S. Brianzoni

Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings as in Bohm and Kaas (2000) while assuming a nonconcave production function in the form given by Capasso et. al. (2010). We prove that complex features are exhibited related both to the structure of the coexixting attractors and to their basins. We also show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained while considering concave production functions (see, for instance, Brianzoni et al. (2007) (2009) and (2011)).

Border collision bifurcations of superstable cycles in a one-dimensional piecewise smooth map

We study the dynamics of a one-dimensional piecewise smooth map defined by constant and logistic functions. This map has qualitatively the same dynamics as the one defined by constant and unimodal functions, coming from an economic application. Namely, it contributes to the investigation of a model of the evolution of corruption in public procurement proposed by Brianzoni et al. [4]. Bifurcation structure of the economically meaningful part of the parameter space is described, in particular, the fold and flip border-collision bifurcation curves of the superstable cycles are obtained. We show also how these bifurcations are related to the well-known saddle-node and period-doubling bifurcations.

Local and Global Dynamics in a Neoclassical Growth Model with Nonconcave Production Function and Nonconstant Population Growth Rate

In this paper we analyze the dynamics shown by the neoclassical one-sector growth model with differential savings as in Bohm and Kaas [J. Econom. Dynam. Control, 24 (2000), pp. 965--980] while assuming a sigmoidal production function as in [V. Capasso, R. Engbers, and D. La Torre, Nonlinear Anal., 11 (2010), pp. 3858--3876] and the labor force dynamics described by the Beverton--Holt equation (see [R. J. H. Beverton and S. J. Holt, Fishery Invest., 19 (1957), pp. 1--533]). We prove that complex features are exhibited, related both to the structure of the coexisting attractors (which can be periodic or chaotic) and to their basins (which can be simple or nonconnected). In particular we show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained with concave production functions. Anyway, in contrast to previous studies, the use of the S-shaped production function implies the existence of a po...

Updating Wealth in an Asset Pricing Model with Heterogeneous Agents

We consider an asset-pricing model with wealth dynamics in a market populated by heterogeneous agents. By assuming that all agents belonging to the same group agree to share their wealth whenever an agent joins the group (or leaves it), we develop an adaptive model which characterizes the evolution of wealth distribution when agents switch between different trading strategies. Two groups with heterogeneous beliefs are considered: fundamentalists and chartists. The model results in a nonlinear three-dimensional dynamical system, which we have studied in order to investigate complicated dynamics and to explain wealth distribution among agents in the long run.

Complex Dynamics in a Growth Model with Corruption in Public Procurement

We study the relationship between corruption in public procurement and economic growth within the Solow framework in discrete time, while assuming that the public good is an input in the productive process and that the State fixes a monitoring level on corruption. The resulting model is a bidimensional triangular dynamic system able to generate endogenous fluctuations for certain values of some relevant parameters. We study the model from the analytical point of view and find that multiple equilibria with nonconnected basins are likely to emerge. We also perform a stability analysis and prove the existence of a compact global attractor. Finally, we focus on local and global bifurcations causing the transition to more and more complex asymptotic dynamics. In particular, as our map is nondifferentiable in a subset of the states space, we show that border collision bifurcations occur. Several numerical simulations support the analysis. Our study aims at demonstrating that no long-run equilibria with zero corruption exist and, furthermore, that periodic or aperiodic fluctuations in economic growth are likely to emerge. As a consequence, the economic system may be unpredictable or structurally unstable.

A Stochastic Cobweb Dynamical Model

We consider the dynamics of a stochastic cobweb model with linear demand and a backward-bending supply curve. In our model, forward-looking expectations and backward-looking ones are assumed, in fact we assume that the representative agent chooses the backward predictor with probability 𝑞_,__0_𝑞_1, and the forward predictor with probability (1−𝑞), so that the expected price at time 𝑡 is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.

Complex Dynamics in an Asset Pricing Model with Updating Wealth

In recent years, several models have focused on the study of the asset price dynamics and wealth distribution when the economy is populated by boundedly rational heterogeneous agents with Constant Relative Risk Aversion (CRRA) preferences. Chiarella and He (2001) study an asset pricing model with heterogeneous agents and fixed population fractions. In order to obtain a more appealing framework, Chiarella and He (2002) allow agents to switch between different trading strategies. More recently, Chiarella et al. (2006) consider a market maker model of asset pricing and wealth dynamics with fixed proportions of agents. A large part of contributions to the development and analysis of financial models with heterogeneous agents and CRRA utility do not consider that agents can switch between different predictors. Moreover, the models which allow agents to switch between different trading strategies make the following simplified assumption: when agents switch from an old strategy to a new strategy, they agree to accept the average wealth level of agents using the new strategy. Motivated by such considerations, we develop a new model based upon a more realistic assumption. In fact, we assume that all agents belonging to the same group agree to share their wealth whenever an agent joins the group (or leaves it). The most important fact is that the wealth of the new group takes into account the wealth realized in the group of origin, whenever agents switch between different trading strategies. This leads the final system to a particular form, in which the average wealth of agents is defined by a continuous piecewise function and the phase space is divided into two regions. Nevertheless, our final dynamical system is three dimensional and we can find all the equilibria. We will prove that it admits two kinds of steady states, fundamental steady states (with the price being at the fundamental value) and non fundamental steady states. Several numerical simulations supplement the analysis.