Annex 4.2 How Many People Can Earth Support in Comfort?

The Impact Inequality (Ch. 4) represents the imbalance between our demand for Nature’s provisioning goods (i.e., our ecological footprint) and Nature’s ability to meet that demand on a sustainable basis.Footnote ¹⁵⁷ It represents the difference between demand and sustainable supply at a point in time. We expressed the inequality as Ny/α > G(S), where N is global population, y is global per capita final output, or global GDP, α is the efficiency with which Nature’s provisioning goods are converted into final output, S is a scalar measure of the stock of biosphere, and G(S) is the biosphere’s net regenerative rate. Currently the ratio of global demand to sustainable supply is approximately 1.7, whence the saying that we would need 1.7 Earths if our current demand was to be met on a sustainable basis.

We have presented the Impact Inequality for the global economy. The corresponding inequality for a national economy (or for that matter for a village community) would require a further term representing the impact on the biosphere arising from exchange with others, involving trade and environmental externalities. It is a simple matter to conceptualise that. So, for brevity we continue to adopt a global perspective.

To convert the inequality into an equality requires that either Ny/α be reduced or G(S) be increased, or both. In Part II (Ch. 18–19) we study ways in which investment in Nature can be used to raise G(S). In the chapters that follow in Part I, we uncover institutional changes and practices that would help to reduce Ny/α.

The Impact Inequality tells us that, if we are to hold our ecological footprint fixed, then other things equal, any increase in N would have to be compensated by a reduction in y, or, conversely, any increase in y would require that N be lower. In Ch. 4* we construct a dynamic model of global economic possibilities. Among other things, the model displays the relationships over time between N, y, α, and G(S). It uncovers the choices over consumption and various forms of investment the global citizen (we previously referred to her as the ‘social evaluator’) faces over time. But because it is prudent to proceed step by step, the model in Ch. 4* does not specify human institutions, nor does it make assumptions regarding human behaviour; instead, it is couched exclusively in terms of stocks (of capital assets) and flows (of the stocks’ yields and our consumption and investment rates). Ch. 13* rectifies this by uncovering the conditions our choices over consumption and various forms of investment must satisfy if they are to lead, in the social evaluator’s judgment, to the ethically best future. Economists label such choices as socially optimal choices.

In Box 4.6 it was shown that if our collective aim is to close the gap between Ny/α and G(S) by 2030, then on the assumption that the global economy will continue to enjoy the average annual growth rate in GDP of recent decades, we would require the efficiency parameter α to increase at an annual percentage rate some four times the rate that has been experienced in recent years. That is so unlikely a scenario that we now study the interplay of N and y in bringing about a sustainable state of affair today. To do that it is simplest to avoid studying social optimum policies, but instead ask a more restricted question: How many people can Earth support in comfort? The idea is to hold all else constant and determine the value of N at which the human ecological footprint equals the biosphere’s net regenerative rate at a comfortable standard of living y.Footnote ¹⁵⁸

There is a commonplace intuition that the current imbalance in our demand for Nature’s provisioning goods is due to high consumption among the world’s rich people; with an accompanying corollary that large additions to human numbers over the past 70 years – N having risen from approximately 2.5 billion to 8 billion – has had little to do with it. The intuition is at variance with evidence. Suppose, for example, the 1.5 billion inhabitants of OECD countries (the Economist newspaper calls the OECD “a club of mostly rich countries”) were to accept a halving of their annual incomes from the current figure of 40,000 international dollars per person to 20,000 international dollars. That’s a huge drop in incomes, but as the Impact Inequality shows, the move would reduce the imbalance from the current ratio of 1.6 to 1.2. And 1.2 is a substantial figure, implying further erosion of the biosphere at a fast pace.

So, we now choose a value of y at which life is deemed to be comfortable. Per capita global GDP in 2019 was approximately 16,000 dollars at 2011 prices. As an exercise let us take the chosen y to be 20,000 international dollars at 2011 prices. As the figure falls in the range of per capita incomes in the World Bank’s list of high middle-income countries, we use it to represent a comfortable standard of living.

We assume that people apply their labour on produced capital and natural capital to produce an all-purpose commodity that can be consumed. As of now we have little quantitative knowledge of the biosphere’s dynamics when viewed in the aggregate (i.e., we have no estimates of the G-function in the Impact Inequality). But as produced capital is complementary to natural capital in production (any expansion of the former makes further demands on natural capital), an expansion of the stock of the former depresses the stock of the latter, other things equal. We noted previously (Sec. 4.1.2) that Reference Rockström, Steffen, Noone, Persson, F. S. Chapin, Lenton, Scheffer, Folke, Schellnhuber, Nykvist, de Wit, Hughes, van der Leeuw, Rodhe, Sörlin, Snyder, Costanza, Svedin, Falkenmark, Karlberg, Corell, Fabry, Hansen, Walker, Liverman, Richardson, Crutzen and FoleyRockström et al. (2009) have found evidence in the Earth system’s signatures that several planetary boundaries are so close to being breached, that further deteriorations in the state of the biosphere would take it into terrains that are unchartered and therefore should be avoided. Let us then regard K to be an aggregate measure of produced capital and natural capital and hold it fixed to ensure that there is no further deterioration of the biosphere. The idea is to stop K on its tracks by a global quota on what we are permitted to take from the biosphere.Footnote ¹⁵⁹

Let Q be aggregate output. In Ch. 4* we construct a complete model of economic possibilities involving produced, human, and natural capital. Here we present a truncated version of it. If global population is N and φ the proportion of N in production, we assume that output Q is a power function of K and N, that is,

$Q=K^{(1-\rho )}{\left[\phi N\right]}^{\rho },0\le \rho <1,0<\phi <1$(A4.2.1)

We now estimate K^{(1− ρ)} from the current size of the world economy.

