issue control on bond issue
Rate
Figure 2. Sub-model representing the financial system of the economy.
Figure 2. Sub-model representing the financial system of the economy.
3.1.1.In
Interest Rate above and in the following equations, INIT(·) means the initial value
the equation
of a variable. It should
The interest be recognized
rate adjusts towardsthat interest rate,
an indicated as with
value any other
determined byprice, can be
the relative
efficiently
money linkedthat
velocity to money velocity
represents only whenbetween
the imbalance it is not money
fixed bydemand
a centralcreated
bank, but arrived
by average
at by a competitive
income and money financial market,
supply held which
in bank is an implicit
accounts assumption
and currency of circulation.
notes in Equation (1).
(1)
Interest rate(t) = ∫3.1.2. Money
(indicated Supplyrate−Interest rate)/interest rate adjustment time) × dt
interest
The money supply is an aggregate of currency notes in circulation and the balances
held in bank
indicated interest accounts.
rate It is equivalent
= (INIT(Interest rate)) ×ofrelative
moneymoney
with zero maturity (MZM) that represents
velocity
the total liquidity of the economy [31]. Money supply increases through bond and T-bill
redemption,
relative moneypayment of dividends
velocity on bonds and
= Av income/Money money creation for meeting government
supply
expenditure such as payroll, infrastructure construction, and the purchase of goods and
In the
services. equation
Money above
supply and in the
decreases following
through bondequations, INIT(·) means the initial value
issue and taxation.
Z of a variable. It should be recognized that interest rate, as with any other price, can be
Money supply(t) = (money efficiently
issuedlinked to money
from govt velocity
payments only when
− money it is notfrom
reduction fixed by aand
taxes central
bond bank, but×arrived
issue) dt
at by a competitive financial market, which is an implicit assumption of Equation (1).
money issued from govt payments = government spending + bonds redeemed + dividends paid
Systems 2022, 10, 84 6 of 19
money reduction from taxes and bond issue = taxes collected + bonds issued
dividend rate = Interest rate × interest dividend parity
dividends = public debt × dividend rate
The model does not track the change in money supply from changes in saving behavior
driven by interest rate that would move money into time deposits, as it would be offset by
corresponding changes in lending by the banks. The government can reduce money supply
by shredding or erasing money, but it must first capture it from the economy. Taxation is a
possible way to capture excess money, although it will also reduce economic growth since
it affects household entitlements. In extreme circumstances, governments have removed
money by demonetizing certain currency denominations so their holders can no longer
exchange them for goods and services, or devaluing money so its holders can exchange
the bills they hold with fewer goods and services. Those measures are excluded from the
model of this paper.
3.1.3. Perceived Deficit
Although expenditure and taxation are considered fiscal policies, they concomitantly
impact money supply, thus affecting the transactions in the economy as monetary policies
would. When the government says it has a balanced budget, it really means the money
removed from the system through taxes equals the money injected through spending.
When the government says it has deficit, it means that the money spent is more than the
money removed through tax collection. The difference between taxation and spending is
the indicated deficit and its average represents its perceived value that can be acted upon
to determine bond issue and deficit finance. Deficit finance implies creating new money for
government spending, but whose injection into the economy would also accommodate the
transactions demand of a growing economy.
Z
Perceived deficit(t) = ((indicated deficit - perceived deficit)/deficit perception time) × dt
deficit finance = Perceived deficit - bonds issued
3.1.4. Public Debt
Government bonds held by the public are represented as the stock of public debt. It
consists of the currency tokens soaked up from the households and put away until they
are redeemed. Bond issue is therefore deflationary in the short run. The outflow from the
Public debt stock represents redemption rate after the life of the bond. Bond issue is often
sporadic and motivated by the need for funds to spend by a government. From a control
perspective, it is proposed to be linked to the market interest rate which mimics money
velocity. Several bond issue policies, including a control regimen, are tested. All aim to use
public debt to regulate money supply rather than meet government expenditure.
