Page 52 - Special Topic Session (STS) - Volume 2

STS452 Joseph M.
in the production process of sector 3. The chain of production and bisectoral
trade in intermediates continues until the product of sector 3 valued X3 is
either exported (E3) to the ROW or consumed by the domestic final use sector
(F3) and is thereby no longer used in the economy’s domestic production
processes.

Figure 3.1: Input Output Transactions Table

A salient feature of the IOT is that it provides the mechanism for detailing
the direct and indirect linkages between production and trade in a systematic
and mathematical manner. Since every sector-specific production process
(resulting in the production of Xj >=0) can be represented as the linear
combination of the contributions of all industrial sectors (zij>= 0) in the sector
i – sector j space (i, j = 1,..,n), the intermediate use matrix (Z) and the associated
matrix of technical coefficients (A) are square. Further, in the matrix
representation of a realistic economy, no column sum in A is greater than 1,
and at least one column sum is less than 1 (implying non-negative value added
in every sector). Given these characteristics of the technical coefficient matrix
A, a powerful economic analytical tool known as Leontief inverse can be
derived from it. Formulaically, it is expressed as

L = (I – A)
–1

where I is the identity matrix whose dimensions are same as that of A. L is also
known as the total requirements matrix, whereas the matrix of technical
coefficients, A, is also referred to as the direct requirements matrix. The matrix
of total output X (accounting for all direct and indirect effects) required to
support final demand F is given by

rr –1
X = (I – A ) F r
r
rr
where r refers to the economy being analyzed. A is the technical coefficient
matrix of transactions within r.

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