The cost of carbon trading schemes

Plenty of numbers being bandied around, but one which many conservative Americans are quoting is this number from the Free Enterprise Education Institute (FEEI) - 5.2% of US GDP by 2020, equivalent to a reduction in income of $10,800 for a family of four (here), if the US used a cap-and-trade scheme to move to a putative Kyoto protocol target (carbon dioxide emissions of 7% under 1990 levels). The FEEI is a think tank which has managed to secure the services of Arthur Laffer, known to econ undergraduates as the chap who came up with the Laffer curve (something also very popular with the Bush administration, who used it as one justification for cutting US taxes).

5.2% smaller isn't that bad, especially when it's an opportunity cost number. It represents a difference of a few tenths of a percentage point a year in GDP growth rate, if we're talking about a horizon of 13 years. This is well within the bounds of error, and would probably be drowned out by other factors (say the current sub-prime mortgage crisis). But there's a different way to see this, using Fermi estimation and the equivalence example (family income) quoted for easy understanding.

What's the total reduction in GDP?

1. 5.2% reduction in US GDP being the same as a reduction in income of $10,800 for a family of four.
2. Say there are approximately 100m families in America (a population of 400m people - I'm deliberately overestimating here, to allow for growth).
3. Then the total reduction over 13 years is $10,800 * 100m = about 1 trillion dollars. That's today's dollars.

How much GDP will the US economy generate over that time?

1. On the same basis, the US economy this year is worth about $13 trillion and a bit (real), let's say 13 trillion.
2. Then over the next 13 years (2008-2020), it should generate $169 trillion of GDP (again, let's be conservative and not put any growth rate in).

What's the opportunity cost each year?

1. The cumulative opportunity cost of a cap-and-trade scheme and the Kyoto protocol is approximately $1 trillion out of $169 trillion, or about 0.6% of GDP.
2. Let's say that's a per annum figure (it's not, most the costs will be front-loaded, but this is Fermi estimation, so we're allowed to make it easy). Then that's about $77 billion a year in opportunity cost. This compares favourably to the cost of financing the war in Iraq, which is about $100bn a year according to the last Congressional report on the matter.

What's a similar number for the world?

1. World GDP is about $48 trillion at PPP and today's dollars.
   
2. Using the heroic assumptions that the global economy has similar energy intensity and energy sensitivity to the US economy, then the global economy would suffer approximately $284 billion a year in opportunity cost. Call that $350 billion a year to account for more energy intensive countries.

The sense to attach to those numbers, even the ones being pushed hard by the US government in response to pressure for it to control emissions, is that they are actually rather small. Although they are significant, they aren't a major obstacle to growth. Remember, these numbers are before the impact of any alternative energy sources (say from more nuclear power plants) are taken into account. They merely describe the impact on economic growth of reducing carbon-based energy consumption and allocating the remaining consumption more efficiently.