Jean Pierre van Rossem

Initial remark: I presented the first part of the text below already in 1978 at the KUL University in presence of Ernest Mandel. Paul de Grauwe was one of the followers of my presentation. In 2010 a student preparing a thesis on greenhouse gases asked me after a debate in Louvain if it was possible to use my energy value theory for pricing carbon emissions. I enlarged my theory with a second part and gave him the complete version to be used in his thesis. Although he wrote – apart from the introduction of my text on the energy value theory – a  high standing thesis himself, his work was only quoted 13 to 20, supposedly by the fact he was so frivolous to start from the work of Karl Marx, just as Marx was no economist at all, just some obscure philosopher.

Let’s start from the appointment that production is a physical process requiring input of energy, because without such input, production of wanted commodities or production in order to reduce unwanted commodities, is impossible. Input of energy concerns use of human energy, of bestial energy, of natural energy and of mechanical energy (of machines). Only the efficient used energy may be considered, not the wasted energy. Under conditions of capitalist production the owner of production means capitalises all forms of energy other than human energy. The milkman who used formerly a draught-horse on his milk-round considered bestial energy as his capital. The miller considers the used natural (wind) energy as his energy. The rail-company considers the mechanical energy consumed by his locomotives as his capital. Contrarily the worker, owning no capital, sells his labour force (=human energy) to the owner of production means. Labour force is not measured in labour time but, as any force, it is measured in spent energy (kilowatt, petroleum-equivalent, coal-equivalent, etc.) Without input of efficient human energy, there can be no input of all of capitalised forms of energy (bestial, natural and mechanical).

Commodities reduce needs, needs on more as well as needs on less. In their commodity form needs have an exchange value. The exchange value [w(i)] of a commodity reducing the need can be quantified as the (non-composite) efficient human energy eH(i) necessary for the production or reproduction of the need-reducing commodity iIt’s well understood that on the quantification we reduce the composite efficient human energy, delivered by schooled and skilled workers, to simple (= non-composite) efficient energy as should have been delivered by workers without schooling and without labour experience. From our definition of the exchange value we know that w(i) = eH(i), expressed in e.g. kilowatt-hour.

The transformation of the value of commodity i, expressed in energy quanta, into the monetary value of the same commodity is given by its price p(i) multiplied with the produced quantity x(i) of commodity i. The transformation of value i into prices depends upon what we can call the transformation coefficient θ(i) of commodity i. We thus can put that the monetary value of commodity equals the exchange value of i multiplied by its transformation coefficient, or that:

            p(i) x(i) = θ(i) w(i)                                                                                   [1]


            p(j) x(j) = θ(j) w(j)                                                                                   [2]

Equal change implies that commodities are exchanged against each other following their exchange value, or more that the transformation of exchange values, under conditions of equal change, into monetary values will be the same for all producers, i.e.      

            θ(i)  = θ(j)|"i, "j  = θ                                                                                  [3]

As soon as on a market of perfect competition one producer can increase the labour productivity more than his competitors j the value  of his commodities will be lower than those of and θ(i) ¹ θ(j) with  θ(j)|"j = θ

From the definition of the exchange value, nl. that w(i) = eH(i), and [1] en [2] follows:

            p(i) x(i) = θ(i) eH(i), and that                                                                   [4]

            p(j) x(j) = θ(j) EH(j)                                                                                  [5]

Under conditions of equal change all transformation coefficients are the same, as expressed by [3], so that the exchange ratio is given by:  

            p(i) x(i)/ p(j) x(j) = eH(i)/eH(j) w(i)/w(j)                                                  [6]

what implies that monetary expenditures for commodities are in the proportion of their exchange values.

