Westropa:Price index of imported commodities(x) 167.
„home-produced„(y) 152.
„all„155.
Hesperides:„imported„(x´) 148.
„home-produced„(y´) 163.
„all„160.

[28]

For 10x = 11y
8y + 2x = 1550

11x´ = 10y´
8y´ + 2x´ = 1600.

Thus it appears that the purchasing power parity of the Westropean currency in 1923 compared with 1913 is (160/155 = )103; whereas the rate of exchange, compared with the 1913 parity, is (163/167 = 148/152 = )97. If the worsening of Westropa’s equation of exchange with the Hesperides is permanent, then its purchasing power parity (on the 1913 basis) will also remain permanently above the equilibrium value of the market rate of exchange.

A tendency of these two measures of the value of a country’s currency to move differently is, therefore, a highly interesting symptom. If the market rate of exchange shows a continuing tendency to stand below the purchasing power parity, we have, failing any other explanation, some reason to suspect a worsening of the “equation of exchange” as compared with the base year.

In the charts and tables below, the actual results are worked out of applying the theory to the exchange value of sterling, francs, and lire in terms of dollars since 1919. The figures show that, quantitatively speaking, the influences, which detract from the precision of the purchasing power parity theory, have been in these cases small, on the whole, as compared with those which function in accord with it. There seems to have been some disturbance in the “equations of exchange” since 1913,—which would probably show up more distinctly if it were not that the index numbers employed in the following enquiry are of the type which is largely built up from articles entering into international trade. Nevertheless general price changes, affecting all commodities more or less equally, due to currency inflation or deflation, have been so dominant in their influence that the theory has been actually applicable with remarkable accuracy. In the case, however, of such countries as Germany, where the shocks to equilibrium have been much more violent in many respects, the concordance between the purchasing power parity based on 1913 and the actual rate of exchange has suffered, whether temporarily or permanently, very great disturbance.

The first of these charts, which deals with the value of sterling in terms of dollars, shows that whilst the purchasing power parity, calculated with 1913 as base, is often somewhat above the actual exchange, there is a persevering tendency for the two to come together. The two curves are within one point of each other in September-November 1919, March-April 1920, April 1921, September 1921, January-June 1922, and February-June 1923, which is certainly a remarkable illustration of the tendency to concordance between the purchasing power parity and the rate of exchange. On inductive grounds it would be tempting to conclude from this chart that the financial consequences of the war have depressed the equilibrium of the purchasing power parity of sterling as against the dollar from 1 to 2½ per cent since 1913, if it were not that this figure barely exceeds the margin of error resulting from the choice of one pair of index numbers rather than another from amongst those available.[29] It will be interesting to see what effect is produced by the payment, just commenced, of the interest on the American debt.

[29] Nevertheless, if I had used the Board of Trade or the Statist index number in place of the Economist index number in the table below, the presumption of a slight worsening of the “equation of index” against Great Britain would be somewhat strengthened.

This chart brings out clearly, as also do those for France and Italy, the susceptibility of the foreign exchange rates to seasonal influences, whereas the purchasing power parity is naturally less affected by them.