TWO PARADIGMS OF PRODUCTION AND GROWTH
Emeritus Professor Robert U. Ayres, INSEAD and Chalmers Institute of Technologya
Dr. Benjamin Warr, INSEAD
Center for the Management of Environmental Resources (CMER)
Boulevard de Constance
mail to : Benjamin.Warr@free.fr
This article contrasts two incompatible paradigms of economics and their implication for
economic growth. The first paradigm is consistent with the micro-foundations of neoclassical
theory, which assume that all goods and services are produced from other goods plus value added
by some combination of capital and labor. The theory does not explain growth, but simply
assumes that technological progress (or multi-factor productivity gains) will continue indefinitely
along the supposedly `optimal’ path. Related endogenous growth theory, attempts to explain the
so-called Solow residual in terms of spillovers and/or increasing knowledge embodied in `human
capital’, but this theory is unquantifiable – lacking satisfactory metrics for knowledge or human
capital – and it still neglects the role of energy and materials The second paradigm focuses on the
economy as a material resource processor-convertor. It interprets economic growth as an
evolutionary process driven mostly by technological innovations (not by capital accumulation),
with a strong focus on materials processing and energy (exergy) conversion. We measure
resource inputs and resource conversion efficiency in thermodynamic terms. Using a new
a This work was initiated when the first author was a part-time visiting professor at the UN University, Institute for Advanced Study in
Tokyo, during 2000 and 2001. It has also been supported by the European Commission under project TERRA (FP5-IST) and by the Center for
Management of Environmental Resources at INSEAD.
variable exergy services or ‘useful work’ as a factor of production, historical economic growth in
the US since 1900 is reproduced quite accurately. Much of the previously unexplained residual is
the result of productive improvements in the efficiency with which useful work is delivered to the
economy, the cumulative result of innovation, learning-by-doing and economies of scale.
1. The neoclassical paradigm
The neo-classical paradigm is a collection of assumptions and common understandings going
back in some cases to the marginalist revolution in the 19th century. It has been increasingly
formalized in the second half of the 20th century. The formal version is sometimes characterized
by Solow’s so-called `trinity’: namely, `greed’, rationality and equilibrium. `Greed’ means
selfish behavior; rationality means utility maximization and equilibrium refers to the Walrasian
hypothesis. There are, of course, other features of the paradigm. Production and consumption are
abstractions, linked only by money flows, payments for labor, payments for products and
services, savings and investment. These abstract flows are governed only by equilibrium seeking
market forces (the “invisible hand”). It assumes perfect competition, perfect information, Pareto-
optimality and Walrasian equilibrium. The origins of physical production in this paradigm remain
unexplained, since the only explanatory variables are abstract labor and capital services. In the
closed economic system described by Walras (Walras 1954), Cassel, (Cassel 1932) von Neumann
(von Neumann 1945) and Koopmans (Koopmans 1951), every product is produced from other
products made within the system, plus capital and labor services.
The unrealistic neglect of materials (and energy) in the economic system was pointed out
especially by Georgescu-Roegen (Georgescu-Roegen 1971), although his criticism did not
immediately lead to a paradigm shift. Growth theory remained primitive because it lacked any
empirical base until the 1950s when it was discovered by Fabricant (Fabricant 1954) and
Abramovitz (Abramovitz 1956) that growth could not be explained by the accumulation of
capital. But the key innovation in growth theory in the 1950s was the explicit introduction of an
aggregate production function of labor services and capital services (Solow 1956; Solow 1957),
(Swan 1956). Capital services are derived from an artifact called `capital stock’. This, in turn, is
an accumulation based on investment and depreciation, although some have argued that
aggregate capital cannot logically be measured independently of its rate of return, and – for this
and other reasons – that the concept of production function itself is faulty (Robinson 1953-54;
Pasinetti 1959; Sraffa 1960; Sylos Labini 1995). Labour services were considered to flow in
proportion to the total number of hours worked.