What, however, happens under much more realistic conditions of unequal change? Then θ(i) ¹ θ(j). Let’s now have a look on the production functions in both sectors i and j. Eventually all production is a function of (1) the input of efficient used human energy eH and of (2) all inputs of capitalised energies eC, where the last is the addition of efficiently used bestial, natural and mechanical energy. In general terms that means that:

            x = f(eH, eC)                                                                                            [7a]

Without any input of human energy no production is possible. But technological progress makes it possible that capitalised energy replaces more and more human energy. If we name the substitution possibility of human energy by capitalised energy sHC the production function can also be written as;

            x = f(eH, sHC)                                                                                           [7b]

Substitution of [7b] in [4] and [5] learns:

            p(i) fi[eH(i)sHC(i)] =  θ(i) eH(i), and                                                         [8]

            p(j) fj[eH(j)sHC(j)] =  θ(j) eH(j)                                                                 [9]

That means that the transformation coefficients multiplied by their energy inputs are in proportion to the commodity prices multiplied by their energetic production function:

            p(i) fi[eH(i)sHC(i)] / p(j) fj[eH(j)sHC(j)] = θ(i)/ θ(j) * eH(i)/ eH(j)             [10]

Under perfect competition as dominant market form, prices for similar commodities are equal. Making profit is in those circumstances only possible by increasing a firm’s labour productivity more than that of the other competitors. If in the same sector the labour productivity of firm is higher than in all firms j, the commodities made by will be manufactured with a smaller input of human energy [and a sHC(i) > sHC(j)]. An increase in productivity leads always to a decrease of the produced value. Under conditions of perfect competition that implies that the transformation coefficient of will be higher than that of all j, so that (a small) profit will be possible for but not for the other j. Firm will be able to sell its commodities above their value because θ(i) > θ. So, the more an enterprise on a market of perfect competition can increase its productivity, the more it will be able to sell commodities above their (exchange) value. From [4] and [5] we learn, after dividing left from the equality sign and right from it by eH that:          

            p(i) LP(i) =  θ(i)  and                                                                                     [11]

            p(j) LP(j) =  θ(j)                                                                                             [12]

where LP is the labour productivity x/eH. The higher the labour productivity, the more enterprises will be able to sell commodities above their value. That induces a continuous run to increase the use of capitalised energy. In the long run perfect competition cannot persist and the dominant market form of perfect competition will switch into oligopoly capitalism or monopoly capitalism by expulsion of the weaker firms from the market. The continuous accumulation of capital (increasing continuously the input of more capitalised energy in the production) will lead to the disappearing of perfect competition and of the equal exchange. The new market form will be oligopoly capitalism or monopoly capitalism where unequal exchange has replaced equal exchange.

The advent of production under conditions of oligopoly- or monopoly capitalism had a serious impact upon the realisation of profit. Profit (PRF) is nothing else than realised surplus value m on selling produced commodities on the market. Under conditions of perfect competition no firm is able to set prices [p(i) = p(j)|"i, "j ] and the lonely way to make profit is by producing commodities with a higher labour productivity than the rest of the competitors within the same sector s. Indeed surplus value per unit is:

            m(i) = w(s) – w(i)                                                                                          [13]

then profit equals

            PRF(i) = p m(i) = θ(s) w(s) – θ(i) w(i)                                                             [14]

In view of [11] and [12]:

            PRF(i) = p m(i) = p LP(s)w(s) – p LP(i)w(i) = p eH(s) – p eH(i) =

            p [eH(s) – eH(i)]                                                                                              [15]

so that

            m(i) = eH(s) – eH(i)                                                                                         [16]

The lonely way to make profit on a market of free competition is to create a surplus value by producing more productively than the rest of the sector. Under condition that all what was produced by is effectively sold, the realised profit PRF(i) = p m(i) will be [eH(s) – eH(i)]. That profit will be modest, something that was always hold by the neoclassical economy on analysing the situation of perfect competition. Only if per commodity the input of efficient non-composite human energy of a firm is lower than the similar input on the rest of the market, profit can be realised.

A whole other situation is the case on a market where imperfect competition is the dominant market form. Here producers are no longer dependent from the market: they have the possibility to set their own price as p(i) ¹ p(j), the more the less number of competitors on the market is. They can sell their commodities far above their value by increasing the transformation coefficient. So they have the possibility to realise extra profits (symbol Δ), something being excluded under perfect competition.  Under the condition that all produced commodities are sold total profit of enterprise I, selling commodities above their value, can be written as:

            Δ(i) = p(ix(i) – θ(pfw(i) = θ(iw(i) – θ(pfw(i) = [θ(i) – θ(pf)] w(i)                     [17]

Where  θ(pf) is the transformation coefficient as it should have been on a market of perfect competition.

Two remarks.

