Growth within Planetary Boundaries II

Growth Dynamics

Now that we’ve emphasized the planetary boundaries, let’s see how hard the challenge is from the point of view of the economic growth.

We have a world now of 80 to 90 trillion dollars a year, 7.2 billion people. Approximately $12,000 per person per year on average around the planet. But the rich countries are roughly three times that average level, say $36,000 per person per year. Suppose that the poor countries, the developing world, successfully caught up with the rich world, closed the gap. That by itself would imply a three time increase of the world output, just the catching up process. Even putting aside the fact that the rich countries are still hoping to achieve some more economic growth of their own. Taking into account that in addition to the increase of total output that would come from catching up, the world population itself is also rising, from 7.2 billion people now to more than 9 billion by mid-century. To almost 11 billion at the end of the century according to the medium fertility forecast of the United Nations.

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Well that means that the three time increase at our given population might amount to a four time increase taking into account the population increase as well. So imagine our situation. Our situation is one in which humanity is already causing big dislocations on the planet. But here’s a world where six-sevenths of humanity lives in developing countries. They’re looking at the high income world, they’re saying we want to live like that. In fact, they’ve deciphered a lot of the key to that, how to mobilize technology, markets, education in order to be able to have that catching up growth. And that would imply a four time increase of world output. How could it be? Could we withstand four times the human impact on the planet? Of course not. We can not even withstand what we’re doing right now. So the key, the central point of sustainable development is, that in order to reconcile economic growth and planetary boundaries we have to grow in a different way. We have to have different approaches to using energy, different approaches to transportation, different approaches to growing food in a safer and ecologically more sustainable manner.

Right now I want to look at that total increase though a little bit more carefully. A little bit more analytically. To ask, what could we expect? If we are able to solve the problem of the environmental crisis, what could catching up growth deliver in terms of aggregate output in the world in the coming decades? To do that we start with the concept of convergence.

Remember that economic convergence means that poor countries have a tendency to grow faster in output per capita, or gross domestic product per capita than do the rich countries. The reason poor countries have that chance to grow faster is not that they’re better, but because we all share similar technologies, access, knowledge and so forth. The reason they’re able to grow faster is that they have a gap to catch up. They are not yet fully using the technologies and the know-how that are already more deployed in the high income world. So a poor country has a kind of backlog that it can quickly take on of more advanced technologies to narrow the gap with the countries in the lead that we say are at the technology frontier. To understand this is, sometimes economists draw a downward sloping curve of the kind shown in this picture. You see that on the horizontal axis is a country’s level of development as a fraction of the US, the frontier country, the country at the high end of the income curve. And on the vertical axis is the growth rate of the country.

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Now what’s graphed here in the solid line is the theoretical curve that says that for countries that start poor at the left hand side of the graph, their potential growth is high. And countries all the way on the right-hand side, where their income is close to the U.S. level per person, are at a lower point on that downward-sloping curve, meaning that their potential growth is lower because they have less catching-up space. And then what’s shown on this graph is the actual growth rates of a number of selected countries between the years 1990 and 2005. Lo and behold, the actual experience of countries, for instance the rapid growth of China which started quite poor, and the slow growth of Finland which started quite rich, basically fits this downward sloping line. So convergence is not only an idea, it is a practical implication of growth that we observe in, in recent years. Now, based on the experience and based on statistical analyses that have been done of this tendency towards convergence, again meaning faster growth in the poorer countries, there’s a kind of rule of thumb. The rule of thumb goes something like this. A country that is at half the income level of the country in the lead can grow about 1.4 percentage points per year faster than the leading country.

Let me give me an example. Say the United States is at $50,000 per person per year. A country at $25,000 dollars per person per year having some head room for fast growth would grow about 1.4 percentage points per year faster in GNP per capita, GDP per capita than the United States. So if the US has a growth rate per person of 1%, then the country at $25,000 would have a growth rate of 2.4% per year. Now consider a country half of that level. $12,500, so that’s one fourth of the US. Add another 1.4% per year, so that makes 2.8 percentage points per year faster than the US. So if the US is growing at 1% per annum in per person terms, a country that starts out at $12,500 per capita would be growing at 3.8% per year, 2.8 percentage points faster than the US growth rate. Well each time you cut by half the starting point of income. You raise the expected growth rate, or the average convergent growth rate by another 1.4 percentage points per year. So that a country that is 132nd say, of the United States that would be a country at about $1,562 per year just dividing 50,000 by 32. Country at 1,500, pretty poor country, maybe a country in Sub-Saharan Africa would have so much headroom that it could grow seven percentage points faster than the United States. So if the US is growing 1% per year per capita, that very poor country could be growing at 8% per capita. You get the idea. The idea is the poorer the starting point, assuming no poverty trap or other fundamental barriers to the growth of that country The headroom for rapid catching up is bigger, and one can calculate based on the statistical evidence the extent to which the growth rate will tend to be faster than the high-income country.

