Untangling Complex Systems, page 32
egy of solving the economic problem of how to make the best use of limited resources depends on
the features of the economic environment. A free-market economic environment finds solutions that
are appreciably different from those offered by a command economy and from those determined by
a mixed economy. In a free market, what to produce is determined by consumers, how to produce is
determined by producers, and who gets the products depends on the purchasing power of the con-
sumers. At the heart of a free market economy, there is the pursuit of self-interest by both producers
and consumers. When a government decides what, how and for whom to produce, we have a com-
mand economy. In between the two extremes, there are also mixed economies that merge market
forces and governmental planning to try to determine the best solutions to the economic problems.
In a mixed economy, what to produce is fixed partly by consumers’ preferences and partly by the
government; how to produce is chosen partly by the producers seeking their profits and partly by
the government that, hopefully, looks for social justice. For whom to produce is determined partly
by purchasing power and partly by government preferences. In practice, all economies are mixed,
although they differ in the balance between public and private sectors.
6.3 LINEAR AND CIRCULAR ECONOMY
Whatever is the kind of economy, three factors allow producing goods and provide services (sym-
bol GS). They are (1) land and natural resources (symbol R), (2) capital (symbol C) including tools, equipment, and factories, (3) labor (symbol L) including skills, risks, and efforts of entrepreneurs.
GS = f ( R, C, L) [6.1]
Productive processes transform natural resources in goods and services by increasing (a) their Helmholtz
free energy A that measures the maximum obtainable work, 5 and/or (b) their content of information I (see Figure 6.1). The value added (symbol VA) to natural resources is the increment of value, represented by the sum (A+I)
, that the natural resources undergo by labor. The value added is trans-
added
formed into the well-being of the buyer. However, when goods and services cease to be useful because
they are not used to do further work or give the required information, they are at the end of their lifetime.
They become waste, and they are usually dumped because they have no more or a little A+I value.
The scheme sketched in Figure 6.1 represents how the linear economy works: it transforms
natural resources into waste, but also into the physical and immaterial psychic well-being of
humans. The linear economy is driven by the ambition of relentless exponential growth: the GDP
of a nation must always increase. Commonly it is said that a linear economy is affected by the
“bigger-better-faster-safer” syndrome, which means progress, emotion and fashion to satisfy the
endless human thirst for well-being. Companies make profits if they contrive, produce, and sell
appealing and cheap goods or services. Unfortunately, the growth-mania of the linear economy
determines an unavoidable fast depletion of natural resources. In fact, our planet, Earth, is like a
spaceship (Georgescu-Roegen 1976). The “spaceship earth” is embedded in the gravitational fields
of our closest star and moon; its fuels are the flow of electromagnetic energy coming from the
sun and the thermal energy produced by the decays of unstable nuclei under the terrestrial crust.
4 The economic problem was outlined by Paul Anthony Samuelson (1915 – 2009 AD) who was the first American to win the Nobel Prize in Economic Sciences in 1970. As the same Samuelson declared, in the age of specialization, he thinks of himself as the last “generalist” in economics, with interests that ranged from mathematical economics to financial journalism.
5 From Clausius’ inequality dS ≥ dq/ T and the first principle of Thermodynamics dU = dq + dw, it derives that
− dw ≤ − dU + TdS . The work carried out by the system is dw′ = − dw and − dA = − dU + TdS a T constant. Therefore, dw′ ≤ − dA. The maximum work that can be performed is given by − dA.
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Untangling Complex Systems
G&S
E
VA
xp
anufacturing
l
A + I
oi
M
ta
Natural
tio
resources
n
Waste
Birth
Death
Lifetime of G&S
FIGURE 6.1 Scheme describing how the sum of Helmholtz free energy (A) and information (I) of natural
resources change when they are transformed in goods and services ( GS) through manufacturing, and finally
in waste after exploitation.
Within the “spaceship earth” there are stocks of mineral resources, fossil fuels, and all other
chemicals that are finite. In a thermodynamic sense, the earth may be conceived, approximately,
as a closed system.6 We might delay the exhaustion of natural resources by choosing a strategy of de-growth, which corresponds to negative growth. This radical program proposed by Georgescu-Roegen (1976) wanted to downsize the world economy to the point where it makes use of a very
minimum of exhaustible resources. Such proposal has remained unexplored in societies ground-
ing their economy in the accumulation of capital and mass consumption. A valid alternative is the
strategy of sustainable growth. Economic growth is sustainable when growth can be maintained
without exhausting natural resources and creating environmental problems, especially for future
generation. In the last decades, societies have become aware that sustainable growth is feasible if
economy mutates from linear to circular. A circular economy works as if it were an ecosystem.