 (1) The energy theory of value, contrarily to the Marxian labour theory of value, comes not to the conclusion that the surplus value is the direct result of exploitation of the workers by the capitalist. Such conclusion was only possible by using time as measurement of value: value of commodities as well as value of labour force. In Marxian thinking the workers create the value of commodities by selling their labour force to the capitalist. For the reproduction of their labour force less time is needed than for the production of commodities. The difference is the surplus value which is appropriated by the owner of production means (capital). But how Marx calculated the value of the delivered labour force? He put that it is the value of all commodities the worker needs to reproduce his labour force. That is a very subjective criterion. The Cambridge UK specialist in value theories, Maurice Dobb, has admitted, together with Marx, that the time needed to reproduce the labour force had an “historical and moral” basis. On speaking about Marx’s labour force, Dobb wrote:

Labour power (…) he (= Marx, jpvr) defined in Capital as ‘energy transferred to a human organism by means of nourishing matter’ and as ‘the aggregate of those mental and physical capabilities existing in human being which he exercises whenever he produces a use-value of any description’. The ‘nourishing matter’ needed to replace the energy used-up in work was the material input; and the possibility and dimensions of surplus-value depended upon the value of the former being less than the value ‘created’ as output by the labour is sustained.

But if the reproduction of labour force is a question of energy why then working with time units and not with energy units?  If we express the input of labour in the production process in e.g. kW, what else can we say over its reproduction than it needs the same quantity of kW? Surplus value originates not as a result of exploitation, but as a possibility to sell commodities slightly above their value under conditions of perfect competition (cf. [16]) or heavily above their value under conditions of imperfect competition (cf. [17]).

(2) It should be incorrect to believe that it is impossible to quantify θ(pf). Reasoning in the style of the neoclassical marginalists pricing on a market of perfect competition demand and supply determine the market prices so that the average revenue and the marginal revenue fall together, being a line parallel to the x-axis. Where the marginal cost curve intersects the marginal revenue line one finds which quantity a firm should produce. On a monopoly market the average revenue is a line with a negative slope, and the marginal revenue a line with a slope twice as sharp as for the marginal revenue. Where the marginal cost curve intersects the marginal revenue line one finds which quantity of a commodity should be produced at what price to realise the maximum profit. If we remember that under conditions of perfect competition perfect equal exchange is the rule, the price guaranteeing a break even is the one allowing no profit. That corresponds in the neoclassical economy with the intersection of the average cost curve with the average revenue curve. θ(pf) can thus be perfectly quantified without any need on the marginal concepts of the neoclassical economy.

*   *   *

An advantage of the here presented energy theory of value is that it can be used in pricing the emission of greenhouse gases. Let’s thus apply the energy value theory on the abatement (As) of greenhouse gases in a sector (where is e.g. one of the sectors as enumerated by the IPCC, i.e. the Inter­governmental Panel on Climate Change) Let’s assume that – certainly in the short run – the emission of greenhouse gases in sector is a fixed amount as of the production xs in a certain sector s. Then the total production of greenhouse gasses xs(gg) = as xs. The need on less greenhouse gases is a collective need – a need on less – and an authority (regional, national or supranational as in the EU ETS system) has to decide with what percentage ls the emission of greenhouse gases must be reduced to reach the wanted abatement (As). Then As= las xs, where As is the quantity of greenhouse gases (not in percentage, but in tCO2) the authority decided to reduce, so that 

            As= ls xs(gg) las xs                                                                                        [18]

Following the by us proposed energy theory of value, the exchange value of the abatement, reducing the need on less greenhouse gases, can be quantified as the (non-composite) efficient human energy necessary for the production or reproduction of the wanted abatement. From ps xs = θs ws (conform with [1]), and thus also xs = θs ws / ps we know after introduction in [18] that

            As= ls  xs(gg) las θs ws / ps                                                                            [19]

Due to xs(gg) = θs(ggws(gg) / ps(gg) equation [19] can be rewritten as:

