Neoclassical economics seems to have rejected the concept
of limits to growth by assuming that the market and the technological advances
invoked by it will make it possible to tap new resources and create substitution
of production factors, while it has outright excluded limitations invoked by the
political, psychological and social institutions in its analysis. Classical
economics, other the other hand, appears to have been cognizant of a multitude
of limitations to growth, including demographic, environmental, and social. This
paper reconstructs classical economic growth models using system dynamics method
and demonstrates their behavior using computer simulation. A case is made for
taking a pluralistic view of the growth process and reincorporating a multitude
of institutions driving it into our models to arrive at realistic policy
options.
Key words:
economic growth, classical economics, system dynamics, computer simulation,
environment, limits to growth.
Introduction
This paper reconstructs the
demographic, environmental, and social limits to growth as posited in the
classical economic growth models of Adam Smith, David Ricardo, Thomas Malthus,
Karl Marx and Joseph Schumpeter. System dynamics modeling and computer
simulation is used to demonstrate the systemic perspective and the richness of
these models. The multiplicity of the institutions and the non-quantifiable
factors the classical economics models took into account while attempting to
explain the dynamics of the growth process, according to Baumol (1959), indeed
described magnificent dynamics that were relevant to their respective empirical
contexts. The purpose of the paper is to provide a vehicle for understanding
classical thought on economic growth and to reiterate the importance of the
variety of behavioral and demographic factors and the non-quantifiable soft
variables it subsumed. In the complex world of today, it would be impossible to
ignore these variables without losing sight of the important dynamics that we
experience in reality.
System dynamics modeling allows
including such variables in a formal analysis framework. Elsewhere, I have also
attempted to understand the development of many of the present day problems
including income distribution (Saeed 1987, 1988), political instability (Saeed
1990), global terrorism (Pavlov, Radzicki, Saeed 2005), environment (Saeed
2004), technological development (Prankprakma and Saeed (1997) and innovation in
organizations (Saeed 1998) by taking including soft variables in my models and
the reader is referred to these studies for the modeling details of such
variables.
The concept of limits in
economic thought
Neoclassical economics mostly
excluded environmental, demographic and social limitations from its formal
analyses until early 1970s, although it extensively addressed the periodic
limitations to growth arising out of the stagnation caused by imbalances in the
market. As an exception, Hotelling (1931) dealt with exhaustible resources with
concerns that the market may not be able to return optimal rates of exhaustion,
but without pessimism about the technology to bring to fore new sources as old
ones are exhausted. These early concerns have been followed by a blissful
confidence in the ability of the technological developments and prices to
provide access to unlimited supplies of resources (Devarajan and Fisher 1981,
Smith and Krutilla 1984).
Solow’s 1974 Richard T Ely lecture
made a strong argument for integrating depletion of resources into the models of
economic growth (Solow 1974), but the momentum of orthodox economics effort has
nonetheless not deviated much from its earlier focus on optimal rates of
depletion and pricing of resources (Nordhaus 1964, 1979) without concerns for
environmental capacity, which are mostly expressed in passing. There have been
some concerns also expressed about intergenerational equity, but its treatments
remain tied to arbitrary rates of discount (Hartwick 1977, Solow 1986).
Environmental analysis seems to have appeared as an add-on in response to the
environmental movement spearheaded by the famous Limits to Growth study
(Forrester 1971, meadows, et. al. 1972, 1974, 1992). In this add on, the
neoclassical economic theory has continued to assume mineral resources to be
unlimited and to expect prices and technological developments to continue to
unearth richer mines so existing mines may be abandoned (Saeed 1985). The
reality of political power, the creation and resolution of social conflict and
the psychological and behavioral factors also remain excluded from the classical
analysis, although they contribute significantly to the performance of the
economies (Street 1983).
Classical economics, on the other
hand seems to have addressed a rich variety of limiting factors covering social,
political, demographic and environmental domains often dealing with soft
variables that are difficult to quantify but that have significant impact on
behavior of the economy. In particular, the growth models proposed by Adam
Smith, Karl Marx, David Ricardo, Thomas Malthus and Joseph Schumpeter dealt with
such limiting factors using soft variables that cannot be measured and
quantified in the neoclassical economics tradition. System dynamics modeling
allows us to subsume these variables in the formal models and understand the
structure of the classical growth theories with relative ease. The models
discussed below are programmed in ithink software.[1]
Model equations and machine readable versions are available from the author on
request.
