Role of Entropy in Sustainable Economic Growth

Role of Entropy in Sustainable Economic Growth Angelina DE PASCALE Faculty of Economics University of Messina, Italy E-mail: adepascale@unime.it ABSTRACT This paper investigates a possible relationship among economic growth, entropy and environmental preservation. Physics shows that energy is necessary for economic production and, therefore, economic growth but the mainstream theory of economic growth, pays no attention to the role of energy. Economics has attempted to address this question from different point of view. The classic literature focused on exhaustible resources puts at the core the importance of the price mechanism and the substitution possibilities of manmade inputs for natural resources. At the same time, others stressed the economic implications of thermodynamic laws and ecology. They insisted on the limits that physical and natural processes impose on economic activity and the difficulties in invoking the price mechanism because establishing property rights on environmental assets is often impossible. Because thermodynamics implies that energy is essential to all economic production, criticism of mainstream economic growth models that ignore energy appears legitimate. On the other hand, theories that try to explain growth entirely as a function of energy supply, while ignoring the roles of information, knowledge, and institutions, are also incomplete. This paper discusses ecological economics views on energy and growth. KEY WORDS Entropy, Sustainable Economic Growth, Technical Change JEL CODES O11, O44 1. Introduction When the economic system contributes each period more to welfare by creating more value, economic growth arises. Economic value creation (and hence economic growth) is measured by calculating real market prices, which reflect the consumers willingness to pay for marketed goods and services. However, also activities outside the formal economy affect well-being so that GNP or NNP growth is not an index for overall well-being. NNP growth may be accompanied by deterioration in other fields so that, on average, welfare falls. This notion, of course, lies at the base of concern for environmental problems. In 1798, R. Malthus published An Essay on the Principles of Population, where he predicted that world population growth would outpace economic growth, which would be constrained by the limited amount of arable land. This difference would lead to social misery. Two centuries later, Nicolas Georgescu-Roegen in 1971 pointed out that economic processes, as generally assumed, are not cyclical at all, and will in the long run lead to exhaustion of the world s natural resources. In 1972, the Club of Rome published, The Limits to Growth, which described the relationship between economic growth and damage to the environment. The model s shocking conclusion was that, if nothing were done, exhausted natural resources would cause a global collapse well before the year 2100. The grim outlook was that even if we could add resources or implement new technologies, the collapse could not be 293

avoided. This happens because the fundamental problem is an exponential growth in a finite and complex system. Consequently, in 1989, J. Rifkin, published Entropy Into the Greenhouse World. On these bases, in this article, it will show how the Second Law of Thermodynamics impacts the economic processes that affect environment. Although, in the last few years, ecological economists have paid increasing attention to the true impact of entropy on economics, the concept remains controversial within the mainstream economic community. 2. Thermodynamics Theory Thermodynamics is a basic science that formulates the rules for the conversion of energy and matter from one form into another. The word energy belongs to our daily vocabulary and usually refers to the ability to perform work. However, it is not easy to give a precise definition of energy. Each object ( system in thermodynamic language) contains a certain amount of energy. Moreover since Einstein s E=mc 2 it is recognized that mass and energy are equal. It is, however, impossible to determine the energy content of a given system and, therefore, ignorance remains about the energy of a system. This is not much a problem. It is more important that changes in the energy content can be determined exactly. Such changes may result from two types of process: a) by performing work on types on the system or letting the system perform work and b) by exchanging heat between the system and the environment. The first and second laws of thermodynamics are, respectively, the law of conservation of mass/energy and the so-called entropy law. The law of mass/energy conservation reduces in practice to two conditions that must be satisfied by any physical change or transformation whatever and, by extension, to any economic activity involving physical materials. Hence, the conservation of mass/energy implies separate conservation rules for energy and mass. The law of conservation of energy implies that energy inputs must equal energy outputs for any transformation process. The law of mass conservation, on the other hand, is