Greenhouse gases emissions, wealth, energy intensity, population... How can we link together, in a simple way, all these physical and economical notions - that each are of common use for part of the protagonists of this file - in the context of the problem we are presently adressing ? An equation, said to be of Kaya, for it is named after the japanese professor to whom the rumor attributes the "discovery" of this equation (a sure thing is that this professor is a well known researcher in the energy policy sector), allows to show how these notions can be linked to one another.

This equation derives from the simple fact - that generations of high school students surely remember ! - that it is always possible to multiply or divide both sides of an equality by the same number.

Our first equality couldn't be more simple. Let's call GHG the world emissions of CO2, the main greenhouse gas of human origin, and we can write :

So far, everyone should be able to follow ! Let's now call TOE the world energy consumption (abreviation meaning Tonne of Oil Equivalent, of common use for energy people ; 1 TOE = 11600 kWh = 42 billion Joules). We can at the same time multiply and divide one side by TOE, what leads to :

What is the point ? It is that we just wrote :

Indeed, the ratio (GHG/TOE) bears the name of "carbon content of the energy" : it is the amount of CO2 that we must free in the atmosphere to get a certain quantity of energy for our activities. This quantity is not the same whatever primary energy we use (primary energy is the one that we find "as is" in the surrounding world : crude oil, coal, falling water, fissile atoms, etc, as opposed to final energy, that designates forms of energy that we can use for our applications but are not found as is in nature : electricity, refined petrol, etc) and can therefore vary depending on the technological choices we make (for exemple electricity productions is more or less CO2 intensive depending on the primary energy used).

"greenhouse gas content" (actually essentially "carbon content") by tonne oil equivalent of final energy, for various types. Electricity is converted with the final energy equivalent (1 TOE = 11,6 MWh). Question marks mean that I only have a rough idea of the emissions, but no precise figure could be found. From UNEP, Ademe, EDF.

This figure already allows to see that, for a given energy consumption, CO2 emissions may vary a lot depending on the energy mix we decide to have (or are able to have...).

We can go on repeating the same operation of multiplying and dividing by the same term. Let's multiply and divide the right side of the equality by GNP, that is the unit that measures the economic activity.

We have now written :

Indeed, dividing energy by GNP (TOE/GNP) bears the name of "energy intensity of economy" : it is the given quantity of energy that we must spend to get a million euros (or dollars) of goods or services. This energy intensity is on a decreasing trend since the beginning of industrialization, because the efficiency of techniques has always progressed, in first approximation.

Energy spending by million euros of GNP in France, index = 100 in 1970 (be careful : the vertical axis does not start from zero !). Most occidental countries evolved the same way. From Observatoire de l'Energie

Even though this value is decreasing, it is easy to understand that focusing on this sole term of the equation is forgetting the rest, and in particular failing to debate the following question : are we certain that if the energy intensity of the economy decreases it is not essentially because....the GNP increases faster than the energy consumption ? And actually it's exactely what happens (energy consumption increases slower than GNP, but nevertheless it increases....).

Eventually we must now include demography to start an interesting discussion. Let's call POP the world population, and let's multiply and divide the right side bythis term, what leads to :

Translated into english, we have now written :

The ratio GNP/POP is of very frequent use, and can indistinctely be called "production per person" or...wealth. We have now expressed the CO2 emissions (but the same reasoning could apply to all greenhouse gases) as a function of terms that economists are accustomed to. Now, the interesting debate begins !

Well, so we have a beautiful equation. Then what ? Then we see again that any debate focusing on one only of the terms is not sufficient to reach a conclusion. For example, when Mr. Bush says that he will fight climate change by cutting the energy intensity of the american economy by 18% in 10 years, it is easy to see that this will only concern the term TOE/GNP. And what about the rest ? If the economic output per person (GNP/POP) rises by 25% in the same time (that is 2,5% of growth per year, a conservative objective), with a population (POP) rising by a couple % (simple prolongation of trends), and a carbon intensity of energy staying the same (reasonnable assumption given the present trends, particularly in the electricity sector), the result will be a growth of CO2 emissions, not a diminution !