Adam Smith and the demographic
constraint to growth
Although Adam Smith did not
explicitly discuss the constraints to growth, implicit in his model is the
demographic constraint since labor is an autonomous production factor assumed to
be freely available, while capital is endogenously created through investment of
profits (Smith 1977). Also, land which is a proxy for renewable resources, can
be freely substituted by capital (Higgins 1968, pp 56-63). Figure 1 illustrates
the simple relationship between the production factors and the output implicit
in Adam Smith’s model.
Figure 1: Growth of output and
production factors
When land is excluded from the
production schedule, the capital input and the labor constraint return a Cobb
Douglas type production function, while the influence of technology is
exogenous. Growth in any one of the inputs to production can create a growth in
the output, however, while Adam Smith gave an endogenous explanation of how
capital and technology grew, he did not discuss any limitations on the growth of
labor, assuming in default that population growth would continue to provide
sufficient quantities of labor so the labor constraint on output does not become
active.
Investment, which is driven by
profits, drives all: capital formation, technological growth and labor hiring.
In the absence of any demographic constraints this would create three powerful
positive feedback loops causing explosive growth as long as the wage bill
remains less than the output and the system yields positive profits. Add the
labor market constraint and wage escalation when labor market becomes tight as
shown in Figure 2a, and the profits go to zero pretty quickly while the system
equilibrates at full employment as shown in the simulation of Figure 2b.
A sustained growth in this system
is possible only when a growth in the total workforce can sustain a pool of
unemployed that also keeps wage rate from escalating. Indeed, a sustained growth
is obtained when population growth structure is added as in Figure 3a.
Simulation of this model is shown in Figure 3b.
Figure 2a: Demographic
constraints added to the model of Figure 1.
Figure 2 b: Behavior of the
model with demographic constraints.
Figure 3a: Population growth
added to the model of Figure 2a
Figure 3b: Economic growth
supported by population growth
A land or renewable resource
constraint added to this system would slow down the rate of exponential growth,
but would not bring it to a halt as long as the labor pool is growing since
capital can substitute land and the marginal product of land can increase as
other production factors grow. This is shown in the simulation of Figure 4b
resulting from the model structure in Figure 4a. Evidently, population growth
that creates a growing supply of labor is critical to maintaining economic
growth in Adam Smith’s model. Hence, the demographic constraint is the unwritten
limit to growth since all else is driven by the profits which would decline to
zero when a tight labor market caused by a fixed population creates wage
escalation. Also note that there is no surplus or deficit of supply and demand
in the model and all production is consumed, implicitly meaning that income is
widely distributed and both profit and wage components are distributed to the
households, hence the demand for goods and services depends on the total income
rather than a part of it. This implies that capital ownership is widespread that
creates household claims to profit across board. This assumption seems to be the
essence of Say’s law that eventually became imbedded in the supply side
neoclassical growth models although it was repudiated in the writings of
Ricardo, Malthus and Marx, who were concerned about the class structure and how
it affected income distribution, supply and demand, and economic growth.
Figure 4a: Renewable resources
constraint (Land) added to the model.
Figure 4b: Behavior with land
constraint, when population is growing
Ricardo’s iron law of wages
and the principle of diminishing marginal rents
David Ricardo was a contemporary
of Malthus and a forerunner of Marx. He initiated a debate on the theories of
value that still occupies economists today. He also outlined the principles of
distribution between the various economic classes, landlords, capitalists and
workers which later became important building blocks of the model of growth and
decline of capitalism that Marx conceived. Last, but not least, he brought in
the constraints to growth by stating his famous iron law of wages and the law of
diminishing returns to land cultivation (McCulloch 1881) .
The iron law of wages linked
population growth to the wage bill and predicted that population would grow
until wage rates equilibrated at a subsistence level. The wage bill divided by
subsistence wage, therefore, returned the demographic capacity to supply labor.
He also assumed that land was a fixed constraint, meaning the resources it
represented did not deplete or were renewable. However, each additional unit of
output would require more extensive use of capital and labor. Thus, when the
population came to a balance, all marginal land would have been used and all
labor employed. At this stage, the marginal returns on cultivating an
additional unit of land would fall to zero while the marginal product of labor
equaled the subsistence wage. Ricardo extended this principle also to mineral
resources, but apparently without expressing a concern for running out:
“The return for capital from the poorest mine paying no
rent would regulate the rent of all the other more productive mines. This mine
is supposed to yield the usual profits of stock. All that the other mines
produce more than this, will necessarily be paid to the owners for rent.”
