Calculus of iterations and labor-capital core-periphery relative redistribution dynamics

Abstract

The objective of this paper is to supply, with the help of the log-linear two-stock and two-location relative dynamics model, a complete description of the qualitative complementarity and competition (i.e. substitution) properties of the relative shifts in the shares of labor and capital distributed between a core and its periphery. Complete analysis of the labor-capital core-periphery relative mobility can be achieved by the movement of equilibria in the phase space. Crossing of boundaries of the stability domain reveals a plethora of possible labor-capital redistribution phenomena from stability, periodicity, arnold mode-locking tongues and quasi-periodicity, to strange attractors and strange containers. The movement of equilibria in phase space reveals the universal properties of the log-linear labor-capital core-periphery relative dynamics: for each preset combination of qualitative properties in labor-capital relative equilibria, it is possible to choose parameters of the considered log-linear model which generate the needed event.