Natural Capital and the Theory

of Economic Growth








Richard W. England

Center for Business and Economic Research

University of New Hampshire

Durham, NH  03824-3593, U.S.A.



July 1998







                This paper explores the theoretical concept of “natural capital” and proposes that it be incorporated into the modern theory of economic growth.  Several implications of such a theoretical revision for economic research are discussed.


            During the past half century, theorizing about economic growth has forced economists to reconsider and revise the capital concept a number of times.  This paper explores the analytical relationship between capital accumulation and economic growth, on the one hand, and the natural world, on the other.  Section I briefly surveys modern growth theory with an emphasis on whether or not the economy is seen as facing biophysical “limits to growth.”  The second section argues that analysis of the role that “natural capital” plays in the production process must occur before one can assess the prospects for economic growth.  Section III inserts natural capital into a simple growth model and explores whether depletion of natural capital, in combination with complementarity in production of natural and social forms of capital, could retard the growth process.  The concluding section proposes several areas for future research by macroeconomists and other scholars.



            The modern theory of economic growth was launched by Domar [1946] and Harrod [1939] half a century ago.  Both authors observed that net investment spending boosts aggregate income immediately while simultaneously expanding potential output of future periods.  Their elementary growth models also suggested that one should expect the capitalist growth process to be highly unstable and marked by periodic crises.

            In his neoclassical response to Domar and Harrod, Solow [1956] argued that opportunities to substitute capital for labor in the production process might permit steady-state growth in the aggregate, instead of periodic crisis of the macroeconomy.  Furthermore, Solow’s growth model envisioned the possibility of rising material living standards fueled by technological progress.

            One of the striking features of these early modern growth models is their disregard for the natural foundation of production.  Capital goods and human labor combine to produce commodity output, but no land is required as a site, no materials are needed from which to form commodities, and no energy is required to drive the process of commodity production and exchange.  As Solow himself [1956, p. 67] remarked, “[T]he production function is homogeneous of first degree.  This amounts to assuming¼ no scarce nonaugmentable resource like land.”

            By the 1970s, the debate over the prospects for economic growth shifted terrain.  Meadows et al. [1972] did not ask whether the historical process of economic growth was stable or not.  Rather, these authors posited the existence of biophysical “limits to growth” which would eventually bring economic growth to an end.  I believe it is fair to say that most macroeconomists greeted this serious claim with disdain and derision.[1] 

            In reaction to the “limits to growth” thesis, the emergence of the environmental movement, and global energy price shocks, modern growth theorists did begin to incorporate natural resources and pollution into their models during the 70s.  Stiglitz [1974], for example, proposed an aggregate production function with labor, capital goods and natural resources as substitutes in production.  His model implied that worsening natural resource scarcity could be offset by technical progress:  “With technical change, at any positive rate, we can easily find paths along which aggregate output does not decline¼  To sustain a constant level of per capita consumption requires a more stringent condition on the rate of technical change.”  [pp. 130-1]  Hence, insurmountable limits to growth seemed to be far from inevitable.

            By the 1980s, technological optimism had come to dominate macroeconomic theorizing about the links between economic growth and the natural world.  Baumol [1986], for example, claimed that the economic inventories of natural resources could increase monotonically and perpetually even if their physical stocks declined incessantly.  That is, resources whose physical quantities are finite and declining “may nevertheless be increased by technological advance in terms of their prospective economic contribution, and may do so for the indefinite future.”  [p. 178]

            Reassuring theoretical analyses such as those of Stiglitz [1974] and Baumol [1986] have apparently left their imprint on the growth theory revival of the past decade.  Aghion and Howitt [1998] do acknowledge that pollution and natural resources are issues worth considering.  However, their Schumpeterian model implies that accumulation of “intellectual capital” can deflect biophysical constraints on economic activity, thereby permitting growth into the indefinite future.  Barro and Sala-i-Martin [1995], on the other hand, do not even mention land, energy, raw materials or pollution in their influential survey of contemporary growth models.  For them, produced capital goods and human skills constitute the entire aggregate stock of capital.  Macroeconomic activity apparently draws upon boundless sources of natural resources and bottomless sinks for waste products, thereby eliminating the need for an explicit discussion of economic growth within a natural world.