Z
Public debt(t) = (bonds issued − bonds redeemed) × dt
bonds issued = MAX(perceived deficit, 0) × fr deficit met from bond issue
fr deficit met from bond issue = normal fr deficit met from bond issue × dynamic control on bond issue
dynamic control on bond issue = f (market interest rate/INIT(market interest rate)), f 0 < 0
bonds redeemed = public debt/av life of bonds
All bonds issued by the government must be redeemed after the promised period.
It is assumed that bonds earn a dividend equal to the market interest rate and have an
average life of 10 years before they are redeemed. In general, it would also be possible to
dynamic control on bond issue = ƒ(market interest rate/INIT(market interest rate)), ƒ’ < 0
bonds redeemed = public debt/av life of bonds
Systems 2022, 10, 84 All bonds issued by the government must be redeemed after the promised period. 7 of 19
It
is assumed that bonds earn a dividend equal to the market interest rate and have an av-
erage life of 10 years before they are redeemed. In general, it would also be possible to
model a portfolio
portfolio of
ofshort-and
short-andlong-term
long-termbonds,
bonds,even
eventhough
thoughsuch
such a portfolio
a portfolio is not
is not part
part of
of this
this model.
model.
3.2. The
3.2. The Macroeconomic
Macroeconomic System
System
All fiscal
All fiscal and
and monetary actions affect
monetary actions affect the
the economy
economy one
one way
way oror the
the other,
other, hence
hence the
the
model of the financial operations is linked with a compact model of the macroeconomic
model of the financial operations is linked with a compact model of the macroeconomic
system shown
system shown in in Figure
Figure 3. It represents
3. It represents aa closed
closed and
and aggregate
aggregate one-sector and one-factor
one-sector and one-factor
3
macroeconomic system subsuming consumption, production, and investment [32].
macroeconomic system subsuming consumption, production, and investment [32]. 3 All
All
flows represent
flows represent real
real values
values measured
measured in in dollars/year while capital
dollars/year while capital and
and inventory
inventory are
are also
also
designated in
designated in terms
terms of
of dollars.
dollars.
output
capital inventory limit
ratio
production
inventory
desired
averaging time
capital Sales
inventory
Inventory capacity
coverage utilization
indicated capital
capital formation availability
life of
desired
capital GDP
inventory
life of income
investment
capital
capital capital
retirement
economic government
growth spending
rate consumption
govt spending as
change in fraction
av income income fraction
financial income
operations.normal consumed
interest rate
Av
income time to tax rate
av income taxes
adjusted
financial collected
income
operations.market
interest
Rate
financial
operations.net cash flow
financial
from bond trade
operations.inflation
and dividends
tax
Figure 3. A simplified model of the macroeconomic system.
3.2.1. Income
Income is computed on the production side, which depends on capital, capital output
ratio, and capacity utilization. On the demand side, it is represented by the quintessential
GDP identity consisting of the summation of consumption, investment and government
spending less taxes collected. Government spending is assumed to be pegged at a percent-
age of the national income since a rise in income would entail enlarging the social services
infrastructure. The following integral equations describe the stocks and their respective
flows in this simple model of the economic system adapted from [16]:
Z
Av income(t) = ((income − Av income)/time to av income) × dt
where income equal production in real terms when the general price level is assumed to
remain steady.
Systems 2022, 10, 84 8 of 19
3.2.2. Inventory
Inventory separates supply and demand. The general price level (GPL) is not included
in the model for simplification, but inventory limitation restricts sales while the unmet
demand is not tracked, which implicitly assumes price adjustment to clear any surplus or
deficit of demand and sales:
Z
Inventory(t) = (production − sales) × dt
production = (Capital × output capital ratio) × f 1 (desired capital/Capital), f 0 1 > 0
desired capital = (Av income + (desired inventory − inventory)/inventory averaging time)/output capital ratio
desired inventory = Av income × Inventory coverage
sales = GDP × f 2 (inventory/desired inventory), f 0 2 > 0
Since money is a legal tender for transactions, a reduction in the household money
balance, whether incurred through taxation or by purchase of government bonds) would
also reduce demand for goods and services. Thus, both taxation of fiat money and money
reduction through bond issue have impacts similar to the medieval taxation practice where
tax often constituted a part of the crop or real commodities. Following equations describe
the composition of demand and its components:
GDP = consumption + investment − taxes collected + government spending
consumption = adjusted income × fraction income consumed
adjusted income = Av income + net cash flow from bond trade and dividends.
