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ECON 301 – LECTURE #13
Liontief Input – Output Models
Recall that throughout the course we have discussed the perfect compliments production
function.
This functional form is often referred to as a fixed coefficients or fixed
proportions function and was named after Professor Wassily Liontief and his seminal
work from the early 1950s.
In its “static” version, Liontief’s input – output
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analysis deals with the following
question:
What level of output should each of the n industries in an economy produce such that that
output will be just enough to satisfy the total demand for that product?
The reason for the term input – output analysis now becomes quite clear.
The output of
any given industry (let’s say the steel industry) is needed as an input in many other
industries, or even as an input into its own industry; thus the correct level of steel output
(i.e. shortagefree and surplusfree) will depend on the input requirements of all of the n
industries in the economy.
In turn, the output of many other industries will enter into the steel industry as inputs, and
consequently the “correct levels of these other products will depend partly upon the input
requirements of the steel industry.
In light of this interindustry dependence, any set of “correct” output levels for the n
industries must be one that is consistent with all of the input requirements in the economy
(so that no bottlenecks will arise anywhere).
So it becomes abundantly clear that this input – output analysis should be of paramount
use in production planning applications, such as planning for the economic development
of a nation or even for a domestic defense program.
CAVEAT:
Strictly speaking, input – output analysis is not really a form of general
equilibrium analysis.
Although the interdependence of the various industries is
emphasized, the “correct” output levels are those which satisfy a set of technical input –
output relationships rather than a set of market equilibrium conditions.
Nevertheless, the
problem posed by the input – output analysis does boil down to solving a system of
simultaneous equations and this gives us a chance to investigate the interdependence
among markets using matrix algebra.
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Liontief, Wassily W.
The Structure of American Economy 19191939,
2d ed., Oxford University Press,
Fair Lawn, N.J., 1951.
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The Structure of an Input – Output Model
Since an input – output model normally considers a large number of industries, its
framework is by necessity rather involved.
To simplify the problem, we will make the
following standard assumptions:
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Each industry produces only one homogeneous good (broadly interpreted, this
implies that they could produce two or more jointly produced goods provided that
they are made in fixed proportions to one another).
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 Winter '09
 COREYVANDEWAAL
 Linear Algebra, Invertible matrix, steel industry

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