Differential savings, factor shares, and endogenous growth cycles

Abstract

The paper analyzes the dynamic properties of the neoclassical one-sector growth model with di!erential savings in the sense of Kaldor}Pasinetti. The economy exhibits unstable steady states and #uctuations if the income distribution varies su$ciently and if shareholders save more than workers. The paper analyzes in detail the dynamics for the case with a "xed proportions technology as well as with a smooth approximation. If the savings propensities di!er by an arbitrarily small amount, the system exhibits topological chaos in the sense of Li and Yorke for an open set of production functions. The analytical results are supplemented by numerical experiments.

The dynamics of the NAIRU model with two switching regimes

“…This is also what occurs in our model (as we shall prove in Section 5). Moreover, in Böhm and Kaas (2000) the authors remark a surprisingly rich occurrence of periods in the cycles, and the same occurs in our model: the rich structure of periodicity regions with cycles of any period and with periodic points in several positions between the L and R regions will be here fully described.…”

“…Recently, a one-dimensional piecewise-linear discontinuous map was considered in the one-sector growth model proposed by Böhm and Kaas in Böhm and Kaas (2000), 5 which is similar to our model. The case in which these authors were interested in corresponds to the one called above of regular dynamics.…”

“…The case in which these authors were interested in corresponds to the one called above of regular dynamics. In Böhm and Kaas (2000) the authors prove that all the existing cycles are globally attracting, and refer to a remarkable paper by Keener (1980) to state that for a set of parameter values of zero Lebesque measure the attracting set is a Cantor set, which however they have never observed. Indeed it is correct, because the attracting set in regular dynamics cannot be a Cantor set.…”

On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders

“…In addition, our paper shows the relevance of discontinuous maps to the analysis of financial market dynamics, a rather new field of applied mathematics that has not yet yielded many results. Nevertheless, note that there are already several interesting economic models that feature piecewise-smooth or discontinuous maps, for example, the pioneering works by Day (1982Day ( , 1994; Day and Shafer (1987); Day and Pianigiani (1991), which have also been used recently in Metcaf (2008) and Böhm and Kaas (2000). It is also worth mentioning the works by Hommes (1991Hommes ( , 1995; Hommes and Nusse (1991) and Hommes et al (1995).…”

A growth-cycle model of Solow–Swan type, I

“…However, more recently, it has been proved that this understanding is not always correct. In fact, by introducing constant but different savings propensities out of capital and labor income, the insightful paper by Böhm and Kaas (2000) showed that complex dynamics emerge. 2 These models are of the discrete-time type.…”