12 results on '"Elisabetta Michetti"'
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2. Asset price-GDP cross feedback. The role of dividend policies in a dynamic setting
- Author
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Francesca Grassetti, Cristiana Mammana, and Elisabetta Michetti
- Subjects
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie ,Numerical Analysis ,Economic development ,Nonlinear dynamics ,Applied Mathematics ,Modeling and Simulation ,Behavioural finance ,Economic growth ,Dividend payout ratio ,OLG model - Published
- 2023
- Full Text
- View/download PDF
3. On the Effect of Labour Productivity on Growth: Endogenous Fluctuations and Complex Dynamics
- Author
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Elisabetta Michetti, Francesca Grassetti, and Cristiana Mammana
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Macroeconomics ,Article Subject ,lcsh:Mathematics ,Differential (mechanical device) ,lcsh:QA1-939 ,01 natural sciences ,Boom ,010305 fluids & plasmas ,010101 applied mathematics ,Complex dynamics ,Bust ,Modeling and Simulation ,Capital (economics) ,0103 physical sciences ,Economics ,Per capita ,Production (economics) ,0101 mathematics ,Productivity - Abstract
This paper introduces a sigmoidal production function that considers production possible even when the only input is labour. The long-run behaviour of an economy described by the neoclassical Solow-type growth model with differential savings is investigated considering the technology presented. It is found that labour productivity influences the existence of boom and bust periods as well as the level of capital per capita in equilibrium.
- Published
- 2018
- Full Text
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4. Border Collision Bifurcations in a Generalized Model of Population Dynamics
- Author
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Jose C. Valverde, Elisabetta Michetti, Cristiana Mammana, and Lilia M. Ladino
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Dynamical systems theory ,Article Subject ,Population ,Population Dynamics ,01 natural sciences ,010305 fluids & plasmas ,Control theory ,0103 physical sciences ,Statistical physics ,0101 mathematics ,education ,Multistability ,Mathematics ,education.field_of_study ,lcsh:Mathematics ,010102 general mathematics ,Phase plane ,Piecewise-smooth ,lcsh:QA1-939 ,Mathematical theory ,Discrete time and continuous time ,Population model ,Modeling and Simulation ,Cycles ,Maps ,Piecewise - Abstract
We analyze the dynamics of a generalized discrete time population model of a two-stage species with recruitment and capture. This generalization, which is inspired by other approaches and real data that one can find in literature, consists in considering no restriction for the value of the two key parameters appearing in the model, that is, the natural death rate and the mortality rate due to fishing activity. In the more general case the feasibility of the system has been preserved by posing opportune formulas for the piecewise map defining the model. The resulting two-dimensional nonlinear map is not smooth, though continuous, as its definition changes as any border is crossed in the phase plane. Hence, techniques from the mathematical theory of piecewise smooth dynamical systems must be applied to show that, due to the existence of borders, abrupt changes in the dynamic behavior of population sizes and multistability emerge. The main novelty of the present contribution with respect to the previous ones is that, while using real data, richer dynamics are produced, such as fluctuations and multistability. Such new evidences are of great interest in biology since new strategies to preserve the survival of the species can be suggested.
- Published
- 2016
5. Complex attractors and basins in a growth model with nonconcave production function and logistic population growth rate
- Author
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Elisabetta Michetti
- Subjects
Numerical Analysis ,Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie ,General Computer Science ,Elasticity of substitution ,Applied Mathematics ,Factors of production ,Function (mathematics) ,Theoretical Computer Science ,Complex dynamics ,Modeling and Simulation ,Attractor ,Econometrics ,Production (economics) ,Population growth ,Logistic function ,Mathematical economics ,Mathematics - Abstract
In this paper we study a discrete-time growth model of the Solow type with nonconcave production function where shareholders save more than workers and the population growth dynamics is described by the logistic equation. We prove that the resulting system has a compact global attractor and we describe its structure. We also perform a mainly numerical analysis to show that complex features are exhibited, related both to the structure of the coexisting attractors and to their basins. The study presented aims at showing the existence of complex dynamics when the elasticity of substitution between production factors is not too high (so that capital income declines) or the parameter in the logistic equation increases (so that the amplitude of movements in the population growth rate increases).
