30 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
Now let the initial exchange rates be the elements of a 
vector x, and the adjusted exchange rates be the elements of 
a vector x,. Then 
(IV. 34) 
(Dp) (x=! x, — 1) =(T’ = Ti 
that is 
(IV. 35) 
x, =x, [I+ Dp)! (IT - T)]i 
The elements of Dp tell us how the total expenditure of region 7 
on the products of region s changes with a uniform change in 
the prices of each of the regions. The elements of x," x, -1 
represent the changes in the exchange rates expressed as a pro- 
portion of their initial levels. And the elements of (T”- T} 
represent the corrections to the initial balances of trade required 
to give t*={o, o, ..., 0}. Consequently the set of exchange 
rates which will lead to a redistribution of purchases such that 
all the trade balances balance is given by (IV. 35). Evidently 
there is no difficulty if we wish to put #*=#** in place of 
t*= lo, 0, ..., 0}. 
For each trading region the initial prices would come out 
of a model analogous to our main model. Having balanced 
all the balances of trade by changing the exchange rates, we 
should alter in each region the relative prices of goods obtained 
from different sources of supply. When we returned to the 
demand equations we should obtain a new set of demands. 
These would balance the balances of trade but, in general, 
would alter production levels in the different regions and so: 
would alter costs and prices. And so on. 
Perhaps enough has been said to show why, in the first 
instance, we adopted a short cut to the problem of foreign 
trade. 
f 1 Stone - pag. 58