Saturday, October 24, 2009

Backs of Envelopes

Hey, I haven't done this for awhile.

The NYT has a story today (HT: Free Exchange) on how some people (none of whom are economists) think that supply and demand curves are moot because the world is going to crash and burn in the near future without a systemic focus on moving away oil and while we're at it, we need to rewrite all our macro models because "Neoclassical economics is inconsistent with the laws of thermodynamics." Not quite sure what that means.

Disclosure: Global warming is pretty obviously real and scary. The chemistry/phyiscs are complicated in that nailing down precise numbers is hard, but signing the effect is simple. Period. But that's not this post.

There are a lot of related points made in the article. The main thrust is, I gather, because oil is becoming increasingly costly to extract in terms of the energy required, the effective cost of providing energy for other uses will skyrocket, and when this starts to happen, bad things happen to society, and that modern economic theory doesn't account for this. (Yes, the modern neoclassical model predicts indefinite growth based on continually improving productivity. Do many economists spend their days figuring out what growth will look like in 200 years? No. Are models designed to talk about this sort of very-long-run behaviour? No. Can I write down such a model? Sure. Would anyone, particularly a journal, care? No.)

I am somewhat personally distressed by these predictions, because my future livelihood will probably depend on there being large quantities of undergrads paying to learn about supply and demand curves, which probably won't realize if society collapses. Further, this is not something I've ever talked about in economics courses (another point calling for rewriting the models, according to proponents of this 'biophysical economics'.) Can I explain this rationally? Maybe.

According to wikipedia, (the links all seem good and this is only a blog, not the AER) world energy consumption is 15 terawatts (15 x 10^12 W). The physicists and chemists just cringed, yes. It's easier to work in watts than joules, even though one can't really convert between them properly.

Consider Exxon-Mobil. Following links I again got on wikipedia to the company's financial statement, I find that they produce less than two percent of the world's energy at a cost of $289 billion dollars. That's their cost, not their revenues. Let's assume that the cost profile of world energy production is approximately similar to the cost profile of energy produced by Exxon, which is a conservative assumption - I bet Exxon makes more profit than average, and does so less renewably than lots of other sources.

Next. Google 'solar panels'. Home Depot will provide 200W for $1,179.99$. Let's round this up to $6000 per 1000 watts. These have a 25 year warranty, too. In order to be safe, let's bump the required world energy supply from 15 TW to 40 TW - solar panels aren't going to work at night, clouds, etc. Now, algebra.

Total world expenditure on providing energy is fifty times what it costs Exxon-Mobil to produce 2%: 50*289 billion = 14.5 trillion.

Cost of providing the entire world energy supply with solar power from Home Depot solar panels: (40 x 10^12 / 1000)*($6000) = 40 billion * 6000 = 240 trillion. (This number of solar cells would cover somewhat less than 50,000 square kilometres, judging by the specs on the website, approximately 1/6 of Nevada.)

Annual payment on 240 trillion amortized over 25 years at the current 30 year mortgage rate of about 5.25% = 17.3 trillion.

The difference between 17.3 and 14.4 trillion is huge in magnitude but not that large in percentage, and I think I've made conservative assumptions at most every turn - Exxon can issue debt at less than 5.25%, let alone governments, 40 terawatts is a lot more than 15, etc, etc.

Yes, there are a lot of issues you can take here, keep reading. The point remains: the cost of extracting and using nonrenewables for energy is rapidly approaching the point where we might as well just do everything in a renewable fashion - and yet the cost of supporting such renewable power hasn't caused any societal catacylsms. So why expect one?

POSTSCRIPT: List of assumptions and bias on the gap between 17.3 and 14.4.
1. World energy consumption. If more than 15 TW, increase.
2. Solar capacity versus throughput. If the world needs more than 40TW installed solar capacity to meet the flow demand for power, increase the gap.
3. Exxon produces < 2% in actuality. Decrease the gap.
4. Exxon more (less) costly than world average. Decrease (increase). [Saudia Arabia is probably considerably cheaper than Exxon, but most other oil majors/current renewables projects are probably more expensive. Actual bias could go either way.]
5. Cost of panels increases would increase gap. Actual bias is probably negative: I bet Home Depot would cut you a deal if you wanted to buy several trillion worth. Plus solar technology would improve.
6. Interest rate increases. Would increase gap.

Other issues:
1. Replacing oil-based infrastructure and methods (see: cars) will not be cheap, but cars don't last forever and it doesn't have to happen in one day. The transition will be costly, but we can certainly sustain the steady-state.
2. If it's close, why haven't we seen a change? The gap is still $2.9 billion, which is big money, uncertainty over future GHG regulation, no incentive to take the lead.
3 ???.
4. Me possibly screwing up the algebra by an order of magnitude somewhere.

POST-POSTSCRIPT: Anyone want to calculate the carbon tax that equalizes the cost of renewables and the cost of current world energy production?

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