Posts Tagged ‘Production functions’

There is an English expression that tells us that you can’t make omelettes without breaking a few eggs. This is usually taken to mean that in order to achieve something or make progress there are often losers in the process – true enough though a little hard. With a slight change of verb we can also state that: “You can’t make omelettes without using a few eggs.” This might sound blatantly obvious but its truth seems to have escaped not a small number of commentators on environmental issues and, it is sad to say, even some eminent economists as well. They tell us that as technology progresses we can dematerialize the economy – so we needn’t be too concerned about any supposed limits of resources or energy.  Of course this is fallacious; to use a nice Anglo-Saxon word, it is codswallop. But why?

If you don’t believe that such arguments for dematerialization are still put forward, consider these three recent examples:

Jesse Ausubel and Paul Waggoner write:

If consumers dematerialize their intensity of use of goods and technicians produce the goods with a lower intensity of impact, people can grow in numbers and affluence without a proportionally greater environmental impact.

Ronald Bailey of the neoconservative Reason suggests:

As long as market-driven technological progress is allowed to proceed, taxing and hectoring people into increased material poverty is not necessary to protect the natural world. And as polls show, people won’t put up with it anyway.

While Marian L. Tupy, of the similarly politically oriented Cato Institute, in an article entitled The Miracle that is the iPhone (or How Capitalism Can Be Good for the Environment), concludes:

Dematerialization….  should be welcome news for those who worry about the ostensible conflict between the growing world population on the one hand and availability of natural resources on the other hand. While opinions regarding scarcity of resources in the future differ, dematerialization will better enable our species to go on enjoying material comforts and be good stewards of our planet at the same time. That is particularly important with regard to the people in developing countries, who ought to have a chance to experience material plenty in an age of rising environmental concerns.

There are many more.

I have sincerely tried to find some validity in such arguments. I’d really like to; but try as I might I can’t.

Dematerialization – An answer to ecological and energy problems?

Utterances such as these are just one manifestation or variant of the belief in “techno-fixes” to the ecological and energy crisis we find ourselves in. They are reassuring but they are wrong. They need to be consigned to the dustbin of sloppy thinking. So let me try to do that, both from a strictly physical point of view and from the vantage point of real economics.

What lies at the heart of the physical arguments for dematerialization, such as they appear both in the quotations I have given above and elsewhere, is the view that as technology advances we are, and will be, more and more able to produce the same quantity of “goods” with less and less resources and also, indeed, that certain goods won’t require any resources at all.

Consider a couple of examples. Thirty years ago I had a stereo system that took up half my small room. Not only was there the large and beautifully designed turntable but also I had to have huge amplifiers, immense loud speakers and even separate “woofers” and “tweeters”. Nowadays, or so the argument goes, we can buy tiny iPods, mp3 players or mobile phones that can store and play thousands of songs – and films and books as well. Surely these use much less (material) resources to produce the same result – listening to music? Another line of argument cites supposedly truly dematerialized goods, like the information stored on software or on the internet. No need for printing books and the associated cutting down of trees!

In the case of iPods and the like I’ll ignore the use of fossil fuels or other energy sources involved in their production and transportation, as well as their use of some decidedly limited natural resources, such as noble metals. But even so it’s still not the case that these types of goods are dematerialized – they are not. For sure they do directly use less materials, such as wood, metal and plastic, in their manufacture than did my huge stereo system, but they still use resources and when we add in energy use to the equation maybe not that much less.

In the case of computer software and the internet, I’ll also put to one side the fact that these have in no way diminished the use of paper – our printers are churning out hard copies in ever greater quantities. Not only that, you can’t use software or the internet without a physical, materialized, computer. Anything that might appear dematerialized needs something material to make it useful, and that means the use of natural resources and, without doubt, energy as well.

Before considering the economics of all this, let’s take a look at physics. The dematerialization argument completely ignores the first two laws of thermodynamics. The first law, called “the conservation of matter and energy” tells us that you can’t make something out of nothing and hence, as ecological economist Herman Daly puts it: “All human production must ultimately be based on resources provided by nature.”

The argument for dematerialization completely ignores the first two laws of thermodynamics.

