THERMOECONOMICS - Vocat International Ltd

14
Copyright: John Bryant, VOCAT International Ltd 2012, for personal use only.
Some of the data exhibited wild swings outside the scale of the charts,
owing to some points where changes in specific price PN were divided by
very small changes (positive or negative) in output volume V (see figure
5.6). An explanation of this effect is given by reference to figure 5.4. For
processes operating at approaching either side of constant output volume
(dV/V=0), the elastic index can approach a very high number (plus or
minus). Figures 5.6 and 5.7 illustrate points in the two economic cycles
where the effect occurred. Readers may note also that these points occurred
at particular ‘recessive’ years, some of which coincided with periods of
turbulence in world oil markets. It can be seen that movements in the
elastic index are the ‘norm’ as an economy develops.
The three charts at figure 5.8 illustrate the effect of a change in the elastic
index n between specific price PN, output volume V and velocity of
circulation T.
To finish this section, we refer back to the polytropic equation (5.7).
Splitting this into its component parts, we have:
( ) n P V
n
P NV
= = Constant (5.10)
N
And taking logs and differentiating we have:
dP
P
dN dV
= − n
(5.11)
N V
Figure 5.9 illustrates actual annualised quarterly changes in the price level
change dP/P, set against projections of price change using equation (5.11)
above for values of elastic index n of 1.5 and 1.0 respectively for the UK
and USA economies, taken from the results following the charts at figure
5.5 of this book. The projections follow the lines of change in price, but
wildly under and over-shoot, because account of the short-term change in
the elastic index n by quarter has not been taken.