Taxes collected combine a simplified version of the traditional taxation modeled as a
fraction of adjusted income and the suggested version of remedial taxation for inflation con-
trol proposed in this paper, which is driven by the market interest rate. For experimentation
with the model, either type of taxation can be activated or disabled.
taxes collected = Av income × tax rate + inflation tax
inflation tax = Av income × inflation tax rate
market interest rate
inflation tax rate = 1 − × max inflation tax rate (2)
INIT(market interest rate)
where max inflation tax rate defines an upper bound for such taxation. This limit determines
the rate of adjustment of the inflation tax rate in response to the changes in interest rate.
Note it can become negative when market interest rate is high. Inflation tax in such a case
would be a rebate.
3.2.3. Capital
All production capital is aggregated into a single stock that is increased through
investment and decreased through retirement:
Z
Capital(t) = (investment − capital retirement) × dt
investment = (Capital/life of capital) × (desired capital/Capital)/(Interest Rate/normal interest rate)
= (desired capital/life of capital)/(Interest Rate/normal interest rate)
capital retirement = capital/life of capital
In case of an open economy, trade imbalance, together with remittances and factor
income flows will create current account balance, which integrates into the national reserves
Systems 2022, 10, 84 9 of 19
of foreign currency in addition to affecting GDP. Foreign trade, remittances and factor
income flows are excluded from the model of this paper, which focusses primarily on the
internal financial management of the economy.
3.3. Performance Measures
The model, although not calibrated for any specific case, must be supplied numbers
for implementing the numerical simulation process. Its output is also plotted in terms
of numbers. The model has many variables and representing all of them in the output
would be confusing. Several relative performance measures have therefore been created,
which are independent of the size of the economy. These measures are used to compare
the various simulations. Not all performance measures are reported in each simulation
experiment. These performance measures are discussed below.
3.3.1. Economic Growth Rate
Economic growth rate is computed as a fractional growth rate as follows:
economic growth rate = Change in Av income/Av income
It computes to zero in initial equilibrium
3.3.2. Relative Money Velocity
Relative money velocity is a measure of the adequacy of money supply
Relative money velocity = Av income/money supply
It computes to 1.0 in the initial equilibrium when
Av income = money supply
3.3.3. Market Interest Rate
Market interest rate is the price of money determined by a competitive financial
market. It is computed in Equation (1) and initially set at 0.05 corresponding to relative
income velocity of 1.0.
3.3.4. Deficit Finance GDP Parity
Deficit finance GDP parity is defined as the ratio of deficit finance to GDP:
Deficit finance GDP parity = deficit finance/GDP
It initially computes to zero when there is no deficit.
3.3.5. Public Debt GDP Ratio
Public debt GDP ratio, as the name implies, is the ratio of outstanding public debt to GDP:
Public debt GDP ratio = public debt/GDP
This measure keeps track of public debt as a fraction of GDP. If public debt supports
welfare expenditure, it indirectly measures private sector contribution to collective good
and it can be seen as excess private capital drawn into social projects. This ratio initially
computes to zero with no public debt.
3.3.6. Inflation Tax Rate
The proposed inflation tax rate is dynamically controlled by the market interest
rate. It is defined in Equation (2) and is initially set at zero, when interest rate is at its
initial value of 0.05.and it can be seen as excess private capital drawn into social projects. This ratio initially
computes to zero with no public debt.
3.3.6. Inflation Tax Rate
The proposed inflation tax rate is dynamically controlled by the market interest rate.
Systems 2022, 10, 84 It is defined in Equation (2) and is initially set at zero, when interest rate is at its 10 of 19
initial
value of 0.05.
4. Model Behavior
4.
