The laws of physics most constraining to technology (and therefore to economics) are the first and second laws of thermodynamics. The first law of thermodynamics is the law of conservation of mass/energy. Since mass and energy are equivalent in the sense of interconvertibility (Einstein's equation, E = mc2), this law actually implies that mass and energy are separately conserved in every process or transformation except nuclear fission or fusion. Putting it another way, any process or transformation that violates this fundamental condition is impossible. In more familiar language, it is impossible to create something from nothing. Tjalling Koopmans expressed this principle as 'the impossibility of the land of Cockaigne', and made use of the theorem in developing his mathematical treatment of 'activity analysis', an extension of input-output analysis and one of the first serious attempts, after Leontief, to model technological dynamics in a multi-sector world (Koopmans 1951).
The impossibility of creating something from nothing and its converse, the impossibility of converting something, such as a waste into nothing, have surprisingly non-trivial consequences for neoclassical economics. Contrary to the more superficial versions of standard theory, where goods and services are mere abstractions, production of real goods from raw materials inevitably results in the creation of waste residuals. In standard economic theory 'consumption' is a metaphor and wastes are not considered at all. In reality, since waste residuals have no positive market value to anyone - in fact, they have negative value - but do not disappear by themselves, they tend to be disposed of in non-optimal ways.
The most common approach to waste disposal in the past, and still normal in most parts of the world, is dumping into waterways or burning. Either method of disposal involves using common-property environmental resources as sinks. This causes harm, ranging from serious illness to dirty collars, to people who obtained no benefit from the original economic use of the material before it became a waste. But standard economic theory does not allow for damages to third parties; it presupposes transactions only between mutual beneficiaries. Disposal of harmful wastes to common property environmental resources by dumping or burning creates a built-in market failure, or externality. In fact, this externality is not rare or exceptional, as earlier theorists sometimes claimed. On the contrary, it is pervasive because it is an automatic consequence of the fact that the economy has a material basis (Ayres and Kneese 1969).
As hinted above, the quantity of waste materials associated with raw material extraction approximates the total quantity extracted. On the other hand, it far exceeds the amount of useful product. For instance, about 160 tonnes of copper ore must be processed to yield a tonne of virgin copper. For scarcer metals, like silver, gold, platinum and uranium, the quantities of waste material per unit of product are enormously large. Even in agriculture, the quantity of biomass needed to support a human population, especially if a significant part of the diet consists of animal products, is many times the actual quantity of food consumed.
The materials-balance principle, derived from the first law of thermodynamics, is evidently a useful tool for estimating waste residuals from industrial processes, since the outputs of one sector become the inputs to another. Comparing inputs and outputs it can be seen that substantial mass is 'missing' at each stage. Even where the process technology is unknown, it may be sufficient to obtain data on purchased inputs and marketed outputs.
The first law of thermodynamics - conservation of mass-energy - is directly applicable to every process and every process network. It is therefore applicable to every firm. This means, in words, that, over the life of the process-chain, the mass of inputs (including any unpriced materials from the environment) must exactly equal the mass of outputs, including wastes. For a continuous process, this balance condition must hold for any arbitrary time period.3 The materials-balance condition is much more powerful than it appears at first glance, since chemical elements do not transmute into other chemical elements under normal terrestrial conditions. (The alchemists were on the wrong track; there is no practical terrestrial process for converting base metal into gold.) Taking this into account, the massbalance condition holds independently for each chemical element. Moreover, in many processes, non-reactive chemical components, such as process water and atmospheric nitrogen, can also be independently balanced. Thus half a dozen, or more, independent materials-balance constraints may have to be satisfied for each steady-state process.4 This fact provides a powerful tool for imputing missing data.
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