The Chemistry of Economics

by Nathaniel Virgo

In order to understand economics, you must first understand chemistry.  That’s my story at least, and I’m sticking to it.  I’m neither an economist nor a chemist (not a real one anyway), but I’ve been thinking a lot about how to understand economics in chemical terms.

In a previous post I discussed autocatalysis, the mechanism by which a bunch of different molecules can react with each other in such a way that they end up producing more of themselves, at the cost of using something else up.  The ideas in that post don’t only apply to chemistry – you can use them to think about just about any kind of physical process.  In this post I’ll talk about how to think about the economy as a whole in autocatalytic terms. But let’s start with something on a smaller scale, the process of baking bread:

(You can click on the images for bigger versions.) This is a variation on the diagrams I used in my previous post, except that I’ve changed the conventions a bit: I’m now using boxes to represent “stuff”, because it’s more traditional and because it’s easier to fit text into them, and I’m using hexagons to represent processes, because hexagons are cool.

Arrows always either go from a box (stuff) to a hexagon (process), meaning the process uses up the stuff, or the other way around, meaning the process creates stuff. The above diagram means that the process of baking takes in water, fuel, flour and human labour to produce bread.  It also uses up oxygen and gives off carbon dioxide, mostly because baking involves burning the fuel to create heat. I haven’t drawn the heat on the diagram, but it could be drawn just like the other products. In chemistry terms, the heat given off per unit bread produced would be called the enthalpy of the baking reaction.

The baker’s shop itself acts as a catalyst – it doesn’t get created or used up by the baking process, but it’s necessary in order for the process to occur.  I’m assuming the baker grows her own yeast, so she always ends up with a bit more yeast than she started with.  This means that, according to the definition in my previous post, the yeast is autocatalytic. This shouldn’t be surprising, because making more of themselves is what organisms do.

If I was being rigorous I would put numbers on all of the arrows, indicating how much of each of these things gets used or created, per unit of bread. In chemistry these would be called the “stoichiometric coefficients” of the baking reaction, and the coefficient on the outgoing yeast arrow would be slightly higher than the one on the incoming arrow. Since I don’t know the numbers and don’t want to clutter the diagram, I’ve drawn the outgoing arrow as a double one as a kind of shorthand for this.

This picture is a huge simplification of course.  In reality baking consists of many processes, including making the dough, allowing it to rise, kneading it, the burning of the fuel (which might take place miles away in a power station), and the actual conversion of dough into bread in the oven.  But it’s OK to lump all this together into single process as long as we remember that it’s really composed of lots of separate ones. (Chemists do this all the time.)

But instead of zooming in deeper into the details of the baking process, let’s zoom out a bit and look at what happens to the bread after it’s made:

I’ve added a second process to the diagram, representing the bread being eaten by people.  This uses up oxygen and produces carbon dioxide, because breathing is an integral part of how we extract energy from food. It also uses up some other food groups (otherwise you’d get rickets) and produces sewage, which must be disposed of.

I’ve also drawn it as producing “human labour”, representing the fact that once people have been fed they are able to work. Housing acts as a catalyst because it’s very difficult for people to eat and work if they don’t have somewhere to live.

People also reproduce, of course, and we need more things than these basics in order to live and work.  As in the case of baking, a more detailed diagram could include these things, but this one gets the point across well enough for now.

The double arrow from eating to labour represents the fact that you get more labour out of the combined baking/eating process than you put in, otherwise everyone would spend all of their time making bread and no-one would be able to do any other jobs. (It would be possible to work this out from the stoichiometric coefficients of the two reactions if they were included in the diagram.)  This results in an autocatalytic cycle, highlighted below:

More bread leads to more eating leads to more labour leads to more baking leads to more bread – as long as there’s a big enough supply of fuel, water, flour, oxygen, etc.

Here’s the big point I want to make in this post: the way the economy grows is through this type of autocatalytic cycle.  Economic growth is all about the physical self-reproduction of physical stuff.  It’s about more stuff leading to more stuff leading to more stuff, and when we say something contributes to the economy, we really mean it plays a role in this self-reproduction of stuff.  All this might sound terribly materialistic, but it’s not meant to be – the goal here is to understand economic growth, but I’m not saying it’s always necessarily a good thing.  Things like a high quality of living, high employment and a healthy environment are important, and in an ideal world the economy would be organised to maximise these things instead of, or as well as, growth.