far from trivial. The so-called mass-balance principle states that mass inputs must equal mass outputs for every process (or matter). In the first place, this condition implies that all resources extracted from the environment must eventually become unwanted wastes and pollutants. This means that externalities (market failures) associated with production and consumption is actually pervasive and that they tend to grow in importance as the economy grows (Ayres R.U., Kneese A.V., 1969, Kneese et al., 1970). Furthermore, the mass-balance condition provides powerful tools for estimating process wastes and losses for industrial processes, where these cannot be determined directly. Taking these considerations into account derives that the second law of thermodynamics also has economic and environmental significance. 3. Entropy and the Second Law of Thermodynamics The term entropy is too much used and too little understood. Mathematically, entropy (S), can be calculated from the amount of heat exchanged (Q) divided by the temperature (T) at which that heat exchange occurred (S = Q/T). Technically, entropy is an extensive state variable that is definable for any material substance or any system. The term extensive means that it is proportional to the size of the system (like volume or mass) in contrast to an intensive variable (like temperature, pressure or density). The physical law behind the concept is deceptively simple to state: if the system is isolated and closed, so that it does not exchange matter or energy with any other system, its entropy 294

increases with every physical action or transformation that occurs inside the system. Entropy can never decrease in an isolated system or in the universe as a whole. When the isolated system reaches a state of internal equilibrium its entropy is maximized. When two systems interact with each other, their total combined entropy also tends to increase over time. This non-decreasing property is known as the Second Law of Thermodynamics, or just the entropy law. The first economist to consider the subject in depth, Nicolas Georgescu-Roegen, focused on the entropy law as a metaphor of inevitable decline (Georgescu-Roegen N., 1971, 1979). Afterwards, Jeremy Rifkin said: The Entropy Law says that evolution dissipates the overall available energy for life on this planet. Our concept of evolution is the exact opposite. We believe that evolution somehow magically creates greater overall value and order on earth. Now that the environment we live in is becoming so dissipated and disordered that it is apparent to the naked eye, we are for the first time beginning to have second thoughts about our views on evolution, progress, and the creation of things of material value. Explanations and rationalizations aside, there is no way to get around it. Evolution means the creation of larger and larger islands of order at the expense of ever greater seas of disorder in the world. There is not a single biologist or physicist who can deny this central truth... (Rifkin J., 1989). Regrettably, what Rifkin claims to be a central truth is not true at all, because the world is not isolated from the solar system. However, his statement concisely reflects what has come to be known as the thermodynamic view of environmental economics. In contradiction to the mechanical approach, thermodynamics indicates that economic growth leads to increasing disorder. More specifically, increasing the flows of energy and matter through society, as happens in the process of ongoing industrialization, leads to progressive depletion of available energy and matter or, otherwise stated, to increased entropy. Excessive entropy production is reflected in natural disorders such as the greenhouse effect, ozone holes, environmental pollution etc. 4. Relationship between Thermodynamics and Economic Processes Broad definitions of the First and Second Laws of thermodynamics allow their incorporation into a vocabulary in which discussing the issue of relevance of entropy to economic processes. The First Law requires that matter and energy be conserved. The consequences to physical systems are that the total content of matter and energy in an isolated system is fixed, and that the total matter in a closed system is fixed. The First Law is implicit in most commonly-accepted economic theories of resource use. However, the First Law fails to describe irreversibility. The original inputs may never be recovered from the outputs of real or (more precisely) finite-time processes, and in some cases from mathematical or infinitesimal-time processes as well. Thus, while the quantity of energy and materials is conserved as predicted by the First Law, their quality or availability is not all physical processes convert low entropy energy and materials to high entropy wastes, from which the original low entropy inputs cannot be recovered without the conversion of still more low entropy resources to high entropy wastes. This irreversibility is governed by the Second Law. Entropy is defined here as the degree to which finite time processes is irreversible. The optimal macroeconomic scale, then, depends on the Earth s supplies of low entropy energy and materials, and its ability to harness solar energy for economic use. While the economy may not be limited by the solar energy flux in the foreseeable future, the finite limits of materials 295