For want of data to the contrary, we assume that the value of the world’s production of final good and services draws proportionately on all ecosystem services. In 2019 world output was about 120 trillion dollars at 2011 prices. Using the model of production in equation (A4.2.1), we therefore have

$K^{1-\rho }{\left[\phi N\right]}^{\rho }=120\text{ trillion dollars}$(A4.2.2)

World population was 7.8 billion in late 2019. The global dependency ratio, that is, the ratio of the sum of the number of people below age 15 and above age 65 to the number of people between 15 and 65, is today about 1.6 to 1. Thus φ = 1/2.6, which means φN = 3 billion. A huge empirical literature in economics suggests that as a rounded figure, ρ = 0.5 is not unreasonable. Equation (A4.2.3) then says,

$\begin{array}{ccc}{K}^{0.5}& =& 120\times {10}^{12}/{\left(3\times {10}^9\right)}^{0.5}{\text{dollars per producer}}^{0.5}\\ & \approx & 2.2{\text{ billion dollars per producer}}^{0.5}\end{array}$(A4.2.3)

Having calibrated our model of global production, we compute the sustainable population size if y = 20,000 dollars. Let N* denote the size of the sustainable global population. To err on the conservative side of the size of the Impact Inequality today, we assume that the global ecological footprint is currently 1.5. That means if the biosphere and the stock of produced capital were stopped on their tracks, their sustainable value would be K/1.5, which we denote by K*. Using equation (A4.2.3),

${\left(K\text{*}\right)}^{0.5}\approx 1.8{\text{ billion dollars per producer}}^{0.5}$(A4.2.4)

Using eq. (A4.2.2) – (A4.2.4), we have

(A4.2.5)${\left(K\text{*}\right)}^{0.5}{\left(\phi N\text{*}\right)}^{0.5}=\left[1.8\times {10}^9\right]{\left(\phi N\text{*}\right)}^{0.5}=\left(20\times {10}^3\right)N\text{*}$

But φ = 1/2.6. From eq. (A4.2.5)) it follows that,

$N\text{*}\approx 3.3\text{ billion}$(A4.2.6)

Global population was about 3 billion in 1960 (Fig. 4.2); which means, in 3.3 billion we have arrived at a figure that prevailed only about 60 years ago. As the finding in Fig. 4.10 showed, if inequality in the distribution of incomes was judged to be inevitable, the size of global population that would support an average income of 20,000 international dollars would be smaller.

But even a global population of 3.3 billion seems so foreign to us today that the above exercise should probably be interpreted less as prescription than as a sign of how quickly we have overstrained Nature. The idea of sustainable development is meaningless unless it ensures that it does not carry with it the Impact Inequality. Subject to all the caveats we have stressed, our finding says that if humanity were to find ways to reside in the biosphere in a sustainable manner and to bring about economic equality, the human population Earth could support at a living standard of 20,000 dollars is approximately 3.3 billion. It is a simple matter to conduct the exercise with alternative figures for the living standard. We resist doing that.

It is informative to flip the question underlying the calculation by asking what living standard we could aspire to if world population was to attain the UNPD’s near lower-end projection for 2100 of 9 billion (UNPD, 2019b). Equations (A4.2.4) – (A4.2.5) provide us with the tools needed to provide an answer. Sustainability requires that,

$\left(1.8\times {10}^9\right){\left(\phi N\right)}^{0.5}=Ny$(A4.2.7)

Set φ = 1/2.6 and N = 9 billion. That means equation (A4.2.7) reduces to

$\left[\left(1.8\times {10}^9\right){\left(9\times {10}^9/2.6\right)}^{0.5}\right]/9\times {10}^9=y$(A4.2.8)

Let y* denote the solution of equation (A4.2.8). Then we have y* ≈ 11,840 dollars at 2011 prices. The figure falls within the range of middle-income countries. But 11,800 dollars at 2011 prices was the global living standard in about year 2000 (Fig. 4.3). At that time, however, world population was only a little over 6 billion. That 3 billion fewer people did not enjoy a higher living standard should not surprise, because the global stocks of produced capital and human capital were a lot less 20 years ago than it was in 2019 and our model was calibrated with the stocks in year 2019.

How should we read these exercises? It would be easy enough to dismiss them for their naivety, for example that they don’t allow for the technological advances we should expect to be made to enable even 9 billion people to enjoy a standard of living a lot higher than 11,800 dollars. But that would be to overlook that unless the global economy finds ways to charge for our use of Nature’s provisioning goods, technical advances will continue to be directed at economising on human capital and produced capital and will continue to be rapacious in the use of natural capital. If by some miracle it was possible to make us pay for Nature’s services at something like their accounting prices (or social worth), our consumption patterns would be very different. Not only would our household budgets look different, but entrepreneurs would have the incentive to invest in the technologies that economise on the use of natural capital, not be rapacious in its use. The human economy would move in such a different direction that it could even be that our descendants would have a better life than the average person does currently. Today, much of Nature is free, and we add to that insult by subsidising its exploitation to the tune of some 4–6 trillion dollars annually. That makes Nature come to us with a negative price! Our efforts should be directed at so improving our institutions that these distortions are eliminated.