            Although the notion of biophysical limits to growth has not taken root in modern macroeconomics, it has recently enjoyed a resurgence of popularity among those biologists, economists and other scholars who identify with "ecological economics."  Daly [1996] has argued that biophysical and ethical factors will eventually require a "steady-state economy" with constant populations of humans and their artifacts and a restrained physical throughput of materials and energy to reproduce those populations.[2]

            Assessing Daly's claim is difficult, however, in part because his thesis of an eventual stationary state has not been derived from a conventional growth model.  In the following sections, I will generalize the capital concept to include "natural capital" and then insert that broader notion of capital into an elementary model of economic growth.  After that exercise, some tentative conclusions about the prospects for economic growth in a finite world will be drawn.

                                      II.  NATURAL CAPITAL AND PRODUCTION

            Theorizing about the linkages between economic production and the natural world requires us to formulate a concept which is broader and richer than "land."  That classical notion has heavy agricultural connotations and tends to focus our attention on spatial location and area, differential soil fertility, etc.

            Ecological economists have recently proposed that we recognize explicitly the essential role of "natural capital" in commodity production.  Daly [1994, p. 181] points to climate and mineral deposits.  Ayres [1996, p. 241], in turn, refers to aquifers and stratospheric ozone as specific forms of natural capital.

            Vivid examples such as these, although highly instructive, can guide us only so far along the path of analysis.  We also need a rigorous formal definition of what we mean by "natural capital."  Drawing upon earlier work by Boulding [1978, ch. IV] and Georgescu-Roegen [1972, ch. IX], I have offered such a definition in another recent paper [England, 1998].

            In his excellent discussion of production theory, Georgescu-Roegen distinguished between two very different elements of the production process:  "fund elements, which represent the agents of the process, and the flow elements, which are used or acted upon by the agents" [p. 230].  That is, there are the active subjects of production which physically shape and transport, chemically alter, and in various other ways transform materials and energy.  These fund elements of production cannot play their transformative role, however, without access to the passive objects of production, input flows of low-entropy (high-quality) materials and energy.  During the course of production, fund elements maintain their physical identify (at least approximately) while input flows are typically transformed into output flows of qualitatively different character.  How do stocks enter the picture?  According to Roegen [1972, pp. 223-7], a flow is typically a stock spread over some time interval.  E.g., one can measure the cumulative stock of fossil fuels extracted from the Earth's crust since the Industrial Revolution.

            Georgescu-Roegen's contribution to production theory, grounded as it was in classical thermodynamics, is not a complete foundation for conceptualizing natural capital.  Utilizing the ecological perspective of Boulding [1978], one can argue that the transformative activity of funds should be theorized at the scale of populations interacting within ecosystems, not at the scale of individual agents.[3]

            Putting these methodological dicta to work, let us first identify the fund elements of the global system and then formally define the concept of natural capital.  The fund elements include:


·           (B1, ..., Bm),     the populations of nonproduced organisms, each population representing a particular biological species;

·           (K1, ..., Kn)      the populations of produced means of production, whether biological or mechanical, commonly described as "capital goods";[4]

·           L,                     the population of human producers and their dependents; and

·          S,                     the earth’s surface area, which serves as a site for other funds’ activity and as a solar energy collector.


            The transformative activity of these funds requires input flows of energy and materials in appropriate amounts and at appropriate moments of time.  As Georgescu-Roegen [1972, p. 303] insisted, there are two and only two sources of these input flows: (i) a constant annual flow of solar radiation beyond our control, and (ii) finite terrestrial stocks of minerals which we can decumulate into input flows at highly variable rates.  Let us denote the solar energy flow by φ and the nonliving stocks from which input flows are extracted and into which waste products get discharged as Mk, k = 1, ..., p.

            What, then, are the components of natural capital?  Our discussion suggests an amazingly diverse list of elements:


·          the earth’s nondepreciating surface (S);

·          the solar flux (φ), or perhaps its capitalized value;

·          the set of nonproduced populations (B1, ..., Bm), organized into various ecosystems;[5]

·          the set of material stocks in the earth’s crust and atmosphere (M1, ..., Mp), which yield raw materials and receive waste products.