needed to transform solar energy into economic goods are more apparent, raising serious questions as to how long the Earth's natural capital stocks can sustain present or increased future levels of throughput. Of more immediate concern than depletion of individual natural resource stocks is interdependency and complementary, or co-evolution, among natural capital sources and waste sinks, limiting or preventing substitution the market response that alleviates scarcity. Neoclassical throughput accounting using only First Law principles can fail to account for coevolution, environmental degradation, and suffusion of high-entropy waste sinks, all of which make future consumption thermodynamically more difficult. Resolving the issue of relevancy of entropy to economics assists in determining whether neoclassical theory can be amended to take the Second Law into account and adequately address these concerns. As part of the relevance of entropy debate, economists have argued whether the Second Law applies strictly to energy, or whether matter matters as well (Georgescu-Roegen N., 1971). Because the physical sciences draw no distinction between entropy of energy and entropy of matter (and in fact extend the consideration of entropy to quantum mechanics, information science, biology, cosmology, and to other fields of study as well), the distinction is viewed as purely arbitrary by the authors and not well suited to framing the issue of relevance of entropy to economics. As a result, the authors adopt the broader scientific view, that entropy is a property of matter-energy interactions and thus applies to both energy and matter. The question of entropy s relevance to economics is the question of whether entropy is the fundamental, irreducible economic good. Arguments in support of relevance hold that entropy is a physical law imposing an absolute constraint on economic growth while substitution among individual resources (specific sources of low entropy) is sometimes possible, it is not always possible and will be less possible as time passes. In Daly s (Daly H.E., 1991) words, Substitutability among various types of low entropy does not mean there can be a substitute for low entropy itself. The opposing view is that entropy is an anthropomorphic concept intimately associated with what is useful and, therefore, defined by current technology (Young J.T., 1991). Thus, in this view, new generations of technology can relax the constraint that entropy places on the economy; scarcity of low entropy can decrease or remain relatively constant over time. 5. The Economic Dimension The system within which economic activity takes place can be represented as the interaction between the natural and the human sphere, where each sphere provides particular inputs and generates particular outputs. Boulding (Boulding K.E., 1966) distinguishes between information, matter, and energy as the three important classes of inputs and outputs in a system. Obviously, material and energy are the specific inputs and outputs of the natural system, while information, or knowledge (to use the term that is common in the endogenous growth literature), is provided by the human sphere. Inter-human activity contributes to the system by providing knowledge; matter or energy, in contrast, are not man-made. The economic process combines human inputs (knowledge) and natural inputs (matter/energy) to produce economic goods. Both types of inputs are necessary. It is difficult to imagine an economy with only natural inputs but, in which lacking the knowledge about how to use them. Such an economy would not produce any economic goods. If an economy would have access to knowledge only but not to material or energy, knowledge could not be applied: it would be useless. The combination of knowledge and material/energy 296

yields new inputs/outputs such as physical capital (which is knowledge frozen in material), labor (which is knowledge tied to (human) energy), extracted and processed natural resources (e.g. iron ore and steel), final consumption goods etc. The size and composition of the stock of knowledge determines how productive natural resources will be in creating economic value. The economic process contains technology and preferences. The technology set describes how combinations of physical inputs and knowledge yield goods and services with certain characteristics. Preferences are formulated over these characteristics, since it is not the physical quantities that determine utility but the enjoyment derived from the goods. Entropic processes and economic processes differ fundamentally. Entropy and economic value have no one-to-one correspondence. Many low-entropy types of energy and material are useless from an economic point of view because mankind lacks the knowledge how to use them productively. When new knowledge becomes available, the productivity of the economy increases without necessarily changing physical conditions (i.e. the