Abstract
The main purpose of this paper is to show how to deal with large relative variable systems, where the presence of small parameters makes the norm of some column (or row) blocks tend to zero with them. This will be achieved by using a specific example, namely a model of Classical competition withn goods. In this model capitals move from low-reward to high-reward employments, whilst in the determination of prices the full-cost principle plays the main role and excess-demand only a minor one. We shall also prove that in this model, transformed in relative variable form, if the positive parameter expressing the role of excess-demand in the formation of prices is sufficiently small, the equilibrium vector is asymptotically stable.
Riassunto
Scopo principale di questo lavoro è di mostrare come si possono studiare sistemi dinamici di grandi dimensioni con variabili poste in termini relativi, nei quali la presenza di parametri piccoli fa sì che la norma di certi blocchi di colonne (o di righe) tenda a zero con essi. Per raggiungere questo obbiettivo, viene utilizzato un esempio specifico, cioè un modello di concorrenza d'ispirazione classica conn beni. In questo modello i capitali si muovono dagli impieghi a bassa remunerazione a quelli ad alta remunerazione, mentre nella determinazione dei prezzi il principio del costo pieno gioca il ruolo principale, lasciando agli eccessi di domanda soltanto un ruolo secondario. Si dimostra che per questo modello trasformato in termini di variabili relative, se il parametro che esprime il ruolo degli eccessi di domanda è abbastanza piccolo, il vettore d'equilibrio (che è unico) è asintoticamente stabile.
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Boggio, L. On local relative stability of large sistems with small parameters. The example of a classical model of competition. Decisions Econ Finan 22, 13–30 (1999). https://doi.org/10.1007/BF02912348
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DOI: https://doi.org/10.1007/BF02912348