Notes

1. A first attempt to establish a physical input-output table was made for Austria (Katterl and Kratena 1990) using input-output data for 1983. This pioneering study presented only incomplete results, especially with respect to primary inputs and final products.

2. A fund is defined as an agent in the sense of a natural or artificial system (worker, produced capital good, land) which is used and not consumed, as compared with a stock of goods which is accumulated and de-accumulated by flows. A flow is defined as a stock spread over time. A fund element enters and leaves the production process with its functional unit intact. A fund is a 'stock of services'. (For the production theoretical foundation of a 'flow-fund model', see Georgescu-Roegen 1971, ch. IX.)

3. As a complementary indicator the diagonal elements of the so-called 'Leontief inverse' (I — A)-1 can be used; insofar as the diagonal elements exceed unity the existence of circuits is indicated. In the German case all diagonal elements are very close to unity and therefore circuits are absent (for methodological explanations, see Strassert 2001b). Generally, it should be mentioned that the results also depend on the level of aggregation. In an early version of the German PIOT with nine activities there was also a comparable high degree of linearity, nevertheless some circuits could be identified (see Strassert 2000a, p.325).

4. Therefore, the authors continue: 'This means that water and carbon dioxide consumed in photosynthesis, together with water vapor and carbon dioxide produced by respiration (as well as combustion) must both be included. The same is true of oxygen consumed by respiration and combination and generated by photosynthesis' (Ayres et al. 2000).

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