improvement of the user manual for a complicated consumer product). In a physical sense, entropic processes degrade energy by turning concentrated (ordered) energy into dissipated (disordered) energy. However, the state of knowledge determines energy available for satisfying economic wants. Contrary to the argument of Georgescu-Roegen and Daly, it is important to emphasize that order is continuously created in the biosphere including humans, by self-organized systems including, but not limited to, living organisms utilizing the low entropy solar flux. To be sure, an equal and opposite energy flux is re-radiated away from the earth at a much lower temperature (high entropy). The entropy of the universe increases as the sun shines on the earth (and into space). But this fact, as such, has virtually no significance for human life, or human civilization. The entropy law does not imply that order in the form of artifacts and infrastructure is necessarily being produced at the expense of increasing the entropy (disorder) of the biosphere itself. Of course it is true that human civilization is still addicted to fossil fuels and virgin ores. Our economic system is not currently making direct use of solar energy, except through agriculture, forestry and hydro-electricity. Most energy consumed in the industrial countries is obtained from stocks of fossil fuels embodied solar energy accumulated millions of years ago. From this point of view, it is true that humans are using up the stock thousands of times faster than it was built up. It is also true that this trend is unsustainable. Again, however, this is not a major near-term constraint. In fact, the environmental consequences of excessive fossil fuel use will constrain future use much sooner than the stock itself will be exhausted. In any case, there are a number of technologically feasible alternatives. Fossil fuels are being used up before other sources because they are cheap, not because there are no alternatives. It is economically rational to use the cheapest resources first. Georgescu-Roegen has tried to strengthen his case for entropic limits by postulating a Fourth Law of thermodynamics. In which matter becomes progressively unavailable, just as energy does, and that this process is irreversible even if available energy is plentiful. Moreover, he asserts that the process of mixing, dispersion and dissipation will continue to the point where all matter is unavailable. In other words, he says that the elements become increasingly mixed together and thus more and more difficult to separate from each other, without limit. However, the Geogescu-Roegen fourth law is not consistent with physics. Other economists have been more circumspect in characterizing the economic implications of the second law e.g. (Berry R.S., et al. 1970; Ruth M., 1993, 1995). However, except for Ruth's 297

work on the eco-thermodynamics of natural resource depletion, their results have been more theoretical than practical. For instance, a scientifically defensible statement of the thermodynamic perspective might be the following: Energy and mass conservation, together with the second law of thermodynamics (entropic irreversibility), implies the inevitability of unwanted by-products or waste energy in the course of economic production and consumption (Faucheux S., 1994). This statement of the economic implications of the two laws of thermodynamics is unexceptionable but lacking in headline potential. Certainly, human activity generates waste products capable of disturbing the natural environment. It is also true that humans are currently utilizing fossil fuels representing hundreds of millions of years of bioaccumulation, without replacing this stock of natural capital. This provides some superficial justification for the thermodynamic perspective. But, as many analysts have argued, the supply of natural resources (while finite) is almost certainly not the limiting factor for human survival and prosperity. On the contrary, it is technologically feasible to shift from non-renewable to renewable resources. Most economists believe that this would happen automatically as soon as the cost of extracting and refining virgin resources rises to the point where it exceeds the cost of recovery, reuse and recycling. Resource prices would undoubtedly rise, but this need not reduce consumer welfare in the long run. The long-run dangers arising from human activity probably come from another direction entirely. It is not the finiteness of resource stocks, but the fragility of selforganized natural cycles that we have to fear. Unfortunately, the services provided by these cycles are part of the global commons. They are priceless, yet free. Markets play no role in the allocation of these resources. There is no built-in mechanism to ensure that supply will grow to meet demand. Indeed, there is every chance that the supply of environmental services will dwindle in coming decades as the demand, generated by population growth and economic growth, grows exponentially. In fact, a slightly disguised version of the dilemma posed by Malthus. 