Abstract
Since Stone’s original work, input output methodology has taken a great step forward in standardizing the procedures employed for the derivation of monetary input output tables which in turn, e.g., are used to measure the energy requirements of commodities. In this methodology there exist two basic (mechanical) ways, or “technology” assumptions, by which such measures under circumstances of joint production can be defined. The physical effects of these assumptions on the measures obtained, however, have not yet been analyzed sufficiently. This chapter presents such an analysis on the basis of technological conditions of a quite general kind, including joint production, and shows that even then these two measures of energy requirements will give rise to economically well-grounded expressions, i.e., do not represent measurement without theory. The expressions obtained will allow us to prove several assertions within their respective ranges of applicability, which complement each other to some extent.
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Notes
- 1.
We thereby dispense with the “homogeneity assumption” customarily made (see United Nations 1973, p. 20).
- 2.
See the final remark in Sect. 7.2 for a description of these symbols.
- 3.
Postmultiplying the matrix B of unit-cost structures of industries by C − 1 (to obtain the table A) just converts these structures into the unit cost structures of commodities.
- 4.
This, however, is devoid of economic content as no meaningful interpretation of the matrix XM − 1 will exist in general (see also the following examples).
- 5.
See Armstrong (1975, p. 78ff.).
- 6.
This is because (at least at present) voluminous negative entries of A (and thus negative entries in A ∗ ) are not likely to be reported in the light of the methods currently applied – a fact, which, however, does not deprive the hypothetical situation we have exemplified above of its conceptual importance for a proper development on input–output analysis.
- 7.
Not used here in the narrow sense of fixed output proportions (see Proposition 7.12).
- 8.
Note that by this procedure it is not necessary to know the industrial origin of the inputs (or the destination of the outputs).
- 9.
- 10.
Neither this assumption nor Assumption 1 are of the weakest possible kind to allow for these conclusions. This topic is, however, not central to our problem of analyzing the two different concepts of energy requirements \(\overline{r}\) and \(\overline{c}\) defined here. Weaker assumptions than the one considered above (which assumes that energy is a direct input with regard to every industry) can be obtained, e.g., from the analysis of basic commodities that is supplied in Flaschel (1982). For simplicity, however, the assumption \({\overline{X}}_{1} > 0\) is retained for the remainder of this chapter.
- 11.
In the light of the demonstrated possibility of reducing both of our measures \(\overline{r}\) and \(\overline{c}\) to the monetary expression \({A}_{1}{(I - A)}^{-1}\) (depending only on what type of “technology” assumption is being used), the formula (3) which is proposed in James (1980, p. 176) does not appear entirely convincing to us. Translated into our notation it would be based on an expression of the kind \({\overline{X}}_{1}\hat{{g}}^{-1}{(I - A)}^{-1}\), that is, one where no full transformation of the vector of energy inputs X 1 (into A 1), corresponding to the complete set of rearrangements made with regard to the matrix A, is accomplished.
- 12.
A solution to this program describes the extra energy consumption that is absolutely necessary to allow for the assumed change in final demand with regard to the technological alternatives that are now available.
- 13.
This theorem is often considered as a justification for the assumption n − m we made in Sect. 7.3.
- 14.
Related with this distinction between optimal and average energy requirements is the fact that the latter (but not the former) can be supplemented by the important concept of individual energy costs [compare (7.9)].
- 15.
A similar situation and proposition with regard to single-product activities, prices of production and the primary factor labor is examined in Roemer (1977).
- 16.
Note in this connection that the employed assumption on cost reduction p′U + ≤ p′U (a vector inequality in terms of initial prices p solely!) means that the new activities, i.e., the columns of matrix U which actually change, will be regarded as superior and will therefore be adopted by entrepreneurs (if static price expectations prevail). As a consequence of the implied technical change, however, prices p in all probability will be subject to change. But, though this may cause further changes with regard to energy costs \(\overline{c}\) which may endanger the derived inequality \({\overline{c}}^{+} = \overline{c}\), this cannot invalidate the assertion made on total energy saving (Proposition 7.13) if no further change in \({\overline{c}}_{1}^{+}\) takes place.
- 17.
