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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 .
The concept of productive matrix was developed by the economist Wassily Leontief (Nobel Prize in Economics in 1973) in order to model and analyze the relations between the different sectors of an economy. [1] The interdependency linkages between the latter can be examined by the input-output model with empirical data.
Here is the identity matrix and is called the input–output matrix or Leontief matrix after Wassily Leontief, who empirically estimated it in the 1940s. [2] Together, they describe a system in which
Two input Leontief Production Function with isoquants. In economics, the Leontief production function or fixed proportions production function is a production function that implies the factors of production which will be used in fixed (technologically predetermined) proportions, as there is no substitutability between factors.
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 ...
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).
Wassily Wassilyevich Leontief (Russian: Васи́лий Васи́льевич Лео́нтьев; August 5, 1905 – February 5, 1999), was a Soviet-American economist known for his research on input–output analysis and how changes in one economic sector may affect other sectors.
Indeed, a Leontief economy is not guaranteed to have a competitive equilibrium. There are restricted families of Leontief economies that do have a competitive equilibrium. There is a reduction from the problem of finding a Nash equilibrium in a bimatrix game to the problem of finding a competitive equilibrium in a Leontief economy. [3]