Any ecosystem grounds on solar energy (see Figure 6.2). Plants, algae, and phytoplankton feed
SUN
Primary consumers
(Oxidators; Herbivores)
Products
Secondary consumers
(Reducers; Autotrophs)
(Oxidators; Carnivores)
Detritivores
(Decomposers;
Mineralizers)
FIGURE 6.2 Schematic structure of an ecosystem fueled by solar radiation.
6 Rigorously, the earth is an open system because compounds may escape from the terrestrial atmosphere and because nuclear particles and meteorites can enter our atmosphere.
The Emergence of Temporal Order in the Economy
151
G&S
Exploitat
Natural Manufacturing
ion
resources
Waste
Recycling
FIGURE 6.3 Sketch of the lifetime of Goods and Services in a circular economy.
on solar radiation. They photosynthesize carbohydrates from CO and water. They use carbohy-
2
drates as chemical fuel for themselves and for the primary consumers that are the herbivores. The
herbivores are the food of carnivores. Both plants and herbivores and carnivores produce dead
organic matter through their metabolism. Their waste products feed the detritivores that are fungi
and bacteria. The detritivores decompose waste products more effectively and release products
that feed the producers. Nothing is wasted.
The same should occur in a circular economy. Circular-economy business models turn old
goods into as-new resources by recycling the materials, but at the same time foster reuse and
extend service life through repair, remanufacture, upgrades, and retrofits (see Figure 6.3). Waste is nothing but a spring of resources to be harvested. The ultimate goals are industrial loops to turn
outputs from one manufacturer into inputs for another. Virgin materials may undergo many cycles
of manufacturing. The consumption of virgin materials’ stocks is reduced, and the generation of
waste is shrunk, too.
6.4 THE LAW OF SUPPLY AND DEMAND
In economy, the value of Helmholtz free energy A and information I of a good or service is
expressed through its price. Who determines the prices of goods and services? The protagonists
of the economic processes determine the price, i.e., producers and consumers who meet in the
marketplace. The number of products the consumers are willing to buy depends on their prices.
If the price of a product is low, consumers are encouraged to buy it in a significant amount; on the
other hand, if the price of a product is high, few consumers are interested in it (see the Demand
curve in Figure 6.4). Producers decide by reasoning oppositely. When a product is sold at high
Price
Demand
Supply
Quantity
FIGURE 6.4 The curves of demand and supply and their intersection representing the best price for a prod-
uct or service.
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Untangling Complex Systems
Peak
Peak
Decline
Decline
GDP
Growth
Growth
Recessio
Recession
n
Recovery
Recovery
Depression
Depression
Time
FIGURE 6.5 Oscillations of GDP over time in business cycles.
price, they are strongly willing to manufacture it, whereas, whenever it has a low price, they are
not encouraged to invest on it (see the Supply curve in Figure 6.4). The right price for a product is that corresponding to the intersection point of the demand and supply curves. However, the price of
a product does not remain constant over time because the economy is a complex adaptive system.
In fact, fashion changes people’s habits; technology evolves; the availability of natural resources
decreases, and so on. The demand and supply curves shift continuously. For example, when the
salary of consumers increases, the demand curve shifts towards the upright part of the graph in
Figure 6.4. The technological progress allows producers to manufacture much more commodities
by cutting costs, and the supply curve moves towards the down-right part of the same graph. When
there is limited supply with respect to the demand, producers increase production and prices rise.
As soon as the prices rise, consumers decrease consumption. On the other hand, if there is too
much supply for the available demand, then prices fall, producers decrease production, and con-
sumers increase consumption.
In macroeconomics, a graph like that of Figure 6.4 is still valid, but it refers to the aggregate demand and the aggregate supply. The aggregate demand is the total amount of money spent by
all consumers to buy goods and services, whereas the aggregate supply is the total amount of
money spent by all the producers to manufacture commodities, offer services and including their
profits. Producers and consumers determine a circular flow of money. The GDP of a nation can
be measured by counting either the money spent by the consumers to buy goods and services or
the money spent by producers to manufacture commodities, offer services and store profits. The
GDP does not remain constant, but moves up and down, periodically (see Figure 6.5). Usually,
it is possible to distinguish the phases of growth, peak, decline, recession, depression, recovery
that repeat cyclically. In fact, business analysts talk about economic cycles, and they strive to
predict them.
