Elasticity of Temperature and Carbon Dioxide

Time to apply some basic economics to anthropogenic climate change.

Economists advocate figuring out how sensitive one thing is to another by calculating elasticity: a ratio of percentage changes.

Why do this? In short, because it prevents the sort of mistakes that alarmists make when pointing at data on climate change.

One pitfall in doing these calculations is that atmospheric carbon dioxide concentration is a ratio measurement, while the temperatures we’re used to are interval measurements. The solution is easy: use the Kelvin temperature.

Data on temperature is easy to come by. World average temperature is about 290º (big differences in that guesstimate will have little bearing on my final result). Over the past 50 years, temperatures have increased from about 289.8º to 290.5º. That’s a change of 0.25%.

Data on carbon dioxide concentration is also easy to come by. Over the past 50 years it has increased from 315 to 392 ppm. That’s a change of 24.44%.

Very roughly, the elasticity of temperature with respect to atmospheric carbon dioxide concentration is the ratio of those two percentages: 0.25%/24.44% = 0.01.

This is close to zero. Economists call that inelastic.*

Really inelastic. Elasticities for cigarettes with respect to price 20 to 50 times higher.

That’s right: smokers will change their consumption in response to price increases far more readily than the planet will change its temperature in response to carbon dioxide.

So … if most of us know we can’t change smokers, why are we trying to change carbon dioxide concentrations when it won’t do much good?

This is why it’s so important to invoke possible non-linearity or hysteresis in climate processes … along with the all important claim that there will be bigger effects mañana. 

* There’s a lot of quibbles in the details and method, but none of them change the fact that we’re looking at nearly perfect inelasticity.

P.S. This post is motivated by an oldie but goodie from Bigwig at Silflay Hraka.

Technorati Tags: anthropogenic,global,warming,climate,change,elasticity

Comments

[Eli Rabett]

Two mistakes. First the base for the temperature calculation should be the temperature of the Earth w/o greenhouse gases, ~255 K (also the temperature of the surface of the moon) not 0K, so the temperature difference is 0.7K/35K

Second, the effect of CO2 is not linear, but logarithmic so you have to use the logs of the mixing ratios,
[log(392)-long(315)]/log(392)

That gives an entirely different answer.

Best
Eli

[David Tufte]

1) I don't agree with your first point, but I'm willing to take it at face value. With your numbers, the elasticity comes up to be 0.08. This is far less sensitive than smokers are to change in the price of cigarettes.

2) The relationship may well be log-linear, but that isn't relevant to calculating elasticities. One could, and I'm guessing that you are, make the argument that the elasticity should be with respect to the (base 10) log of carbon dioxide concentration. Taking that at face value, you'd get an elasticity of 0.07.

Further, combining both of your issues, one would get an elasticity of 0.53. This is still quite inelastic. For example, it is somewhat more inelastic than say, the response of residential electricity demand to prices.

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