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Endogenous cycles in standard growth models with capital accumulation of the Solow or the OLG type occur only when there is some degree of heterogeneity among consumers, differential savings, income diversity, or market specialization. Otherwise, without income effects or distribution effects long run steady states are mostly asymptotically stable predicting stable balanced growth for many of the commonly accepted growth models under most aggregative concave neoclassical production functions. This paper provides an attempt to exhibit a full richness of bifurcation scenarios for endogenously generated cycles using minimal extensions concerning preferences, technologies, and ownership of capital by extending the models of Kaldor, Pasinetti, and others to allow for ownership of capital among OLG consumers of workers and capitalists. It is shown that, under a sufficiently low but constant elasticity of substitution, the interaction of the nonlinear income distribution with heterogeneous logarithmic intertemporal preferences of consumers causes a variety of local bifurcation scenarios (Neimark–Sacker, fold, period doubling), multi-stability, as well as a rich variety of complex global dynamic features, such as homoclinic tangles, periodicity regions originating from Arnold tongues, closed curve attractors, and complex basins. The paper provides a detailed numerical analysis under a CES production scenario of several global bifurcations arising from heterogeneity which does not exist under the specific ownership restrictions imposed in the original Kaldor/Pasinetti models.

We study the discrete time neoclassical one-sector growth model with differential savings while assuming Kadiyala production function which shows a variable elasticity of substitution symmetric with respect to capital and labor. We show that, if workers save more than shareholders, then the growth path is bounded from above and the boundary is independent from the savings rate of shareholders. Moreover, the growth path for non-developed countries is influenced only by the savings rate of shareholders while level of capital per capita of developed economies is influenced by the savings rate of workers. We also show that multistability phenomena may occur so that the model is able to explain co-existence of under-developed, developing and developed economies. We prove that fluctuations and complex dynamics may arise when the elasticity of substitution between production factors is lower than one and shareholders save more than workers.

The inequality of wealth in China has increased rapidly in recent years. Prior to 1978 all Chinese households possessed negligible wealth. China therefore presents a fascinating case study of how inequality of household wealth increases as economic reforms take place, marketization occurs, and capital accumulates. Wealth inequality and its growth are measured and decomposed using data from two national sample surveys of the China Household Income Project (CHIP) relating to 2002 and 2013. Techniques are devised and applied to measure the sensitivity of wealth inequality to plausible assumptions about the under-representation of and the under-reporting by the wealthy. An attempt is made to explain the rising wealth inequality in terms of the relationships between income and wealth, house price inflation, differential savings, and income from wealth.

This paper extends Goodwin’s growth cycle model by assuming both differential savings propensities and disequilibrium in the goods market. It is shown that both modifications entail an increase in the dimensionality of the dynamical system of the model. By applying the existence part of the Hopf bifurcation theorem, the possibility of persistent and bounded cyclical paths for the resulting 4-dimensional dynamical system is then established. With the help of numerical simulation some evidence is finally given that the limit cycle emerging from the Hopf bifurcation is stable.