With an index “+” in the second case, of course. Note that the change in total energy use \({\overline{X}}_{1}i -{\overline{X}}_{1}^{+}i\) will be equal to the sum of two effects \(\bar{c}' - (\bar{{c}}^{+1})')\bar{f} + (\bar{{c}}^{+})'(\bar{f} -\bar{ {f}}^{+})\) if the assumption \(\overline{f} = \overline{f}+\) is dropped, which thus may lead to an increase in total energy consumption if the demand effect \(({\overline{f}}^{+}{> \atop =}\bar{f})\) is sufficiently strong of offset the saving of energy that is implied by the first item in the above sum (see Reardon 1973, p. 41ff. for a practical computation of this kind).
- 18.
Note in this regard that our object here has not been to consider (marginal) investment decisions based on given prices (see Helliwell and Cox 1979 for a joint product example of electricity cogeneration of this kind – making no use, of course, of the market value method), but to introduce a sensible generalization of average energy costs which overcomes the difficulties of joint production on the abstract level of input–output methodology.
- 19.
See Gigantes (1970, p. 282) for such an assertion.
References
Armstrong, A. G. (1975). Technology assumptions in the construction of U.K. input–output tables. In R. I. G. Allen & W. F. Gossling (Eds.), Estimating and projecting input–output coefficients (pp. 68–91). London: Input–Output Publishing Company.
Dickey, R. I. (Ed.) (1960). Accountant’s cost handbook. New York: Ronald
Flaschel, P. (1982). On the two concepts of basic commodities for joint production systems. Journal of Economics, 42, 259–280.
Folk, H., & Hannon, B. (1974). An energy, pollution, and employment policy model. In M. S. Maerakis (Ed.), Energy: Demand, conservation, and institutional problems (pp. 159–173). Cambridge, MA: MIT Press.
Gigantes, T. (1970). The representations of technology in input–output systems. In A. P. Carter & A. Bródy (Eds.), Contributions to input–output analysis (pp. 270–290) Amsterdam: North-Holland.
Gupta, S., & Steedman, I. (1971). An input–output study of labour productivity in the British economy. Oxford Bulletin of Economics and Statistics, 33, 21–34.
Helliwell, J. F., & Cox, A. J. (1979). Electricity pricing and electricity supply. Resources and Energy, 2, 51–74.
Herendeen, R. A. (1974). Use of input–output analysis to determine the energy cost of goods and services. In M. S. Maerakis (Ed.), Energy: Demand, conservation, and institutional problems (pp. 141–158). Cambridge, MA: MIT Press.
Howe, Ch. W. (1979). Natural resource economies: Issues, analysis and policy. New York: Wiley.
James, D. E. (1980). A system of energy accounts for Australia. The Economic Record, 56, 171–181.
Krenz, J. H. (1977). Energy and the economy: An interrelated perspective. Energy, 2, 115–130.
Lancaster, K. (1968). Mathematical economics. New York: Macmillan.
Matz, A. & Usry, M. F. (1976). Cost accounting, planning and control. Cincinnati, Ohio: South–Western
Nikaido, H. (1968). Convex structures and economic theory. New York: Academic Press.
Reardon, W. A. (1973). Input–output analysis of U.S. energy consumption. In M. F. Searl (Ed.), Energy modeling: Art, science, practice. Washington, DC: Resources for the Future.
Roemer, J. E. (1977). Technical change and the ‘tendency of the rate of profit to fall’. Journal of Economic Theory, 16, 403–424.
Sraffa, P. (1960). Production of commodities by means of commodities. London: Cambridge University Press.
Stobbe, A. (1959). Produktivitätsmessung auf der Grundlage von Input–Output–Tabellen, Weltwirtschaftliches Archiv, 82, 237–271.
Stone, R. et al. (1963). A programme for growth 3: Input–output relationships 1954–1966. London: Chapman and Hall.
United Nations (1968). A system of national accounts. Studies in methods F (no. 2, rev. 3). New York: United Nations.
United Nations (1973). Input–output tables and analysis. Studies in methods F (no. 14, rev. 1). New York: United Nations.
Wright, D. J. (1975). The natural resource requirements of commodities. Applied Economics, 7, 31–39.
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Flaschel, P. (2010). Technology Assumptions and the Energy Requirements of Commodities. In: Topics in Classical Micro- and Macroeconomics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00324-0_7
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