This study investigates an aggregative optimal growth model in which short-lived individuals obtain their labour skill through education. The process of human capital formation is described by an increasing, convex-concave education function relating the success rate to the educational expenditure per student. The cost of education is publicly funded by an income tax imposed on adult workers. Despite the apparent regularity and rationality of this idealized economy, it is shown that the existence of the steady state of the model is not guaranteed. In fact, the steady state only exists for carefully chosen social time rates of preference. However, the steady state, if it exists, is unique and in terms of local stability, a saddle point.

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The paper investigates conditions under which endogenous cyclic behavior may be observed within the context of Predator-Prey (Lotka-Volterra) Models. The analysis also establishes conditions under which such behavior is non-existent and hence establishes conditions for global convergence to the interior equilibrium, whenever it exists. The results are then applied to two diverse sets of economic exercises and shows how the conclusions of those exercises may be established under a much weaker set of assumptions. Based on these discussions, a numerical example of robust periodic behavior is provided.

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In this study we investigate the nonlinear dynamics of the traditional cobweb model with two types of heterogeneous producers who are risk averse and seek to learn the distribution of asset prices, in terms of the sample mean and variance of historical prices, using the arithmetic learning processes (ALP) over different window lengths. We show that heterogeneity has a double edged effect on the dynamics in the sense that heterogeneous learning can stabilize an otherwise unstable dynamics in some cases and destablize an otherwise stable dynamics in other cases as well. When the steady state becomes unstable, the model displays complicated dynamics through a variety of types of bifurcations.

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Recent work has cast considerable doubt on the plausibility of specific assumptions about how rational agents form out-of-equilibrium beliefs in finite extensive games in which beliefs are induced backwards. The point is that the resulting consistently aligned beliefs are incoherent in view of the counterfactuals they rely on. This paper asks: how will the possibility of inconsistently aligned beliefs affect the manner in which rational players play such games? It shows that, provided beliefs are aligned monotonically, some of the interesting qualitative features of the conventional approach remain unchanged.

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In this study we are not arguing that competition as it actually occurs in practice is not socially beneficial. Our criticism is directed instead at the false belief that rational profit-maximizing behavior and competition as defined by neoclassical economic theory will lead to a welfare-maximizing outcome-again, as defined by neoclassical theory.

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In this study we have provided some theoretical foundations for the empirical hypothesis that there exist clockwise-oriented long-phased fluctuations in the core variables unemployment rate, 1-e and inflation rate, on the one hand and employment rate e and real unit-wage costs, on the other hand. We have at first presented two simple prototype models of inflation, stagflation and disinflation in the spirit of Friedman’s reflection of such issues and of employment and real unit-wage costs (or the wage share) in the spirit of Goodwin’s[1] growth cycle model. It has already been observed by Atkinson[2] that in particular models of the Goodwin type tend towards long-phased fluctuations in employment and the wage share for reasonable parameter values. It may however be somewhat surprising that the same holds true (for reasonable sizes of the parameter in the employed Phillips curve) for the employment rate / inflation cycle as well, a cycle mechanism that is formally identical to the Goodwin one as we have shown. We thus arrived at the conclusion that there are cycles with a phase length much longer than the ordinary business cycle (in fact approximately five times as long as we saw in the empirical phase plots of the paper) which are not long waves from a Schumpeterian perspective, but caused by the fact that systematic changes in real unit-wage costs and also in inflation caused by changes in the (un-)employment rate may be slow, giving rise to interchanging long-lasting regimes of economic prosperity on the one hand and economic stagnation on the other hand.

Abstract:

In this study we investigate the nonlinear dynamics of the traditional cobweb model with two types of heterogeneous producers who are risk averse and seek to learn the distribution of asset prices, in terms of the sample mean and variance of historical prices, using the arithmetic learning processes (ALP) over different window lengths. We show that heterogeneity has a double edged effect on the dynamics in the sense that heterogeneous learning can stabilize an otherwise unstable dynamics in some cases and destabilize an otherwise stable dynamics in other cases as well. When the steady state becomes unstable, the model displays complicated dynamics through a variety of types of bifurcations.