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 region,
 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 commodity
 j which come from domestic production or from one
of the possible foreign sources of supply. Initially 4, is unknown
 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 threedimensional
 regional trading matrix: region by region by commodity.

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