Global attractor in Solow growth model with differential savings and endogenic labor force growth

In this paper we study the dynamics of a discrete triangular system T in capital per capita and population growth representing the neoclassical growth model with CES production function and differential savings, under the assumption that the labor force growth rate is endogenous and described by a generic iterative scheme having a unique positive globally stable equilibrium. The study herewith presented aims at confirming the existence of a compact global attractor for system T along the invariant line. Consequently asymptotic dynamics of growth models with constant population growth rate can be related to those with non-constant population growth if the steady state rate is globally stable. Furthermore we prove that the system exhibits cycles or even chaotic dynamics patterns if shareholders save more than workers, when the elasticity of substitution between production factors drops below one (so that capital income declines). The analytical results are supplemented by numerical simulations.chaotic dynamics,,Compact global attractor,,Developing Countries,endogenic population growth.

A Dynamic Stochastic Model of Asset Pricing with Heterogeneous Beliefs

This paper presents a new stochastic asset pricing model in a context of bounded rationality, where beliefs about future prices are formed via an expectations updating rule characterized by a stochastic multiplicative random variable, working as an agent-based time dependent weight of the conditional expectation of the fundamental. The agent’s belief about future prices depends on his confidence in the forecasts made by other agents, measured by the distribution type of agents and by a confidence parameter. The resulting stochastic dynamical system is firstly analyzed in a deterministic setting, deriving conditions for uniqueness and stability of steady states and proving that, for high values of the confidence parameter, no complicated dynamics can be exhibited, hence the new component has a stabilizing effect on the qualitative dynamics. Differently, for small values of the confidence parameter, we prove the existence of a stability region in the parameters plane where the only possible dynamics is convergence to a steady state, while complexity is exhibited outside such region. Starting from the results obtained in the deterministic case, the model is then explored by reintroducing randomness. More specifically, we analyze the stability region in three directions: first of all, a robust estimate of the stability region’s measure is provided; second, a long run equilibrium relation between the parameters of the system is obtained; third, the persistence properties of the series describing the bifurcation curves is performed. We finally underline some economic implications

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

Non-linear Dynamics in a Business-Cycle Model with Logistic Population Growth

We consider a discrete-time growth model of the Solow type where workers and shareholders have different but constant saving rates and the population growth dynamics is described by the logistic equation able to exhibit complicated dynamics. We show conditions for the resulting system having a compact global attractor and we describe its structure. We also perform a mainly numerical analysis using the critical lines method able to describe the strange attractor and the absorbing area, in order to show how cyclical or complex fluctuations may be produced in a business-cycle model. We study the dynamic behaviour of the model under different ranges of the main parameters, i.e. the elasticity of substitution between the two production factors and the one in the logistic equation (namely m). We prove the existence of complex dynamics when the elasticity of substitution between production factors drops below one (so that capital income declines) or m increases (so that the amplitude of movements in the population growth rate increases)

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 poverty trap: by performing a global analysis we study the properties of the regions generating trajectories converging to it

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 while assuming a nonconcave production function. We prove that complex features exhibited are 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

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

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 , and the forward predictor with probability , so that the expected price at time 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

Incorporating PET information in radiation therapy planning

PET scanning, because of its impressive sensitivity and accuracy, is being incorporated into the standard staging workup for many cancers. These include lung cancer, lymphomas, head and neck cancers, and oesophageal cancers. PET often provides incremental information about the patient’s disease status, adding to the data obtained from structural imaging methods, such as, CT scan or MRI. PET commonly upstages patients into more advanced disease categories. Incorporation of PET information into the radiotherapy planning process has the potential to reduce the risks of geographic miss and can help minimise unnecessary irradiation of normal tissues. The best means of incorporating PET information into radiotherapy planning is uncertain, and considerable effort is being expended in this area of research

Recommendations for post-surgical thyroid ablation in differentiated thyroid cancer: a 2015 position statement of the Italian Society of Endocrinology

Post-surgical ablation of thyroid remnant with radioactive iodine (RAI) in differentiated thyroid cancer (DTC) is aimed to destroy any thyroid remnant in the thyroid bed (remnant ablation) and any microscopic foci of cancer cells eventually present within the thyroid remnant (adjuvant therapy). The present text is an attempt to offer practice guidelines for the indication of thyroid ablation and the preparation of DTC patients considering the latest achievement in the field and the changing epidemiology of DTC observed in the last 10 years