2.1. Key Definitions and Concepts
We first establish the link between, on the one hand, the concepts of planetary boundaries and safe operating space in the Earth system science literature, and on the other, the concepts of weak and strong sustainability in economics.
The key rationale for establishing planetary boundaries on anthropogenic processes is to avoid “tipping points” or “thresholds” that could lead to irrevocable changes in this system, with potentially catastrophic impacts for humanity. As noted in the Introduction, scientists have identified nine processes resulting from human activity that should be subject to planetary boundaries [
1,
2,
3,
4,
5,
6]:
Climate change
Loss of biosphere integrity (e.g., marine and terrestrial biodiversity loss)
Land-system change
Freshwater use
Biochemical flows (e.g., effluents that interfere with nitrogen and phosphorous cycles)
Ocean acidification
Atmospheric aerosol loading
Stratospheric ozone depletion
Novel entities (e.g., new substances and modified organisms that have undesirable environmental impacts).
If unchecked, these processes could place human population growth and economic activity on an unsustainable trajectory that crosses critical thresholds and de-stabilizes the global environment. Establishing planetary boundaries therefore “aims to help guide human societies away from such a trajectory by defining a ‘safe operating space’ in which we can continue to develop and thrive” [
4] (p. 737). In addition, the boundary defining the safe operating space should include a “buffer” that both accounts for “uncertainty in the precise position of the threshold” and “also allows society time to react to early warning signs that it may be approaching a threshold and consequent abrupt or risky change” [
4] (pp. 737–738).
Figure 1 illustrates how setting a planetary boundary to designate the safe operating space is impacted by the uncertainty and lack of information over possible future threshold effects.
The concept of a planetary boundary that imposes an absolute limit on human activities that threaten critical Earth system resources and sinks is directly relevant to the
capital approach to sustainability [
9,
10,
11]. This approach suggests that economic wealth comprises three distinct assets: manufactured, or
reproducible capital (e.g., roads, buildings, machinery, factories, etc.);
human capital, which are the skills, education and health embodied in the workforce; and
natural capital, including land, forests, fossil fuels, minerals, fisheries and all other natural resources, regardless of whether or not they are exchanged on markets or owned. In addition, natural capital also consists of those ecosystems that through their natural functioning and habitats provide important goods and services to the economy. For example, [
12] (p. 395) state, “the world’s ecosystems are capital assets. If properly managed, they yield a flow of vital services, including the production of goods (such as seafood and timber), life support processes (such as pollination and water purification), and life-fulfilling conditions (such as beauty and serenity).”
The capital approach to sustainability asserts that the value of the aggregate stock of all capital—reproducible, human and natural—must be maintained or enhanced over time to ensure that overall welfare does not decline. However, within this approach, there are contrasting
weak versus
strong sustainability views, which differ in the treatment of natural capital (see
Table 1). As pointed out by [
9] (p. 42), “the main disagreement is whether natural capital has a unique or essential role in sustaining human welfare, and thus whether special ‘compensation rules’ are required to ensure that future generations are not made worse off by natural capital depletion today”. Weak sustainability assumes that there is no difference between natural and other forms of capital (e.g., human or reproducible), and thus as long as depleted natural capital is replaced with more value human or reproducible capital, then the total value of wealth available to current and future generations will increase. In contrast, strong sustainability argues that some natural capital is essential (e.g., unique environments, ecosystems, biodiversity and life-support functions), subject to irreversible loss, and has uncertain value. Consequently, the sustainability goal of maintaining and enhancing the value of the aggregate capital stock requires preserving essential natural capital.
Thus, scientists [
1,
2,
3,
4,
5,
6] who advocate the need for planetary boundaries to limit human impacts on critical global sinks and resources are aligning with the strong sustainability perspective, which argues that some natural capital may not be substituted and are inviolate. Based on this scientific view, some economists have begun examining how such planetary boundaries should be established, given the uncertainty over thresholds, abrupt and irreversible change, and the magnitude of welfare impacts [
8,
13].
Equally important, however, is determining how to manage efficiently and sustainable the safe operating space available for exploitation by humankind [
4,
8]. For this purpose, the weak sustainability perspective is relevant. Here, we show how such a perspective can be adopted to develop a model that informs “wise stewardship” of any safe operating space defined by planetary boundaries.