Without this natural ensemble of assets, humans (L) and their produced servants (K1, ..., Kn) would be unable to function, develop and reproduce.  Thus, natural capital, denoted hereafter by N, yields a variety of services and materials essential to the human economy.

            Because natural capital is such a new theoretical concept, its empirical measurement has barely begun.  Preliminary measures suggest, however, that the magnitude of natural capital is huge and that its extent varies greatly among the world’s regions.  Dixon and Hamilton [1996], for example, estimate that the value of natural capital in West Africa and the Middle East exceeds the value of produced assets.  Costanza et al. [1997] estimate the annual service flow from 17 categories of terrestrial and marine ecosystems.  Their mean estimate equals $33 trillion per year, which suggests a global capital value greater than $660 trillion at a 5 percent discount rate.

            Two momentous hypotheses about the natural capital stock have recently entered the literature.  I shall call them the depletion hypothesis and the complementarity hypothesis.  The first claims that the value of the natural capital stock has declined significantly during the past century or more because of humanity’s economic practices.  Because we do not have time-series estimates for N, this hypothesis cannot be empirically confirmed or denied, at least not in a rigorous fashion.  However, we do have physical measures of fossil fuel consumption, soil erosion, deforestation and loss of wetlands, thinning of stratospheric ozone, groundwater pollution, etc. which strongly suggest natural capital depletion.[6]

            The second, and perhaps more controversial, hypothesis about natural capital is that it complements -- and cannot substitute for -- humans and their produced capital goods as commodities are produced.  Once again, available empirical evidence can neither confirm nor dismiss this hypothesis.  Thompson and Taylor [1995], for instance, report that more than 50 studies of capital-energy substitutability since 1973 have resulted in estimated elasticities of substitution which are “highly variable between sectors and countries, and across time.”  Some econometric studies have even employed production function specifications which preclude complementarity among factor inputs, a priori.

            These comments about the messiness of the existing econometric literature miss the main point, however.  Even if there is convincing empirical evidence that coal can substitute for petroleum, that steel can substitute for aluminum, or even that telecommunications can substitute for transport services, these substitution measures cannot demonstrate that natural capital, as defined here, is a substitute for humans and their produced artifacts.  Technical opportunities to substitute among specific forms of natural capital do not imply that natural capital in the broader sense can be replaced by humans and their constructions.[7]

            There are two reasons to accept the complementarity hypothesis, at least provisionally.  The first is that human labor and produced capital goods are transformers of energy and materials flows into finished products and that the stock of natural capital is the source of these essential input flows.  Funds can substitute for one another as transformative agents, but each fund requires complementary input flows in order to perform its assigned tasks.[8]

            A second argument for complementarity is rooted in ecological research.  Recall that ecosystems provide a wide array of services to humanity [de Groot, 1994].  If we denote these ecosystem services as then .  That is, the ecological interaction of many nonproduced funds generates a rich ensemble of services enjoyed by humanity.  If every one of these services could also be provided by a specialized human artifact, then society could perhaps destroy all ecosystems and accumulate the appropriate mix of produced capital goods needed to replace the lost ecosystem services.  Many ecologists doubt that this degree of substitution is possible.  If they are correct, and I believe they are, preservation of ecosystems is essential if humans and their artifacts are to remain productive.

            In sum, existing measures of the aggregate capital stock neglect the productive contribution of nonproduced assets provided by nature.  Hence, the conception and measurement of capital should be broadened to include these natural assets.  As we shall see, this expanded view of capital is especially momentous if the natural capital depletion and complementarity theses are correct.


                                         III.  NATURAL CAPITAL AND GROWTH

            Let us proceed by inserting natural capital into an elementary growth model.  Suppose that humans and their produced capital goods substitute readily for one another.  Then one can aggregate the human population (L) and the value of human artifacts (K) to obtain the stock of human-made, or social, capital (H):




If one accepts the hypothesis that human-made and natural capital are complementary in production, then, in general,




where Y is aggregate output of commodities, N is the value of natural capital available for human enjoyment and use, and both coefficients are positive.