6.5 THE BUSINESS CYCLES
For centuries, economists in both the United States and Europe regarded economic downturns as
“diseases” that had to be treated; it followed, then, that economies characterized by growth and
affluence were regarded as “healthy” economies. By the end of the nineteenth century, however,
many economists had begun to recognize that economies were cyclical by their very nature, and
studies increasingly turned to determine which factors were primarily responsible for shaping the
direction and disposition of national, regional, and industry-specific economies. Today, economists,
The Emergence of Temporal Order in the Economy
153
corporate executives, and business owners cite several factors as particularly important in shaping
the complexion of business environments.
There are two main approaches to explaining business cycles (Samuelson and Nordhaus 2004).
The first approach invokes exogenous shocks as the leading causes of business cycles. They might be
technological innovations, wars, natural catastrophic events, political decisions, and so on. The second
approach looks for endogenous factors. In fact, as we have already said in paragraph 6.1, an economic
system is an example of an out-of-equilibrium system that can self-organize similarly to ecosystems.
6.5.1 goodwin’s PredaTor-Prey model
Goodwin (1967) presented a model where workers and capitalists play like the predators and preys
of the Lotka and Volterra model and give rise to oscillations. It was Karl Marx, who, in his famous
book Das Capital (1867), formulated the original idea. Marx believed that profits push capitalists
to make investments and expand production. The consequent growth of activities provokes excess
labor demand. Hence, wages rise. But the rise of the wages squeezes the profit rate of capitalists,
slowly eroding the basis for accelerated accumulation. Therefore, the price of labor falls with the
needs of the self-expansion of capital. When the capital starts to re-grow, labor demand rises too,
again. Then, the entire cycle repeats itself. In Goodwin’s model, the total output, Y, of the macro-
economy is partitioned between wage-earning workers and profit-earning capitalists. If w repre-
sents a single wage and L is the amount of labor employed, the wage bill is wL. The ratio ( wL/Y) will be the wage share. The profit of the capitalists will be
P = Y − wL. [6.2]
The ratio P/Y is the profit share. Of course,
wL P
w
P
+
=
+
=1, [6.3]
Y
Y
λ Y
where λ = Y/L is the labor productivity. It grows at the positive rate θ:
dλ
= θλ [6.4]
dt
λ λ θ
= 0 e t [6.5]
We assume that workers consume all their wages, whereas capitalists invest all their incomes. If K
is the capital, ( K/Y) = κ is the capital-output ratio, which is constant. The capital growth rate g is K
given by:
dK 1
P
w Y
w 1
1
g
1
1
(1 ν )
K =
=
= −
=
−
= −
[6.6]
dt K
K
λ K
λ κ
κ
It is evident that g increases if the wage share v = w λ = wL Y decreases.
K
The growth rate of the labor g is
L
dL 1
1 dY 1 Y d 1
1 dK
gL =
=
+
=
−θ = g −θ. [6.7]7
dt L λ dt L L dt λ K dt
K
From equation [6.7], it is evident that g is high when g is high and when
L
K
θ is small.
7 Equation [6.7] requires some steps to be verified. g = (
/ )(1/ L) = (1/λ)( dY/dt)(1/L) + ( / )( d / dt)(1/λ). But
L
dL dt
Y L
Y = K/v
and L = Y/λ. Therefore, g
θ t
= ( dK/dt)(1/ K) + ( Kλ/ Yv)( d/ dt)(1/λ) =
− λ(θ/ 0
λ e ) =
− θ .
L
gK
gK
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Untangling Complex Systems
If N is the supply of workers and it grows exponentially
dN
= nN [6.8]
dt
N N ent
= 0 , [6.9]
then, the employment rate µ = L/ N decreases exponentially:
Y
Y
µ =
=
[6.10]
λ N λ
θ
( + )
N e n t
0
0
Its relative variation on time gμ is
1 dµ
1 dL
L d 1
1
gµ =
=
+
= g
(
) (1 )
(
)
L − n = gK − θ + n =
− v
− θ + n . [6.11]
µ dt
µ N dt
µ dt N
κ
Equation [6.11] tells us that the employment growth rate is high if the capital growth rate is high.
The wage growth rate g will be
v
1 dv
1 dw
w d 1
gv =
=
+
= gw − g
v dt
vλ dt
v dt λ