(Ricardo 1817)
Ricardo furthermore argued that
rate of profit and rents were determined residually in the agricultural sector.
He then used the concept of arbitrage to claim that the agricultural profit and
wage rates would be equal to their counterparts in the industrial sectors. With
this theory, he could show that a rise in wages did not lead to higher prices,
but merely lowered profits (New School url on Ricardo).
The model I
have presented in Figure 4 is modified further to incorporate the structure
underlying the iron law of wages and the diminishing returns on land suggested
by Ricardo. Figure 5a shows the model with this modification. Wage bill now
determines the demographic capacity to supply labor. As shown in Figure 5b,
workforce growth rate is driven by the discrepancy between the demographic
capacity and the current workforce.
Figure 5a:
Ricardo’s iron law of wages and the concept of diminishing rents added to the
model
The wage rate rises at first as
the economy grows faster than the labor supply thus creating tightness in the
labor market, but as marginal output declines while workforce continues to grow,
a rising unemployment rate forces the wage rate to decline and it comes to a
balance at the subsistence level. The profits (which subsume land rents) decline
also even though they grow at first.
Figure 5b: Simulation of the
Ricardian model of economic growth.
In the final equilibrium, the wage
rate equilibrates at the subsistence level, while and profits decline to zero.
The population has grown to the level determined by the wage bill that provides
enough subsistence to the workers so they can produce, but no more.
Thomas Malthus and repudiation
of Say’s Law
Thomas Malthus, published ideas
similar to Ricardo’s almost simultaneously as Ricardo wrote. He surmised that
population growth by itself is not enough to bring economic advances. He felt
that population growth is an end product in the economic growth process,
rather than a means. He posited that an increase in population cannot take place
without a proportionate or nearly proportionate increase of wealth (Malthus
1920).
Another assumption implicit in the
simple model I have presented is the so called Say’s Law meaning supply creates
its own demand which assures that all production is consumed. While Ricardo
seems to have implicitly subscribed to Say’s Law, Malthus, in fact, repudiated
it by differentiating between profits and wages and emphasizing the importance
of demand that is linked mainly to the wage income. Marx later presented a more
detailed analysis of the consequences of an imbalance between wages and profits.
(Higgins 1968, pp67-75)
Malthus was also concerned with
what he described as population explosion and the scarcity of resources
resulting from it, although it is not clear whether he considered resources in
the framework of fixed land, which does not get depleted or nonrenewable
resources, which get depleted. Hypothetically, if a resource depletion process
is added to the model of Figure 5, an overshoot and decline behavior outlined in
Forrester’s World Dynamics and the Limits to Growth/ Beyond the Limits studies
is obtained (Forrester 1971, Meadows et. al., 1972, 1974, 1992). The structural
modification needed for this is shown in Figure 6a and the resulting behavior in
Figure 6b.
Forrester has sometimes been
accused of replicating the Ricardian/Malthusian model, but he clearly has dealt
with nonrenewable resources while the earlier thinkers seemed to be dealing with
non-depleting land or renewable resources. Also Forrester disaggregated the
limits into an array that further dealt with environmental degradation arising
out of economic growth and population growth which could create constraints on
growth while material resources were still plentiful. He also introduced the
concept of decisions in bounded rationality and the delays in recognition of the
information on which the bounded rational decisions of economic actors are based
and how these limits could cause an overshoot and decline in population
(Radzicki 1988, Morecroft 1985). This way, Forrester provided a far more
succinct theory of limits to growth than posited in the classical economic
theories.
Figure 6a: Ricardian
model with depletable resources
Figure
6b Overshoot and decline behavior obtained from Ricardo’s model with
depleting resources
Marx’s model of the downfall
of capitalism
Marx added a new twist to the
concept of limits to growth by tying them to the social and political factors.
He saw these limits arising out of social conflict emerging from income
distribution rather than resource limitations. He took an exploitative view of
economic growth and posited that it arose out of appropriation of the surplus
value by the capitalists. Such exploitation is made possible only when there is
a large pool of unemployed labor so workers can bargain for only subsistence
wage irrespective of their contribution to production, which is achieved by the
capitalists by creating labor-substituting technological advances.
Marx distinguished between the use
value and exchange value of a commodity, the later being proxied by the market
price. He also postulated a social division of labor, in which
different people produced different products, so an exchange could occur. As the
ultimate volume of demand for these commodities emerged from the disposable
income of the households, a large pool of unemployed would eventually stifle
this demand. Marx thus clearly repudiated Say’s Law.