            During the past 10,000 years, humanity has invented both agriculture and also industry.  These developments have been linked to growth of human population, accumulation of produced capital goods, and labor-saving innovation.  All three of those historic trends have contributed to growth of the stock of human-made capital .  Until recent times, the extent of human settlement and economic development was modest so that H-capital was relatively scarce compared to N-capital.  That is,




It follows that, during the agro-industrial period of the distant and recent past, the aggregate production function assumed a historically-specific form:[9]




            Assume that society accumulates a constant proportion (s) of its aggregate income as additional produced means of production.  Assume, also, that human population grows at a constant percentage rate (n) and that labor-saving innovation proceeds at a constant rate .  It follows that aggregate output and the H-stock will grow at the common rate:





            If population growth and technical innovation proceed sufficiently rapidly, that is, if , then there exists a steady-state growth path along which .  Along this path, exponential growth of aggregate income (Y) and per capita income (y) occurs:







results which will be familiar to any student of modern growth theory.

            Often missed by contemporary growth theorists, however, are the detrimental effects of economic activity and exponential growth on the N-stock.  Suppose that




where M is the terrestrial stock of low-entropy energy and materials available for human use.  Because of the thermodynamic dissipation of energy (and perhaps materials as well) which accompanies economic activity, we can expect that




            On the ecological front, we know that undomesticated species have relatively rigid space, or habitat, requirements:



with population sizes varying directly with the extent of available habitat (SB).  Because human settlements tend to displace ecosystem habitats,




where d is the density of human settlement (people/km2).  Hence habitat for humanity competes with habitat for ecosystems.[10]

            Economic growth and development during the agro-industrial period has tended, therefore, to deplete the stock of natural capital for several reasons.  Exponential growth of human population tends to reduce the land area available to ecosystems at an accelerating rate, thereby threatening the availability of valuable ecosystem services.  Industrialization and urbanization relieve this spatial competition between human settlements and ecosystems for land but tend to intensify the rate at which earthly sources of low-entropy energy and materials are dissipated.  Either way, .

            To the extent that this theoretical tale is accurate, its implications are clear.  If and , then there must arrive a moment when natural capital is no longer relatively abundant and human-made capital is no longer relatively scarce.  (See Figure I.)  At that moment, aggregate output is no longer constrained by the populations of humans and their artifacts and by the productivity of human effort.  Rather, the scale of economic activity is 

constrained by the remaining stock of natural capital and by its productivity.  At that moment, a new era of history has begun.[11]

            Once this new era has arrived, economic growth can continue -- but only if economic institutions and practices are dramatically reformed and, even then, perhaps not indefinitely.  Because (H/N) > (C/A), the aggregate production relation has become




It follows trivially that aggregate output will continue to grow only if .  This inequality can be satisfied only if technological innovation shifts from a labor-saving to a N-saving direction and if preservation of the remaining stock of natural capital becomes a social priority.  Continued growth of per capita income also tends to occur if natural capital is preserved and if technological change favors growth of its productivity.  Reducing the growth rate of human population is also imperative, in part to protect ecosystems from human settlement, but also because if and only if .

            This inequality would seem to provide a simple recipe for rising affluence even if natural capital has become relatively scarce: merely focus enough human ingenuity on preserving and enhancing the productivity of natural capital.  That conclusion would be too hasty, however.[12]  As Ayres and Miller [1980] have pointed out, the relationship between accumulation of technological knowledge and growth of capital productivity is far from obvious.

            These authors argue that knowledge is the ability to copy or reproduce tangible or intangible `objects' given the availability of appropriate energy and materials [p. 358].  What if, however, certain physical principles limit our capacity to intelligently transform energy and materials into commodities?  As Ayres and Miller [1980, pp. 359-60] put the matter,


                        "[T]here is a definite lower limit to the amount of electricity required to produce a horsepower of mechanical work... [and] to the amount of electricity required to produce a given amount of illumination.  And, of course, there is a lower limit to the amount of available work derived from fossil fuels...  There are upper limits to the strength of materials...  Velocity cannot exceed the speed of light.  And so on."[13]


            These arguments imply that the productivity of natural capital (C) might increase as the stock of appropriate technological knowledge (T) rose, but that diminishing returns to additional technological knowledge might eventually set in.  In that eventuality, even though and constant.  After some effort, then, we have identified the conditions which would result in Daly's zero-growth economy: (i) relative scarcity of natural capital, (ii) complementarity of human-made and natural capital in production, and (iii) exhaustion of opportunities to raise N-productivity through accumulation of technical knowledge.  This result is explored briefly in the concluding section.