            As= ls xs(gg) =ls θs(ggws(gg) / ps(gg)                                                                [20]

where ps(gg) is the price we have to pay for the abatement  of one tonne greenhouse gases. From [19] and [20] we learn that:

            as lθs ws / ps  ls  θs(ggws(gg) / ps(gg)                                                     [21]

so that:

            ps(gg) = (ps/as) . (θs(gg)/ θs) . (ws(gg)/ws)                                                        [22]

and since, due to our definition of exchange value, being equal to eH, equation  [22] can also be written as:

            ps(gg) = (ps /as) . (θs(gg)/ θs) . (eH(gg)/eHs)                                                   [23]

In the short run the two transformation coefficients in [23] will be nearly equal [θs(gg) @ θs] (this will certainly be the case when the monopoly degree is the same for gg and s). In absence of the possibility of switching in methods of production the quotient eH(gg)/eHs will be a constant k . as where k  will be the higher  the lower the switching possibilities are (even k = ¥ if there exist no switching possibilities at all). Where switching techniques exist (k = low) an additional input of human energy eH(gg), not only in the emission reducing sector s, but also by its subcontractors, will be needed to succeed the switch. So we can write that:

            eH(gg)/eHs = k . a + ßs  eH(gg)                                                                          [24]

Introduction of [24] and θs(gg)/θs @ 1  in [23] gives:

          ps(gg@ ps . [ k + (ßs/as) . eH(gg)]                                                                       [25]

where ps(gg)/ps is nothing else than a linear equation in eH(gg) so that and ßs acan easily be found with the method of the least squares.

ps(gg) is the price to be paid on reducing emission of CO2 in sector by 1 tCO2. For practical calculation one needs to have access to ps and eH(gg) during several quarters or years. Calculation of eH(gg), that is the input of human energy needed for switching of techniques, is only possible on using input output tables for the studied sector. An iterative calculation process will reveal after a limited number of steps the price to reduce CO2 emission in sector by one tonne.  

The above approach may be considered as a completely method of pricing carbon. As most of the value theories are no longer applied since at least a half century and as they have been replaced by the neoclassical approach with the marginal costs, economists seem to have forgotten that monetary values are still always transformed values instead of “transformed air” as in the neoclassical approach.

The quantified ps(gg)|"with s=1,n don’t show the extreme volatility of the carbon prices as formed under the EU ETS system. Even for the power plants, with their volatile prices ps – due to the impossibility for storing electricity – the quantified ps(gg) will be much more stable than in the EU ETS system. One has to realise that the EU ETS approach is only the second best and that carbon pricing under such conditions has no longer any link with a value theory. Carbon pricing as regenerated by the EU ETS became a pure question of speculation at stock exchange. A large part of what is paid goes now into the pockets of banks and brokers, without the smallest influence on real abatement. The major weak point in the EU ETS is that if the forecasts for production are too liberal (as was the case during the trial period) pricing carbon becomes an illusionary system of real abatement of greenhouse gases. That can explain why in 2007 and early 2008 allowances for carbon emission had no longer any price. For 2008 to 2012 het situation hardly changed. The only effect was, that due to grandfathering and windfall profits, power plants could increase their prices, as asked to the consumers, could be increased with the freely got allowances (grandfathering) without any evidence that there was a real abatement on greenhouse gases. Pricing carbon became a game for speculators, not interested in any abatement, but mainly interested in high speculative profits on the futures market.

On searching again a relationship between pricing of carbon and the exchange value of it, one finds the norm for the real cost of abatement. The difference between the asked abatement [ls  xs(gg)] and the realised abatement [ls  xrs(gg)] should become the ultimate basis for implementation of the carbon tax system. If the difference between the two is positive, that means that the realised abatement by was too low and that a carbon tax of p(gg). l. [(xs(gg) –  xrs(gg)] will to be paid to the controlling authority. Should the difference [(xs(gg) –  xrs(gg)] be negative – what means that the realised emissions reduction is larger than what was required – the sector s, realising such, will receive from the controlling authorities an amount equal to of ½p(gg). l. [(xs(gg) –  xrs(gg)]½ in absolute value.

