The perpetually growing economy is generally regarded as a viable and desirable societal objective [1–4]. Whilst ‘infinite growth’ may not be the words used to characterize and exhort a perpetually growing economy, they are nonetheless an accurate characterization of the objective. The words in current fashion for defending the viability of a perpetually growing economy are phrases such as ‘green growth’, ‘dematerialization’, and ‘decoupling’ [5–9]. The decades old question ‘Is economic growth environmentally sustainable?’ remains contested despite its apparent simplicity. The Limits to Growth [10] was a seminal work that warned of the consequences of exponential growth with finite resources. The World3 models underpinning the Limits to Growth analysis were validated using actual data after twenty and thirty years [11,12]. A further independent evaluation of the projections of the World3 models showed that our actual trajectory since 1972 has closely matched the ‘Business as Usual’ scenario [13]. Increasing recognition of the causes and consequences of climate change have generated a great deal of doubt regarding the feasibility of simultaneously pursing economic growth and preventing and/or mitigating climate change [14–18]. Contemporary work in this broad area of assessing anthropogenic impact on the planet suggests that several ‘Planetary Boundaries’ have been crossed [19].

The question as to whether human society can decouple economic growth–defined as growth in Gross Domestic Product (GDP)–from environmental impacts has not been settled. The decoupling debate itself is polarized with a preponderance of neo-classical economists on one side (decoupling is viable) and ecological economists on the other (decoupling is not viable) [20]. The divide over the compatibility of economic growth and environmental limits extends into the general public [2] with substantial polarization in ideas of decoupling, dematerialization, and limits to growth.

Settling the debate has far reaching policy implications. Decoupling is increasingly being described in popular press as a viable policy objective [21,22]. Decoupling has been incorporated into international indicators of sustainable development [23] and policy objectives such as the United Nations’ ‘Sustainable Development Goals’ [24]. If decoupling is possible, then these policies are valid sustainable goals; however, if decoupling is shown to be nonviable then society will need to shift away from the current ‘infinite growth’ model.

Decoupling is defined as either ‘relative’ (aka ‘weak’) or ‘absolute’ (aka ‘strong’). Relative decoupling refers to higher rates of economic growth than rates of growth in material and energy consumption and environmental impact. As a result, relative decoupling implies a gain in efficiency rather than removal of the link between impact and GDP. Recent trends (1990 to 2012) for GDP [25], material use [26] and energy use [27] in different countries and regions exhibit different behavior (Fig 1). In China, relative decoupling has occurred as GDP (market prices, in current US$) increased by a factor of more than 20 over the 22-year period, while energy use rose by a factor of slightly more than four and material use by almost five. Germany, meanwhile, exhibited slower GDP growth than China, but at the same time reduced energy use by 10% and total material use by 40%. The OECD follows a similar story to Germany, albeit with flat rather than falling energy and material consumption. Although Germany and the OECD give hope that absolute decoupling may be achievable, at the global level we see only relative decoupling with energy and material use increasing by 54% and 66% over the 22 years, respectively.

Similar evidence to that in Fig 1, showing apparent decoupling of GDP from specific resources, has been shown throughout much of the OECD [28]. However, there are several limitations to the inference of decoupling from national or regional data. There are three distinct mechanisms by which the illusion of decoupling may be presented as a reality when in fact it is not actually taking place at all: 1) substitution of one resource for another; 2) the financialization of one or more components of GDP that involves increasing monetary flows without a concomitant rise in material and/or energy throughput, and 3) the exporting of environmental impact to another nation or region of the world (i.e. the separation of production and consumption). These illusory forms of decoupling are described with respect to energy by our colleague [29].

An additional mechanism of decoupling is associated with growing inequality of income and wealth, which can allow GDP to grow overall while the majority of workers do not see a real gain in income [30]. This growth in inequality can manifest as higher GDP without a proportional increase in material and energy flow (i.e. relative decoupling) when a wealthy minority of the population derives the largest fraction of GDP growth but does not necessarily increase their level of consumption with as much demand for energy and materials [31]. In such cases, at the aggregate level decoupling would be observed, but it is doubtful that such unequal sharing of growth in GDP represents an improvement in wellbeing.