The second law of thermodynamics is usually called the entropy law. In non-technical terms this basically tells us that in any closed-system without the input of energy everything will, over time, deteriorate from order to disorder. Everything will become some sort of dead mush. In universal terms a “heat death” which is irreversible. Entropy increases. Not only that, but only things with order can do work and be useful. Over millions of years the sun has supplied energy to allow trees and animals to grow. The trees have order and we can burn them either to do work, to produce useful energy, or to make “ordered” goods. But after that we’re just left with useless waste. Plants die and are fossilized as oil. Oil has order and we can use it, but again after the work we’re left with “high entropic” waste in the form of heat and gases (such as CO2).

Whether in physical or economic terms, the production of any physical thing that has some order, and is thus useful and not a mush, requires either pure energy (as from the sun) or energy stored in matter. Remember Einstein showed energy and matter are convertible.

When asked whether the transformations of matter and energy required by economic activity are constrained by the entropy law, the usually very thoughtful Nobel Prize winning economist Robert Solow replied:

No doubt everything is subject to the entropy law, but this is of no immediate practical importance for modelling what is after all a brief instant in a small corner of the universe.

To which Herman Daly rightly responded:

Solow seems to identify the entropy law only with the ultimate heat death of the universe. … But the entropy law has more immediate and relevant implications: that you can’t burn the same lump of coal twice; that when you burn it once you get soot, ashes, CO2, and waste heat, as well as useful heat. The entropy law also tells us that recycling energy is always a losing proposition, that there are limits to the efficiency of conversion of energy from one form to another, and that there is a practical limit to materials recycling – all in the here and now, not just in the cosmic by and by.

If you want to produce anything at all you need both matter and energy and if you want to produce something with order and structure (and production and consumer goods are absolutely prime examples of this) you need to use at least as much (low entropy) energy and resources as inputs to achieve this as what you will get as outputs. In fact because of the severe wastages in the production process you usually need to input much more than you get out.

To think that physical goods can be produced without physical inputs and energy is to show not the slightest understanding of thermodynamics and science in general.

We can see this impossibility even more clearly when we look at what we actually need, desire and buy. We don’t live by iPods and software alone – though some teenagers seem to believe this to be the case. What do miniaturized or dematerialized houses, cars, planes, refrigerators or production-line robots really look like? Have you ever seen one? Will you?

Let’s look at the iPod/internet example again but this time from the point of view of some simple, though real, economics.

In the 1970s, my stereo “sound system” cost a lot of money. I had to save for some years to be able to afford it. As technology has advanced, not only have things got smaller but they’ve also got cheaper. It costs my daughter only a few weeks pocket money to be able to buy an amazing iPod. I’m even thinking of getting one myself. But what happens when such prices come down? Do we as individuals or as a society generally say: “Well that’s great! I can now use this freed-up disposable income to save for my retirement or give to charity?” In general we don’t. No, what we humans tend to do is go out and buy more stuff – more cars, more computers, more TVs and more mobile phones. This tendency is even exacerbated by the fact that consumer goods are now invariably designed with built-in obsolescence. Your mobile phone or computer starts to play up and go slow after a couple of years. Not only that but in the meantime there have appeared newer models with lots of additional “functionality”. No worries! We throw away the “old” mobile and buy a new one.

The first economic point is this: As technology improves and prices of technological goods fall, we don’t just buy the same amount of stuff (products) using less materials, what we do is buy more of the same stuff and lots more other stuff as well. The marginal propensity to consume out of technologically driven price reductions and the resulting extra disposable income is basically one. Never in the field of human economies has technology and miniaturization ever led to less demand and less resource use and I doubt it ever will. Demand for goods, demand for stuff, is infinite, and as in Say’s law, supply creates its own demand.

Coventional economic “Production Functions” ignore factor complementarity and assume complete substitutability as well as multiplicity.

