Econometrica: Oct, 1962, Volume 30, Issue 4

On the Speed of Establishing Multi-Sectoral Equilibrium

https://doi.org/0012-9682(196210)30:4<818:OTSOEM>2.0.CO;2-6
p. 818-823

Michio Morishima, Yukio Kaneko

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 $\bar{t}^{\ast}$.