Modified neoclassical growth models with delay: a critical survey and perspectives

Феррара, Массимилиано; Guerrini, Luca; Mavilia, Roberto

doi:10.12988/ams.2013.36318

Cited by 9 publications

(8 citation statements)

References 12 publications

(20 reference statements)

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“…The EcoSolow model may also be improved by introducing a delay in the energy production process during photosynthesis relative to the phytomass accumulation process. Economic models of production include a corresponding delay [34].…”

Section: Discussionmentioning

confidence: 99%

Modeling Production Processes in Forest Stands: An Adaptation of the Solow Growth Model

Soukhovolsky

Ivanova

2018

Forests

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The model of forest stand growth proposed in this study is based on R. Solow's model of economic growth. The variables introduced into the model are the "capital" (the phytomass of the non-synthesizing tree components in the stand-the stem, roots, and branches) and the "labor" (the phytomass of the photosynthesizing tree components in the stand-leaves or needles). Root phytomass is calculated with a special independent model. The process of energy production by the trees is described with the Cobb-Douglas equation. The proposed approach is used to describe growth processes in the forest stands comprising various species in Siberia and the age dynamics of net primary production. The model can explain a number of effects (such as death of the forest stand after the needles have been consumed by defoliating insects) that cannot be explained by standard logistic models.

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Section: Discussionmentioning

confidence: 99%

Modeling Production Processes in Forest Stands: An Adaptation of the Solow Growth Model

Soukhovolsky

Ivanova

2018

Forests

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“…This model is usually called the Solow model, less often Solow-Swan. This model describes the dynamics of the variable p = p(τ ), where τ is time. This variable is frequently called the variable capital -labor in economic literature [2,3,4,5,23,24,25]. It is usually defined as the ratio p = K/L, where K = K(τ ) denotes the physical capital, and L = L(τ ) denotes the number of people employed in the economy.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, equation (12) needs modifications. The most natural method is based on the consideration of the delay factor characteristic for economic processes in a market economy (see [2,3,5,15,16,18,19,23,24]).…”

Section: Introductionmentioning

confidence: 99%

Periodic Cycles in the Solow Model With a Delay Effect

Kulikov

Куликов

2019

Mathematical Modelling and Analysis

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The three natural modifications of the known mathematical macroeconomics model of macroeconomics are studied in which a delay factor is presumed. This led to the replacement of the ordinary differential equation, which cannot exhibit periodic cycles on the equations with a deviating argument (functional-differential equations). It was possible to show the existence of periodic solutions that can and are intended to describe the periodic cycles in the market economy in two of the three variants of such changes in the classical form of the model. The mathematical portion is based on the application of the modern theory of dynamical systems with an infinite-dimensional space of initial conditions. This will allow us to apply the Andronov-Hopf Theorem for equations with a deviating argument in such a form that the parameters of the cycles are located. We will also apply the well-known Krylov-Bogolyubov algorithm that is extended to infinite-dimensional dynamical systems that is used and reduces the problem to the analysis of the finite-dimensional system of ordinary differential equations-the normal Poincare-Dulac form.

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“…This hypothesis was introduced by Zak (1999) in a one-sector model with physical capital. However, in their works both Zak (1999) and Ferrara et al (2013) conduct only a local analysis and establish the existence of a Hopf bifurcation. This kind of bifurcation explains the possibility of business cycles in these two frameworks but nothing is said about their stability (see, for example, Ferrara et al, 2014 for some formal results concerning the direction and stability of the Hopf bifurcation in a modified Solow model) and the behaviour of the dynamic system when the time delay goes beyond its bifurcation value.…”

Section: Introductionmentioning

confidence: 99%

A model of economic growth with physical and human capital: The role of time delays

Gori

Guerrini

Sodini

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This article aims at analysing a two-sector economic growth model with discrete delays. The focus is on the dynamic properties of the emerging system. In particular, this study concentrates on the stability properties of the stationary solution, characterised by analytical results and geometrical techniques (stability crossing curves), and the conditions under which oscillatory dynamics emerge (through Hopf bifurcations). In addition, this article proposes some numerical simulations to illustrate the behaviour of the system when the stationary equilibrium is unstable.

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Modified neoclassical growth models with delay: a critical survey and perspectives

Abstract: This paper reviews the relationship between lags and cycles into classical structures of growth models (see Solow-Swan and Ramsey models). Some remarks and perspectives of research are determined.

Cited by 9 publications

References 12 publications

Modeling Production Processes in Forest Stands: An Adaptation of the Solow Growth Model

Modeling Production Processes in Forest Stands: An Adaptation of the Solow Growth Model

Periodic Cycles in the Solow Model With a Delay Effect

A model of economic growth with physical and human capital: The role of time delays

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