Page 35 - Azerbaijan State University of Economics
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THE JOURNAL OF ECONOMIC SCIENCES: THEORY AND PRACTICE, V.80, # 2, 2023, pp. 28-46
The variables in this case are total production (X), final consumption (Y), and a vector
of direct cost coefficients (A). The direct cost coefficient shows how much resources
from the i-th sector are required to make one unit of the j-th sector's product:
x
a = ij , i,j, 1= ,2 ,...,n
ij X j
When we solve equation (1) in relation to X, we obtain:
X = İ ( − A) − 1 Y (2)
-1
Here, B=(İ-A) is called the full cost matrix.
Using equation (3), we can express the change ( X ) in the total output vector X
when any change ( Y ) occurs in the final demand vector Y as:
X = ( E − A) −1 Y = B Y (3)
This is the input-output model's fundamental simulation equation.
It is evident that altering any one of its components can result in a change in the final
demand's volume. For instance, the demand for the final products of different sectors
rises when government agencies' investment and consumption costs are altered
through the state budget. Consequently, the change in the final demand brought about
by a change in any one or more of the aforementioned components can be quantified
by using formula (3) to measure the change in the total output vector. Therefore, any
sector's production rises in response to a rise in the demand for its products.
Simultaneously, the output-input model enables the estimation of the overall sum of
these effects when more intermediate consumption products utilized in other sectors
to make this sector's product are produced. However, only the multiplier effects
resulting from production relations are considered in the input-output model.
Additional multiplier effects are produced during the processes of income distribution,
redistribution, and use. These impacts can be evaluated by utilizing the Social
Accounting matrix.
SAM based multiplier model
A Social Accounting Matrix (SAM) is an extensive database that encompasses an
economy and records information on every transaction made by economic actors
within that economy over a given time frame (Mainar-Causapé et al., 2018). By
include the entire path of income in the economy, a SAM expands the input-output
table.
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