Now what happens over time? The poor country narrows the gap with the richer country by growing faster if it started 132nd of the income of the US, maybe some decades later it would be at a quarter of the income of the US. Then, later still, half of the income of the US. As the gap narrows, so too does the growth of that lagging country slow down. So there’s a convergence of living standards gradually over several decades, and also a convergence of growth rates. The poor country starts out very fast growing and then as it becomes richer and richer and richer, and closer and closer to the technological leader, its growth rate too therefore slows down and eventually, gradually converges with that of the technological leader. And I keep using the United States as the example of that. Let’s take a practical example of this quantitative rule. In the year 2000 the high income world had an estimated GDP per person, or gross world product per person, I can say averaging over the whole world, of about $35,000. And the developing countries had a GDP per capita on average of about 6,900 ,or let’s say $7,000 per capita. In this example if the high income countries grow at 1% per year in per capita terms, then we can calculate that given that initial gap from 35,000 down to 7,000, rounding these numbers, the poorer region should be able to grow about 3.2 percentage points per year faster than the richer region. So the convergence ideas predict that developing countries on a whole would grow at about 4.2% per year, developed countries would grow at about 1% per year. Add in a population growth rate of say, 1% for each, just being very rough. That says that the developing countries would be growing at a little over 5% per year, the developed countries at around 2% per year, because population growth is even faster in the developing countries. Maybe that would push the growth rate up closer to 6% per year compared to 2% per year for the high income countries. That’s more or less what we have been observing in recent years.

The convergence theory helps us to understand why the developing countries are achieving, enjoying faster economic growth than the high income countries. Now, if we trace this out for the next 40 years after 2010 to mid-century, and assume, that’s just an assumption, that the high income world averages 1% per year. And that the poorer regions catch up gradually with the high income region along the lines of that convergence formula that I just described. You get a kind of a graph shown here, and it’s shown with a logarithmic scale for the vertical axis. The countries start out quite far apart basically a 5-time advantage of the high income countries. But they narrow to the point where the high income countries are only 2-times, not 5-times, larger than the developing world by the middle of the century. Well what does this imply for total world production? Because remember we want to understand this to see what kind of pressures are being implied by this kind of total world growth.

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To do that we now have to add back in population dynamics. And for that, we can use the United Nations forecasts of the world population. And the UN taking note of our starting point and fertility patterns, estimates that from 7.2 billion today we will reach 8 billion people sometime early in the 2020s. And we’ll reach 9 billion people somewhere around 2040. And we will exceed 10 billion people in the second half of the 21st century, and by the end of the 21st century in the medium fertility scenario of the United Nations the world will reach about 10.8, almost 11 billion people. That’s shown in this graph here. Again, it’s shown with a logarithmic scale for the vertical axis. Why? Because with that scale the slope of this curve tells us the proportionate rate of growth of the population, so that when we see the curve leveling off by the end of the century it also means that the growth rate of the world population is slowing to a low number. Today the world is growing at about 1.1%. For 7.2 billion people, 1.1% means an additional 75 million people or so added to the world population each year. By the end of the century the growth is much closer to zero to stabilizing the world population, and that’s what’s signified by this flattening of this curve in this logarithmic scale for the vertical axis.

Well we can use the population forecast combined with the convergence idea to give us a sense of what the size of the world economy might be by mid-century. If things go smoothly without disasters, and heaven knows how many disasters are possible and how many we need to fight to avoid. But assuming we don’t have the disasters and assuming that the scale of the planetary boundary challenge can be met so that this kind of convergent growth can continue, then the world economy would rise from around 82 trillion dollars in 2010, rounding a bit because these are all approximations, to around 272 trillion dollars by the middle of the century. In other words, more than a three time increase by the middle of the century. Now that’s a reasonable measure of the huge magnitude of our challenge.

We start with the world already bursting at the seams, with humanity pushing against planetary boundaries. Then we take into account the powers of economic convergence and the desires of poor countries to narrow and eventually close the income gap with the rich world. And that implies a more than threefold increase of world output by the middle of the century.

That’s why we have to think very, very hard about how our economies function because we know there is no way that on a business as usual path we could achieve sustainable development. Business as usual will burst through the planetary boundaries, will create havoc with the climate system, havoc with the water supplies, havoc with the ocean acidity, havoc with the survival of other species. In order to reconcile the growth that we want with the ecological realities, we are going to need our economies to take a fundamentally different course. That’s what we’re going to look at next.

Pedro Pereira Leite

Researcher and professor. He had his PhD. on museology in 2011, with the title “Muss-amb-ike Homeland: The commitment on musicological process”, that was published in 2011. In 2012 he finishes a Post-PhD Research on "Biographical Glances: The intersubjectivity poetry on museology, at Lusófona University (Lisbon). Presently he is working in his Post PhD. Research about: “Global Heritages" with the aims to build a network on local cognizance and memory manager has a tool to build the will of action in 3 different communities, linked by past communed heritages.” He works at CES. He participates on different Research network, presented papers in national and international conferences, and had published books on research subjects.

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