While growth can theoretically be expressed in terms of the derivatives of the production
function (marginal productivities) of the input variables, the simple two-factor version introduced
by Solow does not explain growth. In fact, almost 90% of the observed growth in the US during
the historical period Solow chose to investigate (1909-1949) remained unexplained by the
increasing capital/labor ratio. Solow named this residual `technological progress’ and the annual
increments are called increases in “total factor productivity”(TFP). The annual increments tend to
fluctuate around a long-term trend, and enormous effort has been expended on identifying these
`business cycles’ with various periodicities, and attempting to explain them. Productivity
calculations and projections have become a mini-industry. The new `endogenous theory’ offers
qualitative explanations (spillovers from ‘knowledge capital’ increase TFP), but nothing
quantitative. It is important to realize that in this paradigm the (presumed) long-term trend in TFP
itself is assumed to have been exogenously determined. It is also assumed that it will continue,
much as it has in the past.
It is both common practice and convenient, although somewhat inconsistent with
atomistic competition, to assume constant returns to scale, which implies that the production
function should be a homogeneous function of the variables, of the first order (the so-called Euler
condition). In recent years (since the work or (Romer 1986) the possibility of non-constant
(increasing) returns received a good deal of attention from theorists, as well as support from
empirical studies focused on international comparisons (Easterly and Levine 2001). However, the
work in question is overwhelmingly based on two-factor models, primarily of the Cobb-Douglas
type, assuming a population of perfectly competitive producers of a single all-purpose good.
A simple model of income allocation (applicable, however, only to a single sector model)
implies that the demand for capital services and labor services will be proportional to their
respective marginal productivities. In equilibrium, it follows that, if output (GDP) is only a
function of capital and labor service inputs, the marginal productivities (output elasticities) of the
factors of production should be equal to the corresponding payment shares (factor costs) in the
national accounts. The Cobb-Douglas production function with constant returns is particularly
convenient because it provides an immediate economic interpretation for the parameters of the
function as elasticities. However, when a third factor is introduced this interpretation falters
According to the neoclassical model only labor and capital are productive and the weights
with which the production factors contribute to wealth creation are assumed constant and equal to
the factor cost shares. However, this rather convenient assumption has not withstood empirical
research. Easterly and Levine (2001, Table 1, p 183) present a wide selection of growth
accounting results for individual countries. Only for capital does the empirically determined
exponent approximate its cost share (typically in the range 0.2-0.3 in industrialised countries).
The empircally determined elasticity of labor varies from –0.04 to 0.42, depending upon the time
period, country and study (Easterly and Levine, 2001).
The underlying assumption of growth-in-equilibrium is also troubling. It is important to
note that (1) the real economy is never actually in equilibrium and (2) if it were, there would be
no opportunity or incentives to innovate. Furthermore, (3) the real economy is a complex non-
linear system, and non-linear systems do not exhibit equilibrium states. Moreover, (4) even if the
complex non-linear system could be optimized, a dynamic optimum is not the same as a static
optimum. Finally, and most troubling, (5) the lack of any theory to explain physical production in
physical terms (i.e. in terms of energy and materials.)
While technical progress is normally treated as an exogenous driving force, there is an
endogenous mechanism that can explain some aggregate economic growth-in-equilibrium –
beyond that which is accounted for by labor and capital accumulation -- without radical (structure
changing) technological innovations. The mechanism in question is a simple positive feedback
between increasing consumption, investment, increasing economies of scale and `learning-by-
doing’. These result in declining costs and declining prices, stimulating further increases in
demand and investment to increase supply (Figure 1) This simple feedback has been called the
Salter cycle (Salter 1960) and it corresponds well to many aspects of the neoclassical model.
However, if this is the only type of technological change allowed by the model, there
must be declining returns and an eventual limit to growth as the potential for incremental
improvements in production technology is exhausted. The closed neo-classical economic system
does not explain radical innovations that change the structure of the economy. Neither is there an
essential role for energy or materials, except as a consequence, (not a cause) of economic growth.