Let's get back to the subject : it is established that to stabilize the level of CO2 in the atmosphere (that is to halt the present "CO2 enrichment" of the air) we must divide the world emissions by 2 at least within a couple decades. In the above equation we should therefore aim at a division of the left term by 2, and as we should still have an equality it means that we must also divide the right term by 2.

What are we going to divide ?

Can we divide the world population by two ? Implementing such an objective in a plannified and fast way (50 years, it's not much time) bearing the unpleasant name of genocide, it does not seem likely that it will be considered a serious option by anyone. And relying on an outbreak to do the job for us (that should also divide the population of rich countries by two, for we are the massive emitters) can hardly be wished !

A prolongation of trends rather concludes to a multiplication of the population by 1,5.

Two examples of demographic scenarios for the coming decades, used for the greenhouse gas emission scenarios (left : A1, right : A2). Both these scenarios include a population rising to 9 billion or so in 2050. From IPCC, 2000

Since there is 1,5 times more people on earth while emissions shoud be divided by 2, it means that the total of the other factors should be divided by 3.

Can we then divide the economic output per person (GNP/POP) by 3 ? This would suppose a deliberate choice of a recession, that we can also consider as not likely (which does not mean that recession is not likely ; in a finite world it is on the contrary very likely "someday". It just means that it is very unlikely that it would be decided "coldly" by the representatives to adress a future danger, even though it seems justified to some). We all wish every day that "growth" goes on, among rich countries as well as among poor countries. A very conservative estimate of a 1% growth of the economic output per person, what is well below what every elected representative tries to get, increases the ratio GNP/POP by 65% in 50 years, what means that the remaining terms on the right hand side of the equation have to be divided by 5 (5 is more or less equal to 3*1,65).

Before we go on, let's recall that economic growth designates only the growth of the output of goods or services that are man made, but accounts for zero the concomittent and irreversible vanishing of non renewable resources - ores, fossil fuels... - that are necessary for our production. Including this second factor with figures that are not more stupid than anything else could easily bring us to the conclusion that we are already declining.

We now have a division by 5 to perform on the following expression :

Can we divide the energy intensity by 5 in 50 years ? It has decreased by 25% in 30 years in France (chart above) ; the prolongation of such a rate yields a decrease of 40% in 50 ans, but it is perhaps an optimistic hypothesis, because it is the first efforts that are the easiest to make. Never mind, and let's suppose that we can prolongate. The energy intensity of the economy would therefore be in 2050 of only 60% of what it is today, and we end with a division by 3 to 4 to perform on the ratio GHG/TOE

In other words, the "energy intensity of the economy" should be divided by 3 at least (and more probably 4 or 5), in a context where the global consumption would have risen. Question : what sources are able to be called upon for this, knowing that the contribution of renewables is limited by phycisal factors before it is by economic or technological factors ?

In short the alternative in simple terms could be stated this way : renewables can provide a minimum energy (see solar, wind generation, biofuels), but not everything at the present consumption level, far from it, and the "adjustment variable" to reach the desired quantity of energy without CO2 emissions is nuclear energy (the quantities are not limited if we call on breeders), if we wish to perpetrate the economic growth as long as possible.

Hence it is difficult to separate the debate on wether to call or not on nuclear energy from the debate on the total quantity of energy that we want to consume, if we wish at the same time to prevent humanity from experiencing a potentially disastrous evolution of the terrestrial climate.

Of course, another alternative would be to choose right away a sufficient decrease of the material consumption per person (which, once removed the contribution of stock variations, is equal to the decrease of the material production, and that includes all services requiring ores or energy to be delivered), to which we will all be compelled one day anyway, not because of ideology, but just because, alas, the world is finite.