ON VARIATIONS IN THE VALUE OF THE MONETARY STANDARD. 251 



and July by putting each of them on a level with the price prevailing 

 during the strawberry season, the price which appertains to the bulk of 

 the fruit and concerns the majority of the consumers. A similar difficulty 

 applies to fish, of which the particular prices which go to form the average 

 may be taken at very different distances from the fisheries, the higher 

 prices, it may be, having an undue influence on the average. 



The milder case of this difficulty is where the revision of the standard 

 is performed so frequently that there is not much difference between 

 successive epochs in the distribution of the quantities in time and place. 

 For instance, it might probably be assumed without error that the pro- 

 portions of the supply of strawberries consumed in the months of May, 

 June, and July respectively are not materially different in two successive 

 years. The proportionate quantity of fish used by different inland towns 

 might similarly be treated as constant for short intervals of time. In 

 this case it appears to us that the difficulty under consideration may be 

 avoided by one of two methods which are or have been employed in the 

 statistics relating to the Imports and Exports of the United Kingdom. 

 One plan is to take not the simple arithmetical mean of the particular 

 price-returns, e.g. ^ [6rl. + Sd. + 6d.], the price of strawberries being 6d. 

 in May, 3d. in June, and 6d. in July ; but to weight each of these price- 

 returns with the (more or less accurately estimated) corresponding 

 quantity of goods at each price.' It was partly upon this principle ^ that 

 the prices entering into the ' computed values ' of British Imports and 

 Exports used to be calculated. The prices were taken at London and 

 Liverpool (sometimes Hull), and also the quantities. As the mean price 

 was put the following expression : (Quantity at London x London price 

 -F Quantity at Liverpool X Liverpool price), dividedby (Quantity at London 

 -f Quantity at Liverpool). 



' The proportions might be roughly ascertained by the method of sample, 

 e.ff., examining several markets selected at random, in the respective months. 

 Let the proportions thus determined for the months of Blay, June, and July 

 be, ,a, a, a' (where ,o + a + a' = l). Or, if we consider two successive years, we 

 shall have two sets of ratios, say, ^o,, a,, a',, and ,a„, o^, a'„. Let the total quanti- 

 ties in the respective years be A, and A^. And let the prices for May, June, and 

 July be for the first year as before, Gd., M., &d., and for the second year some- 

 what different, say, Gr/. + ,A, M. + A, 6rf. + A'. Now, according to the rough and 

 ready mode of computation, the term contributed by strawberries to the numerator 

 of our formula (see above) is i (A, + A„) x [5-1- ACA + A + A')]. And the correspond- 

 ing term of the denominator is a (A, + A„") x o. Here, ,A and A' are each put on a 

 level with A ; though the latter variation is far the most important as affecting the 

 bulk of the goods, the majority of the consumers. Tliis error is avoided by using the 

 n-eiglded (instead of the simple) mean of the three prices. The term contributed to 

 the numerator of our formula thus becomes -J (A, -i- A.,) x lfl.J^Qd. + iA) + a.,{M. + A) 

 -V a.,{Gd. + A')] (or some analogous combination, e.g., that which is formed by substi- 

 tuting in the above expression for ,a._, the mean value i (,a, + ,0,), and making similar 

 substitutions for a„ and a'.,). For the corresponding terni of the denominator 

 put the same expression modified by the omission of the A's. It is clear that 

 in the result thus modified ,A and A' play a much more insignificant part than 

 formerly. 



A similar contrast makesitself felt when weadopt the second correction suggested 

 in the text. The average price of the first year is nov/ obtained by dividing the total 

 value by the quantity. The total value will consist of an aggregate of terms ana- 

 logous to (if not identical with) A, x {^fid. + a^Zd + a' fid.). And this, being divided 

 by A,, the total quantity gives us the same sort of expression for the average price as 

 before. 



- As described in a Memorandum by Mr. Messenger, published in the ParUa- 

 WC7itary Papers for 186.5, vol. i. p. 273, 



