Erlich's Equation

Paul Erlich may be the most famous population economist.  Of the malthusian school he famously wrote "The Population Bomb" in the 1970s and, then just as famously, had to eat his words in the 1990s.  That his projections were incorrect at the time do not reduce the relevance of some of his work however.  Specifically, in light of the preceding post, I'd like to focus on his equation for environmental impact.  

Elegant and simple, he claims that environmental impact is directly related to affluence, population and some technology factor that moderates the impact of population and affluence.  It looks like this: 

I = A x P x T

 Where I is environmental impact, A is affluence, P is population and T is the technology factor.  While the relationship can be displayed in greater complexity, this equation captures the heart of the issue. 

I bring it up here, because drawing on numbers from the "Prosperity without Growth" Report, it gives a very good mathematical illustration of why technological change is not going to be sufficient.  In 2007 the global per captia income was $5,900, population was 6.6 billion and carbon intensity (used as a proxy for technology in the case of carbon emissions) was 760gCO2/$.  That results in the following: 

5900 x 6.6 billion x .77 = 30 billion tonnes of CO2

Now, taking the following estimates for global population and affluence in 2050 of 10 billion for population (generally accepted ranges are between 9 and 12 billion) and slightly less than a doubling of per capita income to $11,000 (well below the U.S. today at about $40,000) and using the assumption that a stabilization of CO2 at 450 ppm would require a reduction to 4 billion tonnes of CO2 per year, yields the following: 

4 billion / (11000 x 10 billion) = 0.000035

That says carbon intensity would have to fall to 0.035gCO2/$ in the next 45 years.  In the last 30 it has fallen roughly 250 gCO2/$.  The rate of technological change would have to triple in order to meet that demand.  And it would have to triple globally - not just in the developed world.  That just does not seem like a reasonable projection.  A doubling coupled with significant behavior change seems far more likely.