In its present two-factor form the Cobb-Douglas production function permits future physical
economic growth even with no materials or energy consumption. This is significant, because if
resource consumption is not needed to explain growth, then `decoupling’ growth from resource
consumption is conceptually easy: they were never coupled in the first place. Lacking any linkage
between the efficiency of materials and energy use and productivity, there is no theoretical
incentive to become more efficient. There are also no consequences from generating wastes and
pollutants. In the closed Walrasian equilibrium system, where all products are abstractions, there
is no such thing as material waste. The neo-classical conceptualization implies falsely that wastes
and emissions – if they exist at all – do no economic harm and can be disposed of at no cost.
The evolutionary paradigm
In contrast, the disequilibrium evolutionary paradigm discussed hereafter characterizes the
economy at the macro-level as an open multi-sector materials/energy processing system. The
system is characterized by a sequence of value-added stages, beginning with extraction of crude
resources and ending with consumption and disposal of material and energy wastes, which can do
harm if not eliminated. Referring again to Figure 1, above, if the system is open, then the causal
link between materials and energy consumption and economic growth implied by this mechanism
must be mutual. In other words, causality must be bi-directional, not uni-directional.
This means, ceteris paribus, that a two-factor production function involving only labor
and capital services as inputs cannot reflect this mechanism. A third factor representing resource
flows (in some way) is minimally necessary to reflect the feedback between increasing resource
consumption and declining production costs. This is needed, for example, to explain the long-
term declining resource prices documented by several scholars (Barnett and Morse 1962; Potter
and Christy 1968; Barnett 1979).
However, the simple positive feedback (Salter cycle) mechanism sketched in the previous
section allows for only one type of technological change: namely the combined effects of scale
economies and experience or learning-by-doing at the societal level. These forces do not
distinguish between sectors, hence they cannot explain structural change. But, in reality, there is
not one single aggregate technology of production for a single composite universal product, nor
even a single technology for each product as assumed by activity analysis, but multiple
competing technologies for each product and in each sector1.
The qualitative evolutionary change mechanism at the firm-level (assuming abstract
products) has been described by Nelson and Winter (Nelson and Winter 1974; Nelson and Winter
1982). It applies in a multi-product, multi-sector system, although mechanisms to explain
structural change at the sectoral level are not considered as such. As the rate of improvement of
the existing dominant technology for one product slows down, the incentives to search for, and
find, a new technology (or a new material or even a new product) grow in parallel. If the demand
for continued improvement is sufficiently powerful, there will be enough R&D investment to
achieve a `breakthrough’ enabling some radically new innovations capable of displacing the older
techniques (Ayres 1988). Schumpeter’s evocative word for this process was `creative destruction’
(Schumpeter 1934). Spillovers from radical innovations since the industrial revolution, especially
in the field of energy conversion technology, have been among the most potent drivers of
The disequilibrium evolutionary resource-conversion perspective elaborated below
implies that long-term growth, and progress towards sustainability, will require more than the
gradual efficiency gains resulting from economies of scale and social learning. Radical
innovations, resulting in new products and services and structural change, are also necessary.
Environmental constraints (arising from material extraction, processing and consumption) are
becoming increasingly important. Continued economic growth, in the sense of welfare gains, will
require multiple radical technological innovations, resulting in dramatic (`factor four’/`factor
ten’) reductions in raw materials and energy consumption, as well as more gradual improvements
such as more recycling and end-of-pipe waste treatment. Concommittantly the ‘productivity’ of
consumed materials and energy must increase dramatically. The rate of increase in productivity
of materials and energy use must clearly offset the reductions in total consumption through
dematerialisation (ceteris paribus) ; unless dramatic improvements in the quality of the other
factors of production can substitute for the role of materials and energy in generating wealth.