6. Knowledge Creation Now it has been established that physical and value dimensions matter for economic processes, the attention will turn to economic growth. The core mainstream growth models (Aghion P., Howitt P., 2009), do not include resources or energy. Early growth models, such as that of Solow (Solow R. M., 1956), did not explain how improvements in technology come about, so that these models are said to have exogenous technological change. More recent models attempt to endogenize technological change - explaining technological progress as the outcome of decisions taken by firms and individuals. Early endogenous growth models such as Arrow s (Arrow K., 1962) learning by doing model or Hicks (Hicks J. R., 1932) induced innovation model allowed the state of technology to respond to changes in one of the variables in the model but do not explicitly model an optimizing process. More recent endogenous growth models are represented by the so-called AK models that do not explicitly model research and development activities (R&D), and Schumpeterian growth models that do. In AK models, the relationship between capital and output can be written in the form Y = AK, where A is a constant and K is a composite of manufactured capital and disembodied technological knowledge thought of as a form of capital. Saving is directed to either manufactured capital accumulation or the increase of knowledge. The growth rate is permanently influenced by the savings rate; a higher 298

savings rate increases the economy s growth rate, not merely its equilibrium level of income (Perman R., Stern D.I., 2001). In Schumpterian growth models there is imperfect competition in the capital goods industry and firms invest in R&D in order to receive monopoly profits. Innovations appear stochastically and are embodied in new generations of capital or consumer goods. There are positive externalities to consumers or producers of final goods who benefit from innovation and to future researchers who benefit from past ideas. On the other hand, new innovations make old vintages of capital obsolete. Both capital accumulation and innovation can determine the long-run growth rate. However, if there are diminishing returns in the innovation sector as technology becomes more complex the economy could have a constant growth rate (Aghion P., Howitt P., 1998). 299 7. Sustainability Since the appearance of the report by the Brundtland Commission in 1987 the notion of sustainability or, preferably, sustainable development, has received much attention. Based on Brundtland s definition, sustainable production involves obtaining a sufficient yield at minimum cost of resources, i.e. of energy and raw materials. Because different communities of interests have different views on sustainable development, implementation is not unambiguous. However, in any approach, sustainable development requires a long-term strategy and outlining the strategy may be complicated because science and technology keep shifting the boundaries of human abilities to manipulate nature. However, nature itself does not shift its boundaries and, in view of this, sustainable development takes into account the constraints imposed by nature. It is, preeminently, thermodynamics that indicates the boundaries within which processes in the world around us can take place. 8. Sustainable Growth We can now put together the different concepts to formulate a view on sustainable growth. The resulting framework synthesizes insights from three important approaches. First, the biophysical laws reveal that ultimately a sustainable economy is in a stationary state with respect to physical dimensions (Daly s steady state). Second, insights from endogenous growth theory show that the endogenous accumulation of knowledge may still contribute to growth (i.e. increase the value of marketable goods) within such an economy. Third, neoclassical principles demonstrate effects of prices, taxes and other incentives on resource use as well as the direction and speed of the accumulation of knowledge. Resource use and other physical aspects of the economy can be influenced by taxes on polluting private factors of production, energy and material inputs, etc. However, it may be difficult to exactly predict tax levels that result in constant physical dimensions, which is required for sustainability. The resulting priced scarcity of natural resources stimulates private cleaning-up activities and the development of resource augmenting technology. New technologies that increase the average resource intensity of production are no longer profitable, so that technological progress will be biased in the direction that is necessary for sustainability. Imperfect patent protection, general knowledge spillovers, imitation, and the unintended nature of technology improvements that arise as a side-product of economic activity cause externalities in knowledge creation which may call for technology subsidies or public provision. Technological progress may be slow and costly so that growth is not always sustainable. Neither is sustainable growth, if feasible, necessarily optimal. If time preference is high, future