Defenders of the EU ETS know very well that it is only the second best as compared with a carbon tax based upon a workable value theory. That the carbon tax was never accepted within the EU is explained as follows:

The European Commission proposed an EU-wide carbon energy tax in 1992 (…). Opposition to the proposal came from two powerful sources. First, some nations regard member state autonomy in taxation as a core value, not to be relinquished even if the environment would benefit. The view is that the power of taxation is so central to management of an economy that, if it is foregone, national autonomy will be compromised. While the carbon energy tax was presented, correctly, as a special case, it was regarded by some as the thin edge of the wedge, to be followed inevitably by other taxing initiatives that would incrementally leak fiscal autonomy from member states to the Commission. Because fiscal measures require unanimity, this strong ideological opposition proved impossible to overcome. Second, the main industry lobbies, represented most clearly by UNICE, also opposed the tax, with consistent and persistent case-making at the member state and the EU levels.”

In the end, there was some harmonisation with regard to the minimum rate of taxes and excise duties applicable to energy products. These moves codified what was already in place at the member state level, without any features specific to carbon or greenhouse gases. The opposition to the carbon energy tax proved too strong; the proposal was formally withdrawn in 1997.

Recently Peter Newell and Matthew Paterson studied the possibility if capitalism can survive the challenge of global warming induced by emissions of greenhouse gases. In a review of their book David Levy added the following remark:

On opting only for the second best, not for a radical carbon tax, the question raised if capitalism can effectively respond to climate change being of another order than ozone depletion or acid rain. The development of modern industrial societies relied on fossil fuels as cheap source of energy for manufacturing, transportation and all kinds of energy systems. Carbon intensive lifestyle in the reach of billions of the world’s population, aspiring to own cars and electronic appliances, to live in spacious homes with heating and cooling, and to fly by big planes on vacation let forgot that capitalism had a pay a toll on it, that of global warming. When the Western world became aware of that toll, new rapid growth countries, such as China, Brazil and India, built their welfare upon the same carbon-intense lifestyle the wealthy Western world adopted decades earlier.”

Attempts of climate denial, pouring millions of dollars in lobbying efforts by fossil fuel industry, continue, lobbying against regulation. Forging carbon markets was eventually only possible in a capitalistic context after banks and brokers found a system to earn good money through the emissions reduction system. Going with carbon allowances to stock exchange – much less interested in the real abatement of greenhouse gases than in the real possibilities for speculation – was only possible when banks and brokers received guaranties that they could make enough profits through the system. That also explains why carbon tax was never accepted and why it was replaced by an ersatz mechanism as the EU ETS without clear guarantee that the system would effectively contribute to a serious reduction is the coal abatement. Earning money by grandfathering, through windfall profits, through commissions and speculation, was the lonely language carbon capitalists understood. Earning money in the name of carbon reduction was so much more important than the reduction itself.


In pure Marxist terms the owner of production means capitalizes machinal-, bestial- and natural energy as “constant capital” eC, but also human energy eH as variable capital.

In economic theory conditions of unequal exchange were studied in depth by Alghieri Emmanuel. Cf. Emmanuel, Alghieri (1975), L’Échange inégal. Essai sur les Antagonismes dans les Rapports Économiques Internationaux. Paris : François Maspero.

In 1970 Jean H.P. Paelinck, then of the University of Namur, published an interesting specification of the production function. On working no longer with L (labour) and K (capital) but with inputs of human energy and capitalised energy one comes to a function x(i) =k(i)  eH(i) exp[eH(i)/EC(i)]²  based upon the assumption that the labour productivity (x(i)/eH(i) is a function of the substitution possibility of human energy by capitalised energy, thus sHC. In that equation “exp” stands for the number = 2.71… On introducing a Paelinck variant of the energetic production function in [4] and [5] we obtain:

                  p(i) k(i)  eH(i) exp[eH(i)/eC(i)]²/ p(j) k(j)  eH(j) exp[eH(j)/eC(j)]² = θ(i) eH(i)/ θ(j) eH(j)                                                            [10b]

In this equation we can eliminate behind k(i) the factor eH(i) and behind  k(j) the factor eH(j) after dropping the ratio eH(i)/eH(j) on the right side of the equation. Moreover k(i) exp[eH(i)/eC(i)]² is nothing else than the labour productivity of i, abbreviation LP(i). On a simular way k(j) exp[eH(j)/eC(j)]² is nothing else than the labour productivity of j, abbreviation LP(j). Introduction in [10b] gives:

              p(i)LP(i)/p(j) LP(j) = θ(i)/ θ(j)                                                                                                                                                                                [10c]

