The calculation of E and U for the US - or any country - and the calculation of the efficiency factor f are major computational undertakings in themselves, since much of the underlying data are not collected or published, as such, in official government statistics. The time series for useful work U must be constructed from other time series, for example, on energy consumption by category and information about the uses of energy and the history of technology. However, the results for exergy/GDP and work/GDP, in graphical form, are shown in Figures 7.1 and 7.2, for the US and Japan, respectively.
Note that the exergy required to produce a unit of GDP in Japan is just about half of the amount required by the US economy, and this
relationship has been consistent throughout the 20th century. There is no peak or 'inverted U' when biomass exergy is included along with fossil fuels, although the US data show a slight increase from 1900 to 1925 or so. However the work/GDP ratios for both countries exhibit a very well-marked peak, occurring in the early 1970s. That peak corresponds in time to the Arab oil embargo and the so-called 'energy crisis' that triggered a spike in petroleum prices and prices of other fuels.
From the data plotted in Figures 7.1 and 7.2 it is possible to calculate aggregate exergy-to-work efficiencies for the economies of the two countries. Results are shown in Figure 7.3. It is noteworthy - and surprising -that, according to our calculations, the efficiency of the Japanese economy actually peaked in the early 1970s and began to decline, albeit slowly, whereas the (lower) efficiency of the US economy has increased more or less monotonically up to now, while remaining significantly lower than that of Japan. The explanation is, probably, that as Japan has become more prosperous since the 1960s, inefficient uses of energy (exergy) have grown faster than aggregate efficiency gains. The fact that favorable hydro-electric sites were already exploited has necessitated increased use of less efficient steam-electric generation. Similarly, inefficient personal automobiles have shifted quite a bit of urban traffic away from more efficient public transportation. Finally, household uses of electricity such as hot water and air-conditioning
have become widespread. Details of these calculations, and preliminary results for the US, have been presented in previous publications (Ayres et al. 2003; Ayres and Warr 2005; Warr and Ayres 2006). Details of the calculations for Japan have been submitted elsewhere for publication.
As will be seen below, we think that the increase in total factor productivity (TFP) for both countries is very closely related to - and largely explained by - the exergy-to-work efficiency trend.
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