(environmental and economic) losses are easily compensated by high current (unsustainable) consumption levels. Society is then not willing to invest enough to guarantee non-declining consumption and environmental resources over time. Evidently, strong dependence on exhaustible resources constrains the feasibility of sustainable growth. However, since at least some level of production is feasible by relying solely on renewable resources, the sustainable production level at a certain moment in time, which depends on the backstop technology, is restricted, rather than the sustainable growth rate, which depends on the success and the willingness to invest in technological change that improves the efficiency of (renewable and exhaustible) resource use. 9. Conclusions Energy is important for growth because production is a function of capital, labor, and energy, not just the former two or just the latter as mainstream growth models or some biophysical production models taken literally would indicate. In the economics literature, one can find two opposing points of view: mainstream economists who believe that technological innovation will solve the degradation in quality of both energy and materials and that therefore growth can go on forever; and biophysical economists, who use the thermodynamic laws to argue that mainstream economists do not incorporate long-term sustainability in their models. If entropy production were included in all economic models, the efficiency of standard industrial processes would show quite different results. The real problem is that, in our relentless effort to speed things up, we increase the entropy production process tremendously. Although recycling will help a lot to slow down the depletion of the earth s stocks of materials, it will only partly diminish the entropy production process. So whenever we develop economic processes, we should also take into account the associated rate of entropy production compared to the natural entropy production. We have seen that for reversible processes, the increase in entropy is always less than for irreversible processes. The practical translation of this is that high-speed processes always accelerate the rate of entropy production in the world. In this view, the issue central to the continued relevance of economics in dealing with problems of ecological scarcity is not whether entropy is relevant to economics, but how to measure and respond to entropy constraints on macroeconomic scale and sustainability, and how to structure markets to take account of the common good in balancing between present and future welfare. Acceptance the existence of the limits of economic growth will help us reexamine the current process of economic growth. As a subsystem of the ecosystem, human economic growth cannot exceed the size which the ecosystem can support. Only by shifting our goals from persuading economic growth to improving the quality of economic growth can we truly achieve sustainable development. References 1. Aghion P., Howitt P., (1998), Endogenous Growth Theory. MIT Press. Cambridge, MA. 2. Aghion P., Howitt P., (2009), The Economics of Growth. MIT Press. Cambridge, MA. 3. Arrow K., (1962), The Economic Implications of Learning by Doing, Economic Inquiry, 28. 4. Ayres R.U., Kneese A.V., (1969) Production, consumption and externalities. American Economic Review 59: 282-97. 300

5. Berry, R. S., Heal G., Salamon P., (1970), On a Relation Between Economic & Thermodynamic Optima, Resources & Energy 1, October 1978 :125-127. 6. Boulding K.E., (1966), The economics of the coming spaceship Earth, in H. Jarrett (ed.), Environmental Quality in a Growing Economy, John Hopkins University Press, Baltimore. 7. Daly H. E., (1991) Steady State Economics. Island University Press, Washington, DC. 8. Faucheux S. (1994), Energy Analysis & Sustainable Development, in: Pethig, Rudiger(ed), Valuing the Environment: Methodological & Measurement Issues, Kluwer Academic Publishers, Dordrecht, Netherlands. 9. Georgescu-Roegen N. (1971) The Entropy Law and the Economic Process. Harvard University Press, Cambridge MA. 10. Georgescu-Roegen N. (1979) Energy and matter in mankind's technological circuit. Journal of Business Administration 10: 107-127. 11. Hicks J. R., (1932), The Theory of Wages. Macmillan. London. 12. Kneese, A.V., R.U. Ayres, D Arge R.C. 1970, Economics and the Environment. A Material Balance Approach, Resources for the Future, The Johns Hopkins Press, Baltimore. 13. Perman R., Stern D.I., (2001), Sustainable development, growth theory, environmental Kuznets curves and discounting. Encyclopedia of Life Support Systems. UNESCO. 14. Rifkin, J. (1989) Entropy: Into the Greenhouse World. Bantam Books. New York, USA. 15. Ruth M., (1993), Integrating Economics, Ecology, and Thermodynamics. Kluwer Academic. Dordecht. 16. Ruth M., (1995), Information, order and knowledge in economic and ecological systems: implications for material and energy use. Ecological Economics 13: 99-114. 17. Solow R. M., (1956) A contribution to the theory of economic growth. Quarterly Journal of Economics, 70: 65-94. 18. Young J.T., (1991), Is the Entropy Law Relevant to the Economics of Natural Resource Scarcity? Journal of Environmental Economics and Management 21. 301