Specifically, we consider the safe operating space defined by any planetary boundary to be a depletable stock that has value either as a source of natural resource inputs into an economy or a sink for emitted waste. The safe operating space can therefore be treated as an economic asset that should earn a rate return comparable to holding other assets in an economy. Following the principles of weak sustainability (
Table 1), sustainable management of this asset requires efficient use over time. This has consequences that, in turn, affect the choice of policies that may be adopted to manage and allocate the safe operating space available for humankind.
2.2. The Safe Operating Space as an Economic Asset
The starting point for our modeling approach is to treat the safe operating space defined by planetary boundaries as an economic asset.
Let the initial safe operating space associated with a given planetary boundary be denoted as
S0. Depending on the planetary boundary, this measurable limit could be terrestrial net primary production, available freshwater for consumption, species richness, assimilative capacity for various pollutants, forest land area, or the global carbon budget [
1,
2,
3,
4,
5,
6]. No matter how it is delineated and measured,
S0 is a finite, depletable stock that can be safely used, exploited or converted through economic activity. Consequently, the initial safe operating space can be considered an economic asset.
At time
t, some of the initial
S0 will already have been “used up” by the economy. Define
as the cumulative amount of the safe operating space that has already been depleted by economic activity. The remaining stock of this asset at time
t is therefore
, and it follows that
where a dot over a variable indicates its derivative with respect to
t.
As the safe operating space is an economic asset, its cumulative exploitation must earn a rate of return that is comparable to all other forms of capital available to the economy. Let the average rate of return across all the latter assets be denoted as some interest rate r. Also, assume that cumulative exploitation of the safe operating space up to time t is for various market-oriented activities, which have market prices that can be aggregated into some average price index . For analytical convenience, we assume that the market price is net of any cost of exploitation. Thus, cumulative exploitation is sold at this market price and the proceeds are invested at interest rate r.
Depending on the type of planetary boundary, the available safe operating space at time t might increase, due to natural (i.e., biological) growth or recovery of assimilative capacity. This is especially true for any that is defined in terms of biological or land resources, such as forest land or species stocks. But it might also hold true for sinks of carbon, ocean recovery from acidification, nitrogen and phosphorus cycles, replenishment of freshwater ecosystems, and so on. Representing such natural growth or recovery as , we assume that any such additional augmentation of the available safe operating space at time t will be immediately exploited at the rate , and also sold at the same market price for cumulative exploitation.
There are two additional values of the safe operating space that should be considered. First, the remaining natural asset may realize capital gains or losses if market prices change. These gains or losses at any time t are . Second, the available safe operating space, especially if it includes maintenance of important habitats, ecosystems or biological species, may generate wider social benefits, or “stock externalities”, such as biodiversity values, watershed protection, carbon sequestration and ecotourism. We assume that, for any remaining , the aggregate value of stock externalities is , which can be expressed in turn as a “markup” v of the market price of exploiting the safe operating space. The rationale for such a markup is straightforward: If the social value of any stock externalities is less than or equal to the market price of exploiting the safe operating space, then S(t) would not be conserved. Thus, the social benefit associated with any such stock externalities is .
Consequently, optimal management of the safe operating space at time
t requires choosing the amount of remaining
that maximizes all the above values associated with this asset, i.e.,
Suppressing the time argument for analytical convenience, the first-order condition yields
which is the optimal portfolio balance equation for
. The left-hand side represents the marginal returns for holding on to the remaining safe operating space rather than exploiting it. The right-hand side is the opportunity cost, in terms of foregone interest income from other economic assets, from retaining
. Note that
, which implies that the remaining safe operating space is at risk if
is large, or
and
v are small. Also, if natural growth or recovery and stock externalities are negligible, then (3) resembles the more familiar Hotelling efficiency condition associated with a pure exhaustible resource, i.e.,
.
For analytical convenience, we assume that the marginal rate of biological growth of recovery is constant, so that we can denote
. This allows Equation (3) to be rewritten as
, which yields the following solution for the price path
The market price associated with exploiting the safe operating space should evolve at a rate equal to the net rate of return ρ earned from investing the proceeds from such exploitation. This price path is increasing if , suggesting that there are positive net returns from exploiting and investing the proceeds. Consequently, it pays to exploit the safe operating space today, there will be less available for exploitation in future periods, and so p must rise over time. Alternatively, as , then there are no net returns to the invested proceeds earned from exploiting , and the safe operating space will be conserved indefinitely.