The next section concerns terminology and measures, and can be omitted without serious
loss of clarity, provided the reader is willing to accept that `exergy’ is the correct all-purpose
technical term for `energy’ (as the latter word is normally used), while it is also applicable to
minerals and non-fuel resources.
Thermodynamics and natural resources
The term `resources’ is used in many ways in different disciplines. For purposes of this paper, a
resource is an input to the economic process. Resources may be material or immaterial (e.g.
information) and material resources may be of natural origin or man-made. Services provided by
nature (e.g. climate, air, water, bio-diversity, `assimilative capacity’) are often called resources.
However, in this paper, the term natural resources is restricted hereafter to energy – actually
exergy– carriers, products of photosynthesis (phytomass) and other industrial raw materials
extracted from the natural environment by intentional human activity2.
The word energy is widely misused, and for the sake of precision we will introduce a
different term, exergy that is less familiar but more precise. Energy is a conserved quantity (the
first law of thermodynamics), which means that it can only change form or quality (e.g.
temperature) but can never be created or destroyed. Energy and mass are inter-convertible (by
Einstein’s formula E = mc2), although nuclear reactions convert only infinitesimal amounts of
mass into energy, while there are no practical processes for converting energy to mass. For all
other processes of concern to humans, both the mass and the energy-content of materials and
energy flows are independently conserved, which means the mass and energy of inputs (including
water and air) are exactly the same as the mass and energy-content of the outputs, including
waste products. What has changed is the availability of the energy in the inputs (solar insolation
or fuel) for doing work. This availability is quantifiable. A number of terms have been used for it,
including `available work’, `availability’, and `essergy’, but by general agreement it is now
The formal definition of exergy is the maximum amount of work that can be extracted
from a material by reversible processes as it approaches thermodynamic equilibrium with its
surroundings. Exergy is therefore a quantity that is not definable in absolute terms. It can only be
defined in terms of a reference state, namely the environment. But exergy can be calculated for
any material with reference to whatever environmental medium that material would be likely to
reach thermodynamic equilibrium with, namely the atmosphere, the ocean or the surface layer of
the earth’s crust (topsoil or subsoil). Thus gases tend to equilibrate with the atmosphere, liquids
or soluble solids with the oceans, insoluble solids with the land. (Detailed tabulations can be
found for many materials in (Ayres 1999)).
The exergy content of most fuels, per unit mass, is very nearly the same as the measure
usually tabulated, which is heat-of-combustion (or enthalpy, to be technically accurate) per unit
mass. This means that when economists or engineers speak of energy, they usually mean exergy.
However, even minerals and metal ores have characteristic exergy values, which are really
measures of their `distance’ from thermodynamic equilibrium as defined by the average mix of
materials in the lithosphere. The higher the grade of ore, the more exergy would have to be
expended to achieve that degree of concentration from the crustal average, hence the greater its
intrinsic exergy value. It follows that the greater the exergy content of the ore itself, the less will
be needed to refine it further.
In short, exergy is a very general way of keeping track of physical scarcity and the
difficulty of separation and purification. Evidently different ores and minerals can be
meaningfully compared in exergy terms. This leads to the possibility of measuring all kinds of
resource reserves in common (i.e. exergy) terms, for purposes of both international and inter-
temporal comparison (Wall 1977; Wall 1986). It is possible to measure copper reserves, iron ore
reserves, coal reserves, petroleum or gas reserves and forest biomass in the same (energy) units
e.g. kiloJoules (kJ) or petaJoules (pJ).
Just as resources can be measured in common physical (exergy) units, so can pollutants.
Exergy analysis can also be used empirically as a measure of sustainability, to evaluate and
compare wastes and emissions from period to period or country to country (Ayres 1998). The
exergy content of wastes is not necessarily proportional to the potential environmental harm the
wastes may cause, but the exergy content of a waste stream is certainly a rough measure of its
reactivity in air or water, i.e. its tendency to initiate spontaneous uncontrolled chemical reactions
in environmental media. In this regard, one can say that, although the exergy content of a waste
stream is not a measure of human or ecotoxicity, it is certainly a better measure of its potential for
causing harm, than is its total mass3.
