Input-Output Models

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 222)


Consider an economy that consists of three sectors: agriculture, machinery, and construction. Let the domestic output of each of these three sectors be denoted x1, X2 and X3, respectively. Let the final demand in each sector be denoted yi: final demand is typically broken down to private consumption, government consumption (say for defense), investment and foreign trade (exports less imports). For given final demand, say machines, we write
$$ {a_{21}}{\kern 1pt} {x_1}{\kern 1pt} + {\kern 1pt} {a_{22}}{\kern 1pt} {x_2}{\kern 1pt} + {\kern 1pt} {a_{23}}{\kern 1pt} {x_3}{\kern 1pt} + {\kern 1pt} [\frac{{\$ mach}}{{\$ Agr.}}]{\kern 1pt} [\$ Agr.][\frac{{\$ mach}}{{\$ mach}}][\$ mach][\frac{{\$ mach}}{{\$ Const}}][\$ Const]{y_2} = {x_2} \times {\kern 1pt} [Final{\kern 1pt} Demand{\kern 1pt} for{\kern 1pt} machines][Gross{\kern 1pt} output{\kern 1pt} of{\kern 1pt} machine{\kern 1pt} sector] $$


Gross Domestic Product Government Consumption Private Consumption Trade Balance Final Demand 
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  1. 1.
    Those familiar with conventional input-output analysis as used in the general context of development planning may proceed directly to Section 6.2Google Scholar
  2. 2.
    This input-output model is said to be “open” in the sense that final demand is exogenously specified. It is possible to “close” and I/O model by assuming that final demands can be determined in the same way as interindustry demands.Google Scholar
  3. 3.
    Input-output can be traced back to Francois Quesnay and his Tableau Economique presented first in 1758. This was designed to show how goods and services circulated among the four socioeconomic classes of prerevolutionary France-land owners, farmers, traders and manufacturers. Whilst Quesnay’s work established the fundamental interdependence of economic activities, it was Leon Walras who established the necessary mathematical framework in terms of a set of simultaneous linear equations. In his 1874 work “Elements d’Economie Politique Pure.” It remained for Wassily Leontief, however, to publish the first input-output tables for the U.S. economy, and to bring input-output to the state of being a tool of applied rather than merely theoretical economics. “Quantitative Input-Output Relations in the Economic System of the U.S.” Review of Economics and Statistics, 18, p. 105–25 (1936).Google Scholar
  4. 5.
    Todaro (1971) has an elementary discussion of this subject, with some simple numerical examples to illustrate the implications of such assumptions. For a more advanced treatment, see e.g. L. Taylor “Theoretical Foundations and Technical Implications,” in Blitzer et. al., (1975).Google Scholar
  5. *.
    This section is based on the detailed and much longer report; S. Rogers et al., “Application of the Brookhaven Energy-Economic Assessment Model in the Portugal-U.S. Cooperative Assessment,” BNL 51424, Brookhaven National Laboratory, Upton, NY, June 1981.Google Scholar
  6. 8.
    See e.g., P. Meier and V. Mubayi, “Modelling Energy-Economic Interactions in Developing Countries: A Linear Programming Approach,” BNL 29747, June 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  1. 1.Institute for Energy ResearchState University of New York at Stony BrookStony BrookUSA

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