PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
the elements a*,, of which represent the input of complementary 
import j into a unit of output of R. 
Suppose that we know v, e and m*, but not x or m. From 
(IV. 29) we could calculate a provisional value of the vector 
lg im,!. Given the price of each product in each trading re- 
gion, we could try to allocate the demand for each element of 
ig | m, | over the sources of supply by means of a price-sensitive 
variant of the linear expenditure system [38]. This means 
that for the jth element of ¢ we should use 
IV. 30) 9 = (¢;+ Cyp)+ pt by [ny — pi (¢;+ Cy py) 
where g; is a vector whose elements are the amounts of com- 
modity j which come from domestic production or from one 
of the possible foreign sources of supply. Initially 4, is unk- 
nown and must be adjusted until ig; is equal to the jth element 
of g. The matrix C is a symmetric matrix of parameters and 
is of order equal to the number of:sources of supply. A method 
of estimating the elements of this matrix is suggested in [38]. 
If we applied (IV. 30) to each commodity in each region 
we should generate a complete set of imports and exports. 
These would then have to be added and subtracted to give 
fv+e+x-m im*} and the whole exercise would have to 
be carried out again with this vector in place of the provisional 
Vu te m*,{. This process would then be continued until it 
converged. 
At this point we can recombine the estimates to give a three- 
dimensional regional trading matrix: region by region by com- 
modity. 
From all this information we can construct a region by 
region trading matrix, T say. The element #,, say, of T shows 
the total exports of region 7 to region s, while the element #,, 
shows the total exports of region s to region r. For simplicity, 
11 Stone - pag. 56