                                                     IV.  A RESEARCH AGENDA

            For half a century, modern growth theorists have tried to identify the empirical determinants of economic growth and the theoretical conditions under which steady-state growth can proceed.  For a quarter century, other scholars have argued that there are biophysical limits to growth and that exponential growth of aggregate output cannot, therefore, continue indefinitely.  Those starkly opposing points of view have not led to a sustained and productive dialogue or debate within the scholarly community, a stalemate which has impeded the development of macroeconomic and environmental policy.

            The ultimate purpose of this paper is to propose a research agenda which might help to resolve this intellectual impasse.  The preceding sections suggest the following set of research questions:


·           Can we develop a theoretically rigorous accounting framework with which to gather measures of the natural capital stock?

·           Can we then say whether or not depletion of natural capital is occurring on a regional or global scale?

·           Is there compelling evidence that natural capital is complementary in production with humans and their produced means of production?

·           Can the recent decline in the growth rate of total factor productivity be explained, at least in part, by the emergence of natural capital scarcity?[14]


Questions such as these are, in my opinion, both challenging and also essential to ask.





Aghion, Philippe, and Peter Howitt, Endogenous Growth Theory (Cambridge, MA: MIT Press, 1998).


Ayres, Robert, "Cowboys, Cornucopians and Long-Run Sustainability," Ecological Economics, VIII (1993), 189-207.


__________, "Limits to the Growth Paradigm," Ecological Economics, XIX (1996), 117-134.


__________ and Steven Miller, "The Role of Technological Change," Journal of Environmental Economics and Management, VII (1980), 353-371.


Barro, Robert, and Xavier Sala-i-Martin, Economic Growth (New York: McGraw-Hill, 1995).


Baumol, William, "On the Possibility of Continuing Expansion of Finite Resources," Kyklos, XXXIX (1986), 167-179.


Boulding, Kenneth, Ecodynamics (Beverly Hills, CA: Sage, 1978).


Costanza, Robert, Ralph d'Arge, et al., "The Value of the World's Ecosystem Services and Natural Capital," Nature, 387 (1997), 253-260.


Daly, Herman, "Operationalizing Sustainable Development by Investing in Natural Capital," in AnnMari Jansson et al., eds.  Investing in Natural Capital (Washington, DC: Island Press, 1994).


__________, Beyond Growth: The Economics of Sustainable Development (Boston: Beacon Press, 1996).


deGroot, R.S., "Environmental Functions and the Economic Value of Ecosystems," in Annmari Jansson et al., eds, Investing in Natural Capital (Washington, DC: Island Press, 1994).


Dixon, John, and Kirk Hamilton, "Expanding the Measure of Wealth," Finance & Development, (1996), 15-18.


Domar, Evsey, "Capital Expansion, Rate of Growth, and Employment," Econometrica, XIV (1946), 137-147.


England, Richard, "Should We Pursue Measurement of the Natural Capital Stock?"  Ecological Economics, forthcoming in 1998.


Faber, Malte, R. Manstetten, and J.L.R. Proops, "On the Conceptual Foundations of Ecological Economics:  A Teleological Approach," Ecological Economics, XII (1995), 41-54.


Georgescu-Roegen, Nicholas, The Entropy Law and the Economic Process (Cambridge, MA:  Harvard University Press, 1972).


Goudie, Andrew, The Human Impact on the Natural Environment (Oxford: Blackwell, 1993).


Grossman, Gene, and Elhanan Helpman, "Endogenous Innovation in the Theory of Economic Growth," Journal of Economic Perspectives, VIII (1994), 23-44.


Harberger, Arnold, "A Vision of the Growth Process," American Economic Review, LXXXVIII (1998),



Harrod, Roy, "An Essay in Dynamic Theory," Economic Journal, 49 (1939), 14-33.


