Perturbations of matrices: A theorem on the Perron vector and its applications to input-output models
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.
scientific article; zbMATH DE number 4110425
scientific article