Marx also introduced the concept of
rate of return on capital that influenced the rate of investment. Marx’s logic
is sometimes criticized since in his model investment continues even when the
rate of return turns down. He assumed that available profit will be invested
until the rate of return goes to zero, while profit is the result of the labor
performed by the worker beyond that necessary to create the value of his or her
wages. Thus profit arises out of the surplus value of labor, which is referred
to as the surplus value theory of profit.
This investment structure was indeed
consistent with Marx’s distinction between the capitalists who receive all
profits and do not have to accrue any capital costs to justify an investment
decision, and the asset-less proletariat who received only wages. Thus, unlike
the neo-classical model, the rate of return in Marx’s model was not the only
factor determining investment. So, even when the rate of return declined,
surplus value accrued as profits needed to be invested. Only when both profits
and the rate of return became zero did the investment finally atrophy. Marx did
indeed make the prediction that the rate of profit will fall over time, and this
was one of the factors which led to the downfall of capitalism. The rate of
return declines as the unemployed proletariat is unable to buy the end
commodities and the production capacity cannot be utilized, leading to the
creation of idle capital (Wolff 2003, Higgins 1968, pp 76-87).
Figure 7a shows the structure of
Marx’s model that is common to the earlier models of this paper with the
difference that technological development is assumed to be labor substituting.
Thus technology affects capital labor ratio rather than the output. Also, the
rate of return affects the investment decision in addition to the profits. And
the capital is divided into two categories, capital in use and idle capital. The
hiring depends on the discrepancy between desired labor and labor instead of
being directly driven by the investment rate. The desired labor in turn is
determined by the capital in use and the capital labor ratio. Figure 7b shows
the complete model.
The rate of return on capital is
determined by real profit per unit of capital multiplied by price. The price in
turn depends on supply and demand. Here is where Say’s Law is repudiated. The
demand depends on the wage bill while the supply is created by the capital in
use and the employed labor. The capital in use is the difference between the
capital and the idle capital which depends on capacity utilization. Capacity
utilization, in turn, is determined by the demand relative to the supply over
the past period. Figure 7c shows the simulated behavior of this growth model.
Figure
7a Labor substituting technological development, rate of return and idle
capital added to the growth process as conceived by Marx
Figure 7b Marxian model
of economic growth
Figure 7c
Decline of rate of return and profits, and the creation of a reserve
army of the unemployed in the simulation of Marx’s model of economic growth
As correctly postulated by Marx,
the relationships in his model do indeed lead to a growth and collapse behavior
in the rate of return and profits as capital grows along with a reserve army of
the unemployed since new investments are labor substituting. Investment is
driven down to zero when both the rate of return and the rate of profit go to
zero. Meanwhile, the capacity utilization shrinks and idle capital stock rises.
Figure 8a: Capital decay added
to Marxian model
The decline in profits is due to
the growth in idle capital rather than the wage bill since the reserve army of
the unemployed keeps wage rate at subsistence level. This can be a conflictful
scenario that Marx suggested signaled the end of capitalism. It is not clear
whether Marx thought the reserve army of the unemployed would destroy idle
capital (Baumol 1959), although he postulated that the uprising of the masses
would be concomitant with such destruction. Either way, the stock of physical
capital would decay as suggested by the additional structure in Figure 8a, and
the simulated behavior arising from this structure as shown in Figures 8b and
8c. The decay is faster when the destructive forces arising from the reserve
army of the unemployed are taken into account and slower without them, but the
trend is the same in both cases.
Figure 8b: Decay of capital
with a disruptive reserve army of the unemployed
Figure 8c Decay of capital
with a peaceful reserve army of the unemployed.
Schumpeter’s concept of
creative destruction and economic cycles
While Marx’s model of destruction of capitalism by
an exploited proletariat was based on a class system that locked capitalists and
proletariat in separate compartments, Schumpeter saw the possibility that
entrepreneurship could exist across all social classes. Thus new entrepreneurs
could emerge from the ruins of a fallen capitalist system. They could create a
resurgence of capitalism from an environment in which cheap labor and the
possibility of profiting from it would allow them to mobilize idle capital
resources and create new and marketable goods and services from them. In my
observation, Schumpeter saw the possibility of social mobility between classes
arising from entrepreneurship that would rejuvenate a declining capitalist
economy, while Marx had ruled out such mobility. Schumpeter pointed out that
entrepreneurs innovate, not just by figuring out how to use inventions, but also
by introducing new means of production, new products, and new forms of
organization. These innovations, he argued, take just as much skill and daring
as does the process of invention (Schumpeter 1962).