At this point you might be thinking I’ve neglected something that’s usually considered very important when it comes to the study of economics: money.  You’d be right, but I think one of the biggest mistakes you can make when trying to understand economics is to think it’s all about money.  Money is an important tool by which the physical processes of the “real” economy are organised, but if we lived in a money-less command economy the processes in the diagram above would still happen, they’d just happen for different reasons.  They also happen if you bake your own bread at home. In that case no money changes hands, but the process still produces bread, still produces more capacity for labour, and thus still contributes to the economy.  Although money is terribly important in the general scheme of things, and it’s certainly important to understand it, I’ve chosen to try and understand the physical basis of the real economy first.

So anyway, let’s expand out even further from the diagrams above, and try to see where some of those processes’ other inputs come from.

I’ve included farming and the mining of fossil fuels as well as the economically hugely important production of nitrogen fertiliser through an industrial process called the Haber-Bosch process, which uses up quite a lot of energy. (Mind-blowing stat: globally, we fix more nitrogen per year through this industrial process than the entire biosphere put together.)

Ultimately everything on this diagram is powered by two sources: sunlight and buried fossil fuels.  One of these will last for a few more billion years but the other won’t, so this picture clearly represents a very temporary state of affairs. (The availability of fresh water is also ultimately due to the sun via the water cycle, but I haven’t put that on the diagram. You have to stop somewhere.)

A lot of the power from sunlight enters the system indirectly through the production of oxygen by natural ecosystems. One of the things I like about this approach is how quickly you have to deal with the fact that the economy can’t be seen as a separate system from the natural environment.

This diagram is a massive over-simplification of the real picture, and I’m sure I’ve left off some important arrows, but it’s already become very complicated.  Studying it for a while reveals that it’s absolutely chock full of autocatalytic cycles.  Most of them involve the food-human interaction.  More farming means more grain means more bread means more humans means more farming.  Or more fossil fuel burning means more \text{CO}_2 in the atmosphere means higher crop productivity means more humans means more fossil fuel mining means more fossil fuel gets burnt. (As you might expect from the diagram, carbon dioxide acts as a fertiliser.)

There’s also at least one autocatalytic cycle that doesn’t involve the creation of more humans: oil mining uses fuel but produces more fuel than it uses up (otherwise it wouldn’t be worthwhile). In general the growth of a business is autocatalytic, as well as the growth of the economy as a whole.  A business invests in capital, which then (hopefully) produces a return larger than the investment, allowing the purchase or construction of more capital.  It’s interesting to think about what these cycles look like for different types of business, but I’ll leave that for another time.

For now I’ve got to the point I wanted to get to with this post, where I’ve shown that the economy can be seen as a huge network of interrelated physical processes, some of which can be thought of as being like chemical reactions and others of which (like the Haber-Bosch process) actually are chemical reactions. I’ll leave you with the thought that other place where you’re likely to find big, complicated diagrams mapping interlinked networks of chemical processes is molecular biology, where these diagrams map out the metabolism of an organism. It’s an interesting comparison to think about.

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3 Responses to “The Chemistry of Economics”

  1. Yet another lovely thoughtful piece.

    The diagrams are like those you get from Life-Cycle Assessment (http://en.wikipedia.org/wiki/Life-cycle_assessment#Economic_input.E2.80.93output_life_cycle_assessment) or EIO-LCA (http://en.wikipedia.org/wiki/EIOLCA). They’re used in practice for things like carbon footprinting.

    Have you seen John Baez & co.’s long blog series about network theory on the Azimuth blog? http://johncarlosbaez.wordpress.com/2012/07/18/network-theory-part-19/ They look at the maths behind these reaction networks and link them to other networks like Feynmann diagrams, finding parallels with quantum mechanics and deriving a Markov process version of Noether’s theorem along the way.

    I was wondering if any of that machinery could help to identify the autocatalytic cycles in these networks… but it might not be easy, apparently finding them all is NP-complete (http://arxiv.org/abs/1110.6051).

    • Thank you for your kind comment and for the links. Especially for that last one – I’ve been looking for an algorithm to find autocatalytic cycles for ages (see my previous post http://jellymatter.com/2011/12/12/the-primordial-haze/), so I’ll be studying that paper carefully.

      I just came across John Baez’ network theory stuff the other week, which is part of the reason I got around to posting this. The stuff about generating functions in the last post made me go “huh?” and then “woah, that’s amazing.” But it seems to rely on assuming mass action kinetics (i.e. for any two particles, they have a constant probability per unit time of meeting and undergoing a reaction). This would severely limit its application to things like economics and biochemistry, where the kinetics are highly nonlinear and often unknown. But on the other hand it seems like there should be some clever generalisation that would get rid of the need for that assumption. It might take a while to spot it though.

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