The transformation coefficients of two commodities are in proportion to the prices of those commodities multiplied with the labour productivities in both firms. See also the equations [11] and [12]. The original production function of Paelinck in the wrong L & K terms  was presented at the September Program of the European Meeting in Brussels. Cf. Paelinck, Jean H.P. and J. Soenens (1970), “A Workable Putty-Soft Production Function for Belgium,  Institut für Statistik und Ökonometrie, Vol. 23 (Discussion Paper). Their  specification of the neoclassical production function became popular at the ULB, DULBEA and the Cahiers Économiques de Bruxelles after Françoise Thys-Clément used a Paelinck production function in her doctoral essay at the ULB in 1976.  Until today, always ignoring the results of the Cambridge-Cambridge controversies, several ULB economists continue working with the L & K variant of the Paelinck function. See also: Thys-Clément, Françoise (1976), Une Généralisation Dynamique de la Théorie de Tinbergen sur la Politique Économique, Brussels, Éditions de DULBEA (later also reprinted in Cahiers Économiques de Bruxelles).

If on a market of perfect competition one producer reaches a higher labour productivity than all his competitors he can sell the same commodity at a lower price without making losses. So he can enforce all his competitors to lower also their price so that they are obliged to work with serious losses. That’s the way to expel them from the market.

From the start of the Industrial Revolution until the end of the 19th century the British economy, swearing by the mechanical energy of steam machines was dominating the world economy. Towards the end of the 19th century the United States and Germany started replacing much of the mechanical energy from steam machines by mechanical energy from electrical power plants. It became the start from a new period of accumulation of capital and at the early beginning of the 20th century the United States, later followed by Germany, were the new leading economic powers in world economy. It was the end of a long period of equal exchange and the start of oligopoly capitalism.

Marx, Karl (1867), Capital Volume 1, Harmondsworth: Penguin Books Ltd, 1976, pp. 150-151.

Dobb, Maurice (1973), Theories of value and distribution since Adam Smith. Ideology and economic Theory, Cambridge: Cambridge University Press, p. 152. This survey is obviously inspired by Robinson, Joan (1956), Accumulation of Capital, London: Macmillan Press, 1969, 3rd edition [cf. Dobb (1973), pp. 233-234 and p. 234n]. None of the existing price theories – themselves the weak point in economic theory – can be applied on artificial commodities such as emission allowances.

Ibidem, pp. 150-151.

Ibidem, p. 152: “Just as Ricardo had done, Marx made it plain that he did not intend the ‘value of labour power’ in the sense of purely physical substrance: into the practical definition of what was deemed ‘necessary’ at any time and period there entered an ‘historical and moral element’.” This is a very weak argument to avoid working with energy quanta that let no room for the reproduction of e.g. 20,000 kW human energy, sold as labour force, by a much smaller amount for the reproduced labour force. An amount of kW can only be reproduced by at least kW. And that has nothing to do with ‘historical and moral elements’, at least not if one wants to develop an “objective scientific” value theory which Marx and the Marxians always pretended to exercise.

That does not imply that under conditions of perfect competition the boss of a (small) firm – under perfect competition the majority of the firms are all small firms – and his helpers receive nothing. What they receive will just be the equivalent of an hour wage multiplied with the number of worked hours. Saying that (nearly) no profit is possible under conditions of perfect competition and of equal change, is saying nothing else than that no extra profit is possible (what is well the case on markets of imperfect competition).

It’s obvious that the value of a produced good depends upon all efficient non-composite human energy in the production of that good, included the input of human energy in all parts of that good (e.g. raw materials) plus the wear and tear of the (constant) capital – i.e. the used machines – during the production of that good. That’s why Nobuo Okishio starts his presentation of the labour value theory with the formula ti = Σaij + τi (i = 1, …. ,n), where aij is the amount of jth goods, where τi is the direct labor input needed to produce one unit of ith goods, and where ti is the value op the good, expressed in time units. Cf. Okishio, Nobuo (1955), “Monopoly and the Rates of Profit”, Kobe University Economic Review, 1, pp.71–88. On working that way, one is obliged to use input-output tables in order to know the technological coefficients aij. That implies that the transformation process of values into prices will result in complicated matrix algebra. If one starts from the introduction of transformation coefficients θi  like I did one can avoid those complications. Concerning the calculation of θi  on a monopolistic market, one should consider that the revenue curve is intersected twice by the cost curve in the two break even points. For the calculation of θi  one has to work with the first break even point.