The model is calibrated
calibrated toto initialize
initialize in inaahypothetical
hypotheticalequilibrium,
equilibrium,which whichserves
servesasasa
apoint
pointofofreference
reference toto
compare
compare thethepolicy
policy simulations
simulations with.
with.It has notnot
It has been calibrated
been calibratedfor
anyany
for specific
specific case, hence,
case, hence,relative
relativerather
ratherthanthanabsolute
absolutecomparison
comparison of of the performance
performance
measures would be meaningful meaningful in in the
thesimulation
simulationexperiments
experimentsthat thatfollow.
follow.TheThe model
model is
is initialized
initialized withwithGDP GDP = 100
= 100 unitsunits
(say (say billions
billions of dollars),
of dollars), taxes taxes
= govt=spending
govt spending
set at 10%set
at
of 10% of average
average income,income, no and
no deficit, deficit, and nodebt.
no public public
Thedebt.
model The wasmodel was simulated
simulated for 100 yearsfor
100 years but only 25 years of behavior is shown since thereafter
but only 25 years of behavior is shown since thereafter the system soon settles into a new the system soon settles
into a new equilibrium.
equilibrium.
When
When taxes taxes are
are abolished
abolished andand all government
government spending
spending is is financed
financed by by newly
newly minted
minted
fiat money,
money, the the increased
increased disposable
disposable income
income from from not
not having
having to to pay
pay taxes
taxes stimulates
stimulates the the
economy into growth. Indeed, deficits extensively fueled postwar
economy into growth. Indeed, deficits extensively fueled postwar recovery in Europe and recovery in Europe and
USA
USA and successfully mitigated
and successfully mitigated economic
economicstagnation
stagnation[33].[33].Since
Sincegovtgovt spending
spending is is tied
tied to
to
income in our model, the economy receives continuous stimulus, and the growth rate
income in our model, the economy receives continuous stimulus, and the growth rate
rises,
rises, tapering
tapering off off at
at about
about 5%5% (Graph
(Graph 11 in in Figure
Figure 4).
4). In
In reality,
reality, there
there would
would bebe economic
economic
cycles
cycles ofofvarious
variousperiodicities
periodicities arising
arising outout
of inherent delays
of inherent in workforce
delays adjustment,
in workforce over-
adjustment,
investment and capital self-ordering [34]. There would also be
over-investment and capital self-ordering [34]. There would also be constraints arising constraints arising from
resource limitations
from resource [35] and
limitations [35]conflict [36]. [36].
and conflict The The
structure for those
structure for thosebehaviors is outside
behaviors is outsideof
the scope of the model of this
of the scope of the model of this paper.paper.
4
0.05 4 4 4
1.1
0.06 1
0.0432 3
2
0.025 1
0.75 3
0.03 3
3
0.0216 1 2
0 2
0.4 2
0
1
0
0 6 13 19 25
years
1 economic growth rate 2 relative money velocity
3 market interest rate 4 deficit finance GDP parity
Figure 4.
Figure 4. Model
Model simulation
simulation with
with taxes
taxes abolished
abolished and
and all
all public
public expenditure
expenditure met
met through
through deficit
deficit
finance, showing economic growth with declining money velocity.
finance, showing economic growth with declining money velocity.
The health of the monetary system is reflected in the simulation representing the
relative money velocity (Graph 2), which declines from its designated normal value of
1-tapering off at about 0.5, indicating considerable inflation. Market interest rate (Graph
3), being the true price of money, is strongly correlated with the velocity of money and
can serve as an accurate indicator for it since measurement of money velocity is often
a challenge. Although the causal relation between the velocity of money and market
interest rate is difficult to infer from their association, it makes sense to postulate that
price of money would be determined by its availability evident in its velocity, provided
interest rates are determined by a competitive lending market and not modified by the
central bank 4 .
The current deficit as a fraction of GDP (Graph 4) rises at first but then declines slightly
over time since growth in national income eventually exceeds the growth in government
spending due to multiplier and acceleration effects as postulated by Keynes [37] and first
modeled by Samuelson [38]. It levels off at a value lower than the fraction of income it is
based on, since GDP without taxation will always exceed income.