A bit more economics. How we produce things has long been a central component of economics. Usually this is encapsulated in something economists call a “Production Function”. To use Adam Smith’s example of the production of pins, let’s think of ourselves as manufacturers of pins. I can decide that everything should be made by individual craftsmen, each of whom will take a certain time to produce a pin. The cost to me, before I add in my profit, will be the cost of the craftsman’s wages plus the costs of materials. On the other hand, I might decide that it would be better if I employed a bit of “capital” as well. I could use some capital goods – i.e. machines. If I do this I should be able to employ less labour. I can substitute capital for labour. Although the size of the available machines might be somewhat “chunky”, in general I can choose whatever combination of capital and labour will maximize my profits and chose the optimal combination accordingly. The key point is that the two factor inputs, capital and labour, are substitutes – more of one and less of the other. Economics takes a further step and considers technological progress. As technology advances I can produce more pins with the same amount of both capital and labour. Or I can produce the same with more capital and less labour.

But what is not explicitly considered is the role of natural resources – the metal, wood, and energy that is of necessity used. In economists’ production functions if these are considered at all (and usually they are not) they are seen as just another factor of production which can be had in unlimited quantities at the prevailing price.

Most importantly for the dematerialization issue is that just as capital and labour are viewed as substitutes for each other, so too are raw materials and energy viewed as substitutes for capital and labour.

Robert Solow, the “father” of modern growth theory wrote in 1974;

If it is easy to substitute other factors for natural resources, then there is in principle no ‘problem’. The world can, in effect, get along without natural resources.

Although this seems like a conditional sentence (if…then), Solow and many other economists have assumed it to be true.

 In 1972, economics professors Nordhaus and Tobin put it thus:

The prevailing standard model of growth assumes that there are no limits on the feasibility of expanding the supplies of nonhuman agents of production. It is basically a two-factor model in which production depends only on labor and reproducible capital. Land and resources, the third member of the classical triad, have generally been dropped… the tacit justification has been that reproducible capital is a near perfect substitute for land and other exhaustible resources.

Without any equivocation this means that I should be able to produce more and more pins by using more and more capital and/or labour while using less and less materials. But in the real world – if we can escape the fantasies of neoclassical economics – raw materials are not optional; you can’t endlessly substitute capital and labour for them. In fact raw materials are “complementary” to capital and labour – you need both.

Returning to making omelettes, if I  want to make some I can ask lots of my friends over to help me cook – to provide more labour – I can even invest in lots of stoves and pans. But however many friends, stoves and pans I have I can’t make any more omelettes than my supply of eggs will allow. If I have two eggs then maybe I can make one decent omelette on my own with one pan and stove. Adding more capital and labour will not change this equation. I can’t make 100 omelettes with two eggs however many friends and stoves I throw at the problem.

Not only does conventional economics assume that raw materials are complementary, it also assumes that the output gained from all factors of production are multiplicative, even if natural resources and land are included:

Most production functions are multiplicative forms – that is, the relationship among the factors is one of multiplication (e.g. the Cobb-Douglass production function). After all, what could be more natural than ‘multiplying’ together things that we call ‘factors’ to produce something we call a ‘product’! Unfortunately there is nothing in the real-world process of production that corresponds at all to multiplication. There is only transformation. This means that substitutability is built into these production functions from the beginning as a mathematical artefact, including substitutability between r (resources) and K (capital), and r and L (labour) – between funds and flows. In these multiplicative production functions, we can make one factor as small as we wish, while keeping the product constant, if we increase the other factor sufficiently. The only restriction is that no factor can be reduced to zero, but it can approach zero. But according to this logic, if our cook is making a 5-pound cake, he can increase it to a 1000-pound cake with no extra ingredients – just by stirring harder and baking longer in a bigger oven! – Herman Daly.

Making omelettes is a bit like putting Humpty Dumpty together again. Once you’ve cracked the eggs all the king’s horses and all the king’s men can’t put the egg back together again – the process is irreversible. Cracking eggs, like everything else, increases entropy.  I can eat a raw egg if I want and the energetic order in the egg will be converted into useful energy to keep me alive and, sometime later, will produce a bit of waste as well. If you want to make a tasty omelette or maybe a cake then you’ll have to add some extra ingredients as well. But make no mistake, absolutely anything we want to make that will be useful to us must obey both laws of thermodynamics.

In the real world you can’t make omelettes without using, and breaking, a few eggs. Dematerialization is a myth. A dematerialized economy is oxymoronic – and possibly the shortened version of this word as well.

If we are going to examine seriously possible reductions in the use of energy and material resources in the economy then let’s at least start with some grasp of physics and economics.