Perturbations of matrices: A theorem on the Perron vector and its applications to input-output models
type: Item
instance of: scholarly article
title: Perturbations of matrices: A theorem on the Perron vector and its applications to input-output models
zbMATH Open document ID: 0677.90015
DOI: 10.1007/BF01227544
published in: Journal of Economics
publication date: 1988-01-01T00:00:00Z
review text: The author investigates the effects of perturbations in matrices on the related Perron root (dominant eigenvalue) and its corresponding eigenvector. His main theorem states that ``when certain rows of a matrix are perturbed, the relative changes in the corresponding elements of the right-hand Perron vector form bounds for the relative changes in the other elements.'' Starting from this, he analyses several topics: the effects of technical change on prices in a Sraffa model, changes in output due to changes in final demand and the effects of the introduction of taxes and subsidies in a static Leontief model. He succeeds in unifying the approach to these different problems verifying and extending the results of other authors. Moreover, the author extends his analysis to dynamic models. Due to his main theorem it becomes possible to describe bounds for the change of a balanced growth path caused by a change in the input-output matrix.
Mathematics Subject Classification ID: 91B62
Mathematics Subject Classification ID: 91B66
zbMATH DE Number: 4110425
zbMATH Keywords: perturbations in matrices
zbMATH Keywords: Perron root
zbMATH Keywords: technical change
zbMATH Keywords: Sraffa model
zbMATH Keywords: balanced growth path
zbMATH Keywords: input-output
author: Erik Dietzenbacher
reviewed by: Bertram Schefold
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4110425