At the World aggregate level, Fig 1 shows relative decoupling with a growing gap between GDP and resource consumption. In the context of reaching planetary boundaries and global environmental limits, however, relative decoupling will be insufficient to maintain a GDP growth-oriented human civilization. The only way to achieve truly sustainable growth would be via permanent absolute decoupling. Absolute decoupling theoretically occurs when environmental impacts are reduced while economic growth continues. While relative decoupling has been observed in multiple countries, absolute decoupling remains elusive [32–34]. According to one study [35] no country has achieved absolute decoupling during the past 50 years. Another study [36] reports that population growth and increases in affluence are overwhelming efficiency improvements at the global scale. They find no evidence for absolute reductions in environmental impacts, and little evidence to date even for significant relative decoupling.

It should be noted that technological advances can lead to absolute decoupling for specific types of impact [37]. It is possible, for instance, to substitute a polluting activity with a non-polluting activity, and notable examples have included the removal of tetraethyl lead from automotive fuel and CFCs from refrigerants and propellants. It is also possible to envisage a scenario in which GDP growth is decoupled from the use of fossil fuels and related CO₂ emissions by switching to 100% renewable energy, but this is not the same as decoupling GDP growth from energy use. In the context of this study, we are primarily interested in fundamental resources (matter and energy) as the foundations of economic activity.

In the current paper, we show that decoupling scenarios can be interpreted using an easily understood model of economic growth and environmental impact. The simple model was calibrated against published data derived from sophisticated predictive studies of decoupling, and used to develop a long-term prognosis of environmental impact under continued GDP growth. The results are then used to draw conclusions about the long-term viability of GDP growth as a societal goal.

We use a simple mathematical model to develop insights into decoupling behavior. We start with the IPAT equation [38–40], which is a basic formulation of environmental impact I as a function of economic activity: I=PAT (1) where P is population, A is affluence (GDP per capita in $/person/year) and T, as originally formulated, represents “technology”. More precisely, however, T should be viewed as the economic intensity of a particular resource or pollutant, and therefore both T and I will have different units depending on which resource or pollutant is considered. For energy, appropriate units for T may be joules per $ of GDP; for material use T may be kilograms per $ of GDP. The terms T and I can–and should–thus be evaluated separately, with appropriate units, for individual resources such as farming land, fresh water and energy resources, and/or pollutant emissions such as sulphur dioxide, lead, or carbon dioxide.

To test the hypothesis that continual GDP growth can be sustained, we only require a scenario in which GDP increases exponentially. The economy (as GDP) can thus be simplified to G = PA, leading to I_j = GT_j where I_j and T_j are the impact and economic intensity, respectively, of resource or pollutant j. A simple case is one in which both population (P) and affluence (A) are increasing exponentially, but other combinations (e.g. stationary population with rising affluence) could achieve the same result of rising GDP. There are, of course, scenarios that could lead to falling GDP (e.g. declining population with constant affluence, or both falling) but our investigation is directed explicitly at testing the sustainability of continual economic growth as a societal goal. As such, we assume G at time t is given by: G(t)=G0ekt (2) where G₀ is the initial GDP at time t = 0, and k is the growth rate per year. Hence, impact (for resource or pollutant j) over time is given as: Ij(t)=G0ektTj (3)

If there is no technological change to reduce a particular impact (i.e. T_j = constant; no decoupling), the use of resources or pollutant emissions will rise exponentially, in keeping with GDP growth. For absolute decoupling from resource or pollutant j, T_j must decrease exponentially at the same rate as GDP growth such that I_j remains constant in time, i.e.: Tj=Tj,0e−kt (4) where T_j,0 is the initial level of economic intensity of resource or pollutant j.

Put simply, absolute decoupling from resource or pollutant j requires T_j to decrease by at least the same annual percentage as the economy is growing. For example, if k = 0.03 (steady 3% p.a. economic growth), T_j must reduce 20-fold over 100 years, 100-fold over 150 years, and 500-fold over 200 years, and continue this trend of exponential reduction as long as the economy is growing. If T_j were to decrease at a faster rate than GDP growth, the impact I_j would decline.