Quoting from Schumpeter’s
biography:
Innovation by the entrepreneur, argued Schumpeter, led to gales of
"creative destruction" as innovations caused old inventories, ideas,
technologies, skills, and equipment to become obsolete. The question, as
Schumpeter saw it, was not "how capitalism administers existing structures,...
[but] how it creates and destroys them." This creative destruction, he believed,
caused continuous progress and improved standards of living for everyone
(Library of Economics and Liberty: Schumpeter’s biography)
Figure 9a shows the production system and labor
market structure implicit in Schumpeter’s mental model as outlined by Higgins
(Higgins 1968, pp 88-105).
Figure 9a The
production system and the labor market implicit in Schumpeter’s model.
Please note this structure is more or less similar
to the Marxist model with the exception that labor substituting characteristic
of technology is omitted and the direct link between profits and investment is
deleted. Schumpeter, in fact, distinguished between two types of investment that
he called induced and autonomous. He also introduced a concept of
“saving up” which is different from saving in the neoclassical growth
model. Saving up constituted the part of output that is withheld from investment
and consumption. Induced investment arose from the discrepancy between supply
and demand and autonomous investment from resources and technology created by
the entrepreneurs.
Saving up, possibly extended across social classes
and fueled entrepreneurial activity leading to autonomous investment. Although
one does not get a clear sense of this process from the descriptive writings of
Schumpeter, I detect recognition of social mobility in this concept that allows
workers to become the new capitalists. In the complete model shown in Figure 9b,
I would make a small amendment to Schumpeter’s concept of entrepreneurs creating
resources; I would call it mobilizing resources accumulated through saving up.
Figure 9b Complete structure of
Schumpeter’s model of creative destruction
Both mobilized resources and technology depend on
the number of entrepreneurs which adjusts towards potential number determined by
profits and entrepreneurial climate. According to Schumpeter, entrepreneurial
climate is created by the availability of a high rate of profits and the
availability of cheap labor. I have accumulated the difference between the
saving up, which Schumpeter said depended on interest rate, and the mobilized
resources in a stock of unspent savings which supply the venture capital for the
entrepreneurs. This also allows the model to have a hypothetical equilibrium in
which induced investment is zero and saving up equal the resources mobilized by
the entrepreneurs or the venture capital investment.
Figure 9c shows the behavior of Schumpeter’s model
with a fixed labor supply. Figure 9d shows the behavior with an autonomous rate
of growth in labor. The model shows the cycles extensively discussed by
Schumpeter, although the variety of periodicities he referred to is not shown.
Figure 9c Behavior of
Schumpeter’s model without autonomous population growth
Figure 9d Behavior of Schumpeter’s model
with autonomous population growth
The autonomous investment arising from
entrepreneurial creativity creates competition that expands creative activity
and shrinks profits, while creating tightness in the labor market that takes
away the very elements of the entrepreneurial environment that helped launch it.
Schumpeter called this process the “creative destruction” and postulated that
this would result in a cyclical tendency in the capitalist system, which is
indeed borne out buy the simulation of his model. Although Schumpeter referred
to may types of economic cycles in his writings the feedback processes
distinguishing their periodicities are not clear. The model I have constructed
exhibits a periodicity of about 10 years based on the time constants I have
selected, while it specifically addresses the process of creative destruction
that Schumpeter originally posited.
Conclusion
The concept of limits was tightly interwoven with
the process of growth postulated in the classical theories. These limits
encompassed many domains including demographic, environmental, social and
political. In most instances, the recognition of these limits required dealing
with soft variables that were difficult to quantify in the neoclassical analysis
tradition. It is not surprising that these processes have been excluded from the
formal analyses of mainstream economics, which has greatly reduced the
explanatory power of the neoclassical theory, which has come to attribute all
deviations from the postulated behavior of a hypothetical perfect market system
to the imperfections in the reality, which is a violation of the scientific
principles of modeling. All models are wrong, only reality is right and first
requirement of a model is to replicate some aspect of reality before it can be
accepted as a basis for a policy intervention.
Classical economics, on the other hand did attempt
to replicate empirical realism in its theories often using soft variables in its
explications. System dynamics modeling allows reinstatement of such soft
variables in our models of economic behavior that should reincarnate the rich
insights the traditional economic concepts provided. This indeed requires
reinventing modern economics which should be undertaken without further delay.
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