A word on value: the use of exergy as a quantity metric does not imply that it is a measure
of value (although some have suggested the idea.) Some materials, such as diamonds, gold,
platinum, palladium and rhenium, have enormous economic value per unit mass, because of their
aesthetic or physical properties (e.g. as catalysts). Yet other elements have very little economic
value because they have no especially useful properties or because they are extraordinarily
difficult to work with. For instance, the light metals, beryllium, lithium, sodium, and magnesium
are quite commonplace in the earth’s crust, but rarely used in industry (as metals), at least in
relation to their intrinsic availability. The 9th most common metal in the earth’s crust, rubidium,
has virtually no uses at all.
The Economy as materials processor
From an evolutionary perspective, as noted above, the economic system can be viewed as an
open system that extracts and converts raw materials into products and useful services. The
economy consists of a sequence of processing stages, starting with extraction, conversion,
production of finished goods and services, final consumption (and disposal of wastes). Most of
the non-structural materials are discarded in degraded form. These conversion processes
correspond to exergy flows, subject to constraints (including the laws of thermodynamics). The
objective of economic activity can be interpreted as a constrained value maximization problem
(or its dual, an exergy minimization problem). Value is conventionally defined in terms of
preferences for consumption goods, although other definitions are possible.
The simplest model representation consists of two sectors with a single intermediate
product. The first sector would include extraction and primary processing, e.g. to finished
materials. The second sector would include manufacturing and service activities. Three or more
sectors would obviously add to the realism of the scheme. Of course, the more stages in the
sequence, the more it is necessary to take into account feedbacks e.g. from finished goods to
extraction of primary processing sectors. The N-sector version would be a Leontieff-type input-
output model in which the sequential aspect tends to be obscured.
An adequate description of the materials processing system, in our view, must include
materials and energy flows as well as money flows. These flows and conversion processes are
governed by the laws of thermodynamics, as well as accounting balances. At each stage, until the
last, mass flows are split by technological means into `useful’ and waste categories. Value (and
information) is added to the useful flows, reducing their entropy content and increasing their
exergy content per unit mass (thanks to exogenous inputs of exergy), while the high entropy
wastes are returned to the environment.
From a macroscopic perspective the output of the economic system – viewed as a
materials/exergy convertor – can be decomposed into a product of successive conversion stages
with corresponding efficiencies, viz.
GDP = R x
2 xK x
= R x f x f xKg
where f1 is the conversion efficiency of the resource (exergys) inflow R into the first level
intermediate product, f2 is the conversion efficiency to the second level intermediate product, and
so forth. The term g is just the ratio of output to the last intermediate product. The necessary
feedbacks are implicitly taken into account in the efficiency definitions.
As a first approximation, it is convenient to assume a two-stage system with a single
intermediate product, U. We argue that this intermediate product can conveniently be identified
as exergy services, or `useful work’. Then
Y = Rfg = Ug
where f is the overall technical efficiency of conversion of `raw’ exergy inputs R to useful work
output U, as shown in Figure 2. We consider the derivation of useful work in detail in the next
If we define g = Y/U then equation (1) is an identity, not a theory or model. However, the
right-hand side of (equation 1) might be interpreted as an aggregate production function provided
g is a suitable homogeneous function of order zero, whose arguments are labor L, capital K, and
resource flows R (or, as we propose, useful work, U). We consider production functions again
Energy (exergy) conversion and useful work
Writers on energy commonly use the term `energy conversion’ with reference to the use of
energy to perform `useful work’ (not to be confused with human `labor’, as that term is
understood in economics). The best explanation of useful (physical) work may be historical.
Work was originally conceptualized in the 18th century in terms of a horse pulling a plow or a