Subsequent experiments with the model are aimed at creating control processes us-
ing open market operations and taxation as remedial instruments that should maintain
reasonable economic growth without causing excessive inflation.slightly over time since growth in national income eventually exceeds the growth in gov-
ernment spending due to multiplier and acceleration effects as postulated by Keynes [37]
and first modeled by Samuelson [38]. It levels off at a value lower than the fraction of
income it is based on since GDP without taxation will always exceed income.
Subsequent experiments with the model are aimed at creating control processes us-
Systems 2022, 10, 84 11 of 19
ing open market operations and taxation as remedial instruments that should maintain
reasonable economic growth without causing excessive inflation.
4.1. Remedial Open Market Operations for Regulating Money Supply
Open market
market operations
operations arearealready
alreadyquite
quitewidely
widelyused
usedalthough
althoughfor forsupporting
supportingpublic
pub-
expenditure
lic expenditure[39]. TheThe
[39]. first group
first of experiments
group of experiments aims to assess
aims thethe
to assess impact
impact of of
open market
open mar-
operations
ket on money
operations on moneysupply. Several
supply. options
Several subsuming
options combinations
subsuming of meeting
combinations a part or
of meeting a
whole of the deficit by bond issue and applying feedback control using the
part or whole of the deficit by bond issue and applying feedback control using the interest interest rate
deviation
rate fromfrom
deviation its normal valuevalue
its normal as a controller are tested.
as a controller The results
are tested. of these
The results experiments
of these experi-
are summarized in Figure 5 in which Graphs 1 replicate the results
ments are summarized in Figure 5 in which Graphs 1 replicate the results of Figureof Figure 4 and act as
4 and
the base case for evaluating various policy sets.
act as the base case for evaluating various policy sets.
Figure 5. Impact of regulating money supply through open market operations only, with taxes
Figure 5. Impact of regulating money supply through open market operations only, with taxes abol-
abolished and bond issue controlled by deviation from normal market interest rate.
ished and bond issue controlled by deviation from normal market interest rate.
The first experiment entails an effort to defray 100% of the perceived deficit through
bondThe first Note,
issue. experiment
bond entails an effort
issue here is notto linked
defray to
100% of the
public perceived
spending deficit
but through
to deficit. It
bond issue. Note,
is therefore meantbond issue here
for soaking is not
away linked money
surplus to public
inspending but toand
the economy deficit. It is there-
transferring it
fore meant for soaking away surplus money in the economy and transferring
to public debt. An externality of this process is that surplus private cash, which might it to public
debt. An externality
otherwise of this process
chase speculative is that
portfolios, surplus
is drawn andprivate
held incash, which
a socially might otherwise
beneficial portfolio.
The results of this experiment are shown in Graphs 2 in Figure 5.
When the volume of bond issue completely offsets all deficit, the economic growth
rate is considerably reduced since the investment in bonds reduces adjusted income. The
concomitant reduction in money supply also increases money velocity, which can further
inhibit growth. Bond redemption and dividend payments later stimulate the economy into
growth while also decreasing money velocity. Public debt rises as the growing economy
calls for increasing deficit finance of public expenditure and eventually tapers off at about
50% of the GDP.
When labeled as public debt, that proportion might appear huge. When seen as a
revolving fund that soaks excess money from the market and parks excess entitlements of
the wealthy, it seems to mobilize private surplus into supporting public expenditure. It
is supported by the wealthy not out of charitable intentions, but due to the profit motive
when the dividends are seen to be a low-risk investment. Bond issue therefore can be
deemed to play as a voluntary tax that is rewarded by dividends. Such a tax will also be
quite progressive as the rich will have more spare cash to invest into the bonds than the
poor. Note also, the net cash flow from bond issue, redemption, and bond dividends factors
into the calculation of adjusted income as it affects the entitlement of the households. When
excess money is soaked away by bond issue, money velocity is at first sustained, but then
declines as bond redemption and dividends start adding to the money supply.You can also read
