A New Matrix Theorem: Interpretation in Terms of Internal Trade Structure and Implications for Dynamic Systems
AbstractEconomic systems often are described in matrix form as x=Mx. We present a new theorem for systems of this type where M is square, nonnegative and indecomposable. The theorem discloses the existence of additional economic relations that have not been discussed in the literature up to now, and gives further insight in the economic processes described by these systems. As examples of the relevance of the theorem we focus on static and dynamic closed Input-Output (I-O) models. We show that the theorem is directly relevant for I-O models formulated in terms of difference or differential equations. In the special case of the dynamic Leontief model the system’s behavior is shown to depend on the properties of matrix M=A + C where A and C are the matrices of intermediate and capital coefficients, respectively. In this case, C is small relative to A and a perturbation result can be employed which leads directly to a statement on the system’s eigenvalues. This immediately suggests a solution to the well-known problem of the instability of the dynamic Leontief model. Copyright Springer-Verlag Wien 2005
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Bibliographic InfoArticle provided by Springer in its journal Journal of Economics - Zeitschrift für Nationalökonomie.
Volume (Year): 84 (2005)
Issue (Month): 1 (02)
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leverage matrix; stability analysis; input-output analysis; dynamic input-output models; C62; C67; D57;
Find related papers by JEL classification:
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
- D57 - Microeconomics - - General Equilibrium and Disequilibrium - - - Input-Output Tables and Analysis
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