Khalil, Elias, "Production and Environmental Resources:  A Prelude to an Evolutionary Framework," Southern Economic Journal, LXIII (1997), 929-946.


Meadows, Donella, Dennis Meadows, Jorgen Randers, and William Behrens III, The Limits to Growth (New York: Universe Books, 1972).


Perrings, Charles, Economy and Environment (Cambridge, UK: Cambridge University Press, 1987).


Solow, Robert, "A Contribution to the Theory of Economic Growth," Quarterly Journal of Economics, LXX, 65-94.


Spreng, Daniel, "Possibilities for Substitution between Energy, Time and Information," Energy Policy,   (1993), 13-23.


Stiglitz, Joseph, "Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths," Review of Economic Studies,    (1974), 123-137.


Thompson, Peter, and Timothy Taylor, "The Capital-Energy Substitutability Debate: A New Look," Review of Economics and Statistics, LXXVII (1995), 565-569.


Weinberg, Alvin, and H.E. Goeller, "The Age of Sustitutability," American Economic Review, LXVIII (1978), 1-2.


Wright, Gavin, "The Origins of American Industrial Success, 1879-1940," American Economic Review, LXXX (1990), 651-668.




     [1]There are, no doubt, a number of reasons for this hostile response by the mainstream of the economics profession.  One is that Meadows et al. used computer simulation as a research method, not the differential equation and multiple regression techniques popular among economic researchers at that time.  People who speak different languages often find it difficult to communicate.

     [2]Compare the more recent analysis by Khalil [1997].

     [3]As Faber, Manstetten and Proops [1995, pp. 44-8] have recently noted, "[O]rganisms... interact with each other as part of their mutual maintenance...  We term these interactions as services, and the organisms as funds...  [A]ll organisms are funds, necessarily rendering services to other organisms."

     [4]Whether another population is "produced" or not depends, as Perrings [1987, ch. VI] has implied, on the degree of control that humans exercise over another fund's activity.  Produced capital goods are the mechanical or biological slaves of humanity.  It is commonly assumed that humans and their slaves occupy "developed" land (SH) whereas nonproduced species live on "undeveloped" land (SB), a point to which I will return.

     [5]For a lengthy list of the free services provided by ecosystems to the human economy, see de Groot [1994, p. 154].

     [6]For evidence that natural capital depletion has occurred, see Goudie [1993] and Ayres [1993].  Wright [1990] finds evidence of rising natural-resource intensity of U.S. manufacturing earlier in this century.

     [7]This logical error can be found in the influential essay by Weinberg and Goeller [1976].

     [8]As Daly [1994, p. 26] has remarked, sawmills and forests, oil refineries and petroleum reserves, and irrigated farmland and aquifers complement one another in production.  Oil refineries cannot substitute for forests in lumber production.  See, in addition, Ayres [1996, p. 241].

     [9]Note that the Y = AK production relation favored by endogenous growth theorists is therefore a special case and not necessarily applicable to all periods of human history, past and future.

     [10]One might be tempted to propose dense human settlement to save undeveloped land for ecosystems, since those ecosystems provide valuable services to humanity.  However, since urbanized regions rely relatively heavily on fossil fuels and not solar energy to power their activities, that proposal would accelerate M-depletion.  That is, d and m vary directly.

     [11]One might question my assumptions that for thousands of years.  Hasn't the relative scarcity of H favored innovations increasing its productivity ?  Perhaps, but that path of technological development would tend to lower (C/A), thereby hastening the arrival of natural capital scarcity.  Innovation, it would seem, does not always eliminate social and economic problems.

     [12]Grossman and Helpman [1994, p. 42] are appropriately cautious when they maintain that we face "the difficult question of how best to promote rapid, sustainable economic growth in the face of... [depletion of] natural resources.  Improvements in technology are the best chance we have to overcome the apparent `limits to growth.'"  To their credit, the authors do not assume success.

     [13]This quote invites an exploration of the suggestion by Spreng [1993] that energy, time and information are the ultimate substitutes.

     [14]Harberger [1998, pp. 20-21] has recently observed, "The pervasiveness of declining TFP is perhaps the most profound conclusion... that I have reported...  I find it hard to think of more fertile ground for future research..."