The economics of global warming
by Ravi Verma, Wed Dec 30, 2009 at 12:40:29 PM EST
I have been appalled by the "enlightened" debate currently taking place on the economics of global warming. I am not particularly surprised by the viewpoints of those who would deny the existence of global warming as a human affected phenomenon altogether ~ nothing better could be expected of them ~ but I am very surprised by those who believe that global warming is a human affected phenomenon, and that something should be done about it.
Please let me explain.
Let us consider the economics of global warming. Everyone who believes that global warming is a human affected phenomenon believes that those who have polluted the most should do the most. But how do we define "those who have polluted the most".
The metric generally used in enlightened discussion is annual CO2 emissions, but this is a bogus metric that unfairly penalizes larger countries over smaller ones. Thus, a metric that should be the starting point is per capita annual CO2 emissions. But, even with this metric, one is unfairly penalizing countries that are now developing as compared to countries that developed in the 20th century. After all, it takes the same amount of CO2 emissions (give or take a little bit) to build a Bridge over the River Kwai now, as it did during WWII; and you don't have to build the bridge again (provided you built it right in the first place). It takes the same amount of CO2 emissions to build a large hydroelectric plant now, as it did when the Hoover dam was built. Thus, a more appropriate metric should be Cumulative CO2 emissions, normalized with some measure of population.
Now, we have run into one issues here ~ the population of the US is not the same today as it was when the Hoover dam was built. Thus, any approach to normalizing the cumulative CO2 emissions with population will remain imperfect.
Having said that, let us now look at the economics of global warming.
First, here is a chart from Gapminder that plots the GDP of various countries as a function of their cumulative CO2 emissions.
Note that I have used a log-log scale to illustrate the scaling. The US, China and India are represented by the large Yellow, Red and Blue circles on the top right hand corner. All the data points can be fitted with a power relationship with a slope of almost 1 ~ growing the economy by 10x requires an increase in cumulative CO2 emissions by 10x. Also note the tight fit for all the data points around the linear scaling relationship.
By comparison, here is a similar plot of total income plotted against annual CO2 emissions.
A linear relationship is obvious here as well, but there is more scatter ~ countries that developed earlier tend to be on the top-left side of the linear fit, and developing countries are on the bottom-right side of the linear fit.
Let us now normalize the income and annual CO2 emissions...
Note that India (large blue circle) and China (large red circle) have moved well below the linear fit; while the US and EU countries (orange dots) are above the linear fit as would be expected because we are using annual and not cumulative CO2 emissions. Also note that the data appears to be bounded between the linear (1 scaling) and square root (0.5 scaling) relationships (more on that in a second).
Let us now consider the per capita GDP and cumulative GDP normalized with population. I had to compile this data because gapminder does not give me this dataplot. Happily, with my own spreadsheet, I am able to compute exact fits and not just rely on visual fits.
Several things are to be noted here.
First, the blue line is a power law fit with an exponent of 0.5 ~ increasing the cumulative CO2 emissions by 100x increases the GDP only by 10x.
Second, the scatter around the best power law fit (blue line) is very tight. The largest economies/largest polluters are the US (1068 MT/capita), China (71 MT/capita), India (23 MT/capita) and Brazil (49 MT/capita) ~ and these are marked as red circles. Note that they are all very close to the best fit, even though the best fit does not account for sizes of individual countries. The US (1068 MT/capita) is slightly above the best power law fit, but not by much.
Third, we can now identify those who have benefited the most from global warming: they correspond to countries that are higher than the global averages of 168 cumulative CO2 MT emission /capita and $8500 per capita GDP. The US is in that list, but there are others as well. One arbitrary method of ranking them would be to divide the per capita GDP by the global average, and the per capita cumulative CO2 emissions with the global average, and to add the two ratios. If the sum is greater than 2, then the country is a polluter. As per this method, the top 10 polluters are: Luxembourg, USA, UK, Belgium, Germany, Canada, Denmark, Australia and Norway and Qatar. India, China, Brazil and Russia are not on the list of polluters. Furthemore, even with the forecasted economic expansion, India, Brazil and Russia will not join the list of polluters; and China may or may not join the list of polluters.
So, if we can all agree that the polluters (who have benefited the most from the polluting) should pay the rest for not polluting, then the question becomes by what amount.
We can examine this question in light of the current proposals, and also in light of what would appear to be fair. First, US SoS put forth a plan to develop an annual $100B green energy fund by the year 2020. Let us use this as a starting point.
The chart below plots the 2005 GDP levels versus cumulative CO2 emissions for all countries.
The proposed green energy fund of $100B is marked by the green band. My first reaction is that the proposed 2020 green energy fund appears pitiful, even when compared to the 2005 GDP. A more accurate description would normalize the fund. Let us assume that all the polluters (as defined above) as contributing to the fund equally, and the fund goes to all the non-polluters (as defined above) also equally. Since there were 1.3B polluters and 4.9B non-polluters, the green energy fund corresponds to an annual tax of $76 (in 2020 dollars; corresponding to a green fund "tax" rate of around 0.3%) on all polluters, and green energy investments of $20 for every non polluter. This should suffice to buy one kerosene stove, one pressure cooker, and one pressurized oil lantern for a family of 4.
So what should be the size of the green energy fund ?
Let us say that we want to reduce the cumulative CO2 levels by 6%. Assuming that we cannot reduce the CO2 levels without foregoing economic expansion (this is a very strong assumption until someone can figure out and demonstrate how it can be done otherwise), a 6% reduction in CO2 level would require a 3% reduction in per capita GDP. Thus, the tax rate should be 3%, and not 0.3%.
The green fund needs to be about $1 trillion/year...at least!
At the proposed green fund level $100B/year, there is not much difference between us, and those that deny global warming altogether.