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On the Speed of Establishing Multi-Sectoral Equilibrium

Michio Morishima
Yukio Kaneko

Abstract

The usual ($N, t^{\ast}$)-definition of stability says that an equilibrium point $\bar{x}$ is stable if there exists a finite time $t^{\ast}$ (dependent on a prescribed neighbourhood $N$ of $\bar{x}$ such that, for all $t$ being not less than $t^{\ast}, x(t)$ remains in $N$. The least value, $\bar{t}^{\ast}$ of such $t^{\ast}$ may be a useful concept of dynamic economics, measuring the speed at which the equilibrium is established. In this paper we assume a multi-sectoral model of the Leontief type and obtain various formulas for the measurement of $\bar{t}^{\ast}$.