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In economics, an input–output model is a quantitative economic model that represents the interdependencies between different sectors of a national economy or different regional economies. [1] Wassily Leontief (1906–1999) is credited with developing this type of analysis and earned the Nobel Prize in Economics for his development of this model.
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 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).
Models in which the vector nature of the quantities is maintained are used in practice, for example Leontief input–output models are of this kind. However, for the most part, these models are computationally much harder to deal with and harder to use as tools for qualitative analysis .
Leontief earned the Nobel Prize in economics for his work on input–output tables. Input–output tables analyze the process by which inputs from one industry produce outputs for consumption or for inputs for another industry. With the input–output table, one can estimate the change in demand for inputs resulting from a change in production ...
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.
Input-Output models, developed by Wassily Leontief, take advantage of linear programming and matrices by dividing the economy into interdependent sectors that produce products for both themselves and other sectors; the production in one sector relies in the input of goods from another. [14]
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.