Abstract
Linear production models allow a concise representation of the production process in an economy. The interdependence between production units is its main characteristic as each production unit uses the output of other producing units as inputs. Empirical content is provided by analyzing highly aggregated input–output tables for Germany.
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Notes
- 1.
\(\mathbf{x}\) is a column vector. The prime ′ indicates the transposition of the vector.
- 2.
For example wheat used as input in agriculture.
- 3.
For a formal treatment see Behr and Rohwer (2013), p. 320–323.
- 4.
\(b\) (scalar) denotes the total amount of labor, \(\mathbf{b}\) (vector) denotes the amount of labor in the n production units.
- 5.
A standard cord is considered a 4’x4’x8’ stack of wood including bark and air space. ’ denotes a foot which corresponds to 30,48 cm.
- 6.
The dominant eigenvalue is 0.4 in our example.
References
Behr A, Rohwer G (2013) Wirtschafts- und Bevölkerungsstatistik. UTB GmbH
Gale D (1989) The theory of linear economic models. University of Chicago Press, Chicago
Miller R, Blair P (2009) Input-output analysis: foundations and extensions. Cambridge University Press, Cambridge
ten Raa T (2005) The economics of input-output analysis. Cambridge University Press, Cambridge
Schwartz J (1961) Lectures on the mathematical method in analytical economics. Mathematics and its applications. Gordon and Breach, New York
Sraffa P (1963) Production of commodities by means of commodities. Prelude to a critique of economic theory. Cambridge University Press, Cambridge
Statistisches Bundesamt (2010) Input-output-rechnung, 2007. Volkswirtschaftliche Gesamtrechnungen 18(2), Wiesbaden
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Behr, A. (2015). Linear Production Model. In: Production and Efficiency Analysis with R. Springer, Cham. https://doi.org/10.1007/978-3-319-20502-1_2
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DOI: https://doi.org/10.1007/978-3-319-20502-1_2
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