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Input–output planning was never adopted because the material balance system had become entrenched in the Soviet economy, and input–output planning was shunned for ideological reasons. As a result, the benefits of consistent and detailed planning through input–output analysis were never realized in the Soviet-type economies .
Consequently, () is a matrix with the dimension which contains transfer functions for each input output combination. Due to the simplicity of this matrix notation, the state-space representation is commonly used for multiple-input, multiple-output systems.
Here represents the square matrix of input coefficients, denotes releases (such as emissions or waste) per unit of output or the intervention matrix, stands for the vector of final demand (or functional unit), is the identity matrix, and represents the resulting releases (For further details, refer to the input-output model).
The Regional Input–Output Modeling System (RIMS II) is a regional economic model developed and maintained by the US Bureau of Economic Analysis (BEA).. Regional input–output multipliers such as the RIMS II multipliers allow estimates of how a one-time or sustained increase in economic activity in a particular region will impact other industries located in the region—i.e., estimating ...
This formula is the core of environmentally extended input-output analysis: The final demand vector y can be split up into a domestic and a foreign (exports) component, which makes it possible to calculate the material inputs associated with each. The matrix F integrates material (factor) flow data into input-output analysis. It allows us to ...
For example, if matrix D = 0 and matrix C does not have full row rank, then some positions of the output are masked by the limiting structure of the output matrix, and therefore unachievable. Moreover, even though the system can be moved to any state in finite time, there may be some outputs that are inaccessible by all states.
A MIMO system with m outputs and n inputs is represented by a m × n matrix. Each entry in the matrix is in the form of a transfer function relating an output to an input. For example, for a three-input, two-output system, one might wr
The Hawkins–Simon condition refers to a result in mathematical economics, attributed to David Hawkins and Herbert A. Simon, [1] that guarantees the existence of a non-negative output vector that solves the equilibrium relation in the input–output model where demand equals supply.