For non-substitutable resources such as land, water, raw materials and energy, we argue that whilst efficiency gains may be possible, there are minimum requirements for these resources that are ultimately governed by physical realities: for instance the photosynthetic limit to plant productivity and maximum trophic conversion efficiencies for animal production govern the minimum land required for agricultural output; physiological limits to crop water use efficiency govern minimum agricultural water use, and the upper limits to energy and material efficiencies govern minimum resource throughput required for economic production. Therefore a more appropriate formulation of Eq (4) is to allow T_j to decrease to an ultimate value, T_ult ≥ 0, as follows: Tj=Tj,ult+(Tj,0−Tj,ult)e−rjt (5) where T_j,ult is the ultimate resource use intensity, and r_j is the rate of exponential decline, for resource or pollutant j. In cases where decoupling is occurring, T_j,ult < T_j,0. However, cases where resource use intensity is increasing towards an upper limit can be accommodated with T_j,ult > T_j,0.

The nature of decoupling behavior for different types of resource can be readily predicted from the relationships between r_j, k, T_j,ult and T_j,0 as summarized in Table 1. It is only those resources or pollutants for which r_j > k and T_j,ult < T_j,0 (i.e. efficiency gains are possible and can be achieved faster than the economy is growing) that a period of decoupling can be expected.

A recent predictive study [41] concluded that Australia could–through adoption of specific policies–“achieve strong economic growth to 2050 … in scenarios where environmental pressures fall or are stable” (this study is referred to as “H-D” hereafter). That paper summarized the results of a significant project, the 2015 Australian National Outlook [42] published by the Commonwealth Science and Industrial Research Organisation (CSIRO), and represents a high-profile, contemporary study in decoupling. In all of their modelled scenarios, both population and gross national income per capita increased. In their strong abatement scenario (called “Stretch”), various forms of decoupling behavior were predicted. We will use the Stretch scenario from H-D as a case study in decoupling, and will use Eq (5) to further explore the behavior of energy and material use and implications for longer-term impact. The data used in H-D’s historical and projected scenarios are all available in their Supplementary Information files that accompanied their original publication. Likewise, the data and model results for the following analysis can all be found in the S1 File accompanying this paper.

We begin by calibrating the decline rate r_j from Eq (5) against H-D’s historical energy use (j = 1) and material extraction (j = 2). The term T_j for each resource is found by dividing GDP (G) by resource use (I_j) on a yearly timestep. For energy, units are MJ per thousand $AUD (2010). T_1,0 = 3.783, equal to the value of T₁ in the year 1980. The ultimate resource use intensity T_1,ult is unknown, and depends on future technological advances. To account for this uncertainty, three scenarios are adopted: high decoupling (T_1,ult = 0.25 T₁(2010) = 0.704), medium decoupling (T_ult = 0.5T₁(2010) = 1.408) and low decoupling (T_ult = 0.75 T₁(2010) = 2.113). Under each of the three T_1,ult scenarios, Eq (5) is used to predict T₁, and is calibrated by varying the single unknown parameter (the decline rate, r₁) to give the best fit between our T₁ (predicted) and T₁ (historical) derived from H-D’s data. The calibration was performed using the free statistical package “R” (https://www.r-project.org) with the in-built Non-Linear Least Squares function.

All three scenarios reproduce the observed downward trend in T₁. Calibrated declines rates with standard error (in brackets) were 1.24% (± 0.05%), 1.70% (± 0.07%) and 2.66% (± 0.13%) for high, medium and low respectively. The result is a simple calibrated model that can be used to project forward based on recent trends, for the purpose of comparing against the more complex modelling scenarios from H-D. The results are shown in Fig 2(A), with the modelled T₁ values projected to 2050. The decoupling predicted by H-D is also shown (taking T₁ as their predicted impact divided by their predicted GDP). Clearly H-D predict stronger decoupling than our strongest case. In terms of the simplified IPAT model, even for our most optimistic T_1,ult scenario, this implies a change to a greater decline rate than can be obtained merely by calibrating against historical trends.