- Published
- 2015
6. Market Share Delegation in a Bertrand Duopoly. Synchronisation and Multistability
- Author
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Luca Gori, Elisabetta Michetti, Luciano Fanti, and Cristiana Mammana
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Article Subject ,Discrete time system ,lcsh:Mathematics ,lcsh:QA1-939 ,Complementarity (physics) ,Microeconomics ,Modeling and Simulation ,Bertrand competition ,Attractor ,Economics ,Differentiable function ,Market share ,Duopoly ,Multistability - Abstract
This paper tackles the issue of local and global analyses of a duopoly game with price competition and market share delegation. The dynamics of the economy is characterised by a differentiable two-dimensional discrete time system. The paper stresses the importance of complementarity between products as a source of synchronisation in the long term, in contrast to the case of their substitutability. This means that when products are complements, players may coordinate their behaviour even if initial conditions are different. In addition, there exist multiple attractors so that even starting with similar conditions may end up generating very different dynamic patterns.
- Published
- 2015
7. Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function
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Serena Brianzoni, Elisabetta Michetti, and Cristiana Mammana
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Article Subject ,Elasticity of substitution ,lcsh:Mathematics ,Structure (category theory) ,Factors of production ,Function (mathematics) ,lcsh:QA1-939 ,Discrete time and continuous time ,Modeling and Simulation ,Attractor ,Applied mathematics ,Production (economics) ,Differential (infinitesimal) ,Mathematical economics ,Mathematics - Abstract
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)).
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- 2012
8. Complex Dynamics in a Growth Model with Corruption in Public Procurement
- Author
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Serena Brianzoni, Elisabetta Michetti, and Raffaella Coppier
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Article Subject ,Corruption ,lcsh:Mathematics ,media_common.quotation_subject ,Public good ,lcsh:QA1-939 ,Stability (probability) ,Complex dynamics ,Procurement ,Discrete time and continuous time ,Aperiodic graph ,Modeling and Simulation ,Attractor ,Economics ,Mathematical economics ,media_common - Abstract
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.
- Published
- 2011
- Full Text
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9. Border Collision Bifurcations of Superstable Cycles in a One-Dimensional Piecewise Smooth Map
- Author
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Iryna Sushko, Serena Brianzoni, and Elisabetta Michetti
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Discrete mathematics ,Numerical Analysis ,General Computer Science ,Applied Mathematics ,Mathematical analysis ,Structure (category theory) ,Parameter space ,Collision ,Theoretical Computer Science ,Modeling and Simulation ,Piecewise ,Logistic function ,Constant (mathematics) ,Bifurcation ,Mathematics - Abstract
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.
- Published
- 2010
10. Updating Wealth in an Asset Pricing Model with Heterogeneous Agents
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Serena Brianzoni, Elisabetta Michetti, and Cristiana Mammana
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Computer Science::Multiagent Systems ,Article Subject ,Order (exchange) ,Modeling and Simulation ,lcsh:Mathematics ,Econometrics ,Economics ,Joins ,Capital asset pricing model ,Trading strategy ,Wealth distribution ,Dynamical system ,lcsh:QA1-939 - Abstract
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.
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- 2010
- Full Text
- View/download PDF
11. Endogenous Instability in Credit-Constrained Emerging Economies with Leontief Technology
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Elisabetta Michetti and Cristiana Mammana
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Article Subject ,Moral hazard ,lcsh:Mathematics ,Small open economy ,Monetary economics ,lcsh:QA1-939 ,endogenous instability ,Complex dynamics ,Information asymmetry ,Modeling and Simulation ,Capital (economics) ,Attractor ,border collision bifurcations ,Economics ,Emerging economies ,State space ,Emerging markets - Abstract
This work provides a framework to analyze the role of financial development as a source of endogenous instability in emerging economies subject to moral hazard problems. We propose and study a dynamic model describing a small open economy with a tradeable good produced by internationally mobile capital and a country specific input, using Leontief technology. We demonstrate that emerging markets could be endogenously unstable since large capital inflows increase risk and exacerbate asymmetric information problems, according to empirical evidences. Using bifurcation and stability analysis, we describe the properties of the system attractors, we assess the plausibility for complex dynamics and, we find out that border collision bifurcations can emerge due to the fact that the state space is piecewise smooth. As a consequence, when a fixed or periodic point loses its stability, the final dynamics may become suddenly chaotic. This fact may explain how financial crises occurred in emerging economies.
- Published
- 2008
12. A stochastic cobweb dinamical model
- Author
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Elisabetta Michetti, Serena Brianzoni, Francesco Zirilli, and Cristiana Mammana
- Subjects
Article Subject ,Markov chain ,lcsh:Mathematics ,Discrete phase-type distribution ,Markov process ,lcsh:QA1-939 ,Markov model ,Dynamical system ,symbols.namesake ,Modeling and Simulation ,Bounded function ,symbols ,Applied mathematics ,Cobweb model ,Mathematical economics ,Random variable ,Mathematics - Abstract
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 โ 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.
- Published
- 2008
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