By As we don’t mean the percentage of emission reduction, but the effective reduction of greenhouse gases emissions in (e.g.) million tonnes.

Ellerman, A. Denny, Frank J. Convery and Christian de Perthuis (eds) (2010), Pricing Carbon. The European Union Emissions Trading Scheme, Cambridge: Cambridge University Press, p. 162 give an enumeration of the sectors considered by the ETS proxy.

as  is  the emission rate per unit of output for sector s.  If = Portland cement (Pc), aPc  is  0.7 as the production of one tonne of cement emits 0.7 tonne CO2. For some sectors, e.g. the iron and steel production, one has to make a distinction followed the used production method. A typical Western BOF steel mill (BOF = basic oxygen furnace) emits 1.95 t CO2 per tonne of semi-finished steel (asBOF  = 1.95), whilst electric arc furnace plants emits 0.23 t CO2 per tonne of semi-finished steel (aselecfu  = 0.23). For primary aluminium production one notes 2.4 to 2.8 23 t CO2 per tonne of aluminium  (2.4 < aalum < 2.8).  For oil refining a oscillates between 0.078 and 0.083 t CO2 per tonne of refined oil on using the simple hydroskimming (HSK) method. On combining HSK with such techniques as visbreaking, fluid catalytic cracking, etc. a can reach between 0.129 to 0.154 t CO2 per tonne of refined oil. Sources: Ellerman, A. Denny, Frank J. Convery and Christian de Perthuis (eds) (2010), op.cit., p. 196 (cement), p. 205 (iron and steel), p. 220 (oil refinery) and p. 225-226 (aluminium). The most intensive CO2 intensive of all energy forms produced by the power plants is electricityCf. Enevoldsen, Martin  (2005),  The Theory of Environmental Agreements and Taxes. CO2 Policy Performance in Comparative Perspective, Cheltenham/ UK/Northampton, MA, ISA: Edward Elgar, p. 178. Here there is an extra problem, known as  “abatement through fuel-switching” , cf. Delarue E., A. Denny Ellerman and  W. D’haeseleer (2008), Short-term CO2 Abatement in the European Power Sector, Working paper n° 2008-008, Boston: Center for Energy and Environmental Policy Research, MIT. Depending upon the gas/coal ratio, and depending upon the power output in GWatt the CO2 emission abatement can vary between 0 to 29 kilo tonnes/hour.

That is certainly NOT the simple input of human energy used by s, but also the amount of human energy used by all other factories haven delivered commodities to s.Quantification of eH will always be based upon the technical coefficients of input-output tables. Moreover the human energy necessary for the reproduction of the capital use, both by  and by the subcontractors must also be considered.

It concerns a topic having been studied in depth by Sraffa. Cf. Sraffa, Piero (1960), Production of Commodities by Means of Commodities. Prelude to a Critique of Economic Theory, Cambridge: Cambridge University Press, 1975.pp. 81-87.

Ellerman, A. Denny, Frank J. Convery and Christian de Perthuis (eds) (2010), op.cit. p. 174: “Fuel-switching refers to the ability of power plants with lower emission rates per unit of output, typically fired by natural gas, to substitute within the electrical grid for higher-emitting power plants, typically coal-fired. Electricity is produced by a number of plants, all of which generate electricity and provide varying amounts of power to the electrical grid, from which customers draw the electricity they consume. The amount of electricity generated and supplied by a particular plant depends on the load, or demand, which varies considerably on a daily, weekly and annual basis, as well as on the relative cost of generation at that plant.”

Ellerman, A. Denny, Frank J. Convery and Christian de Perthuis (eds) (2010), op.cit. p. 16.

Newell, Peter and Matthew Paterson (2010), Climate Capitalism. Global Warming and the Transformation of the Global Economy, Cambridge; Cambridge University Press.

Levy, David (2010), “Review of Climate Capitalism: Global Warming and the Transformation of the Global Economy by drs. Peter Newell and Matthew Paterson”, URL:

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