SEMAINE D'ÉTUDE SUR LE ROLE DE L’ ANALYSE ECONOMETRIQUE ETC. 
3 
[ assume that all transactions in T are recorded in terms of a 
single currency, the conversions to this currency being made 
by means of a supposedly consistent set of exchange rates. 
The balances of trade of the different regions are given by 
the excesses of their total sales over their total purchases. If 
these balances are the elements of a vector ¢*, say, then 
(IV. 31) 
=(T -T'): 
It is to be expected that #*#jo, 0, …, of. On the assump- 
tion that trade balances are determined by buying and selling, 
let us consider how to adjust the rates of exchange between 
the currencies so that with the new rates of exchange 
{#*= to, o, ..., 0}. 
Consider first one region, » say, and one commodity, j say. 
From the demand equations we can set up a matrix of order 
equal to the number of regions, D,; say, the elements of which 
are the derivatives of the expenditure in region » on commo- 
dity j obtained from region s with respect to the price of j in 
any one of the regions. For commodity j we can do this for 
each region. Now let us form D ~ wher 
(IV. 22) 
where » denotes the number of regions. Having done this for 
one commodity, we can do it for every other. So let us define 
Dp as 
(IV. = | 
where m denotes the number of commoditie. 
.| Stone - pag. 57