On a spatial Solow model with technological diffusion and nonconcave production function

Capasso, Vincenzo; Engbers, Ralf; Torre, Davide La

doi:10.1016/j.nonrwa.2010.01.016

Cited by 47 publications

(52 citation statements)

References 19 publications

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“…The condition on consumption in (15) states that gross investment should not be negative at any time and at any location; (16) states instead the obvious condition that the abatement share needs to belong to the closed interval [0, 1].…”

Section: The Ramsey-type Problemmentioning

confidence: 99%

Pollution diffusion and abatement activities across space and over time

Torre

Liuzzi

Marsiglio

2015

Mathematical Social Sciences

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We analyze the spatio-temporal dynamics of capital and pollution in an economic growth model with purposive environmental protection activities. The production process of a unique homogeneous good generates pollution, thus the increases in output associated with economic growth tend to rise the stock of pollution. Pollution is a negative production externality which thus feeds back on the economy lowering the level of output; in order to compensate for such a negative effect associated with economic development, pollution is reduced by publicly funded abatement activities. We firstly consider a Solow-type framework in which economic and environmental policies are completely exogenous, and then we move to a Ramsey-type context in which they are endogenously determined. We analyze the spatio-temporal dynamics of the model economy through numerical simulations, and we consider two different specifications of the production function (a globally concave and a convex-concave technology) in order to stress the role that eventual poverty traps might play on both economic and environmental outcomes. We show that in the convexconcave technology framework, whenever rich regions are substantially rich diffusion can help poor regions to escape their poverty traps; if however they are not rich enough diffusion might condemn also rich regions to collapse. However, even if rich regions are particularly rich whenever the pollution externality is strong, the whole spatial economy might be doomed to collapse. Forthcoming in Mathematical Social Sciences AbstractWe analyze the spatio-temporal dynamics of capital and pollution in an economic growth model with purposive environmental protection activities. The production process of a unique homogeneous good generates pollution, thus the increases in output associated with economic growth tend to rise the stock of pollution. Pollution is a negative production externality which thus feeds back on the economy lowering the level of output; in order to compensate for such a negative effect associated with economic development, pollution is reduced by publicly funded abatement activities. We firstly consider a Solow-type framework in which economic and environmental policies are completely exogenous, and then we move to a Ramseytype context in which they are endogenously determined. We analyze the spatio-temporal dynamics of the model economy through numerical simulations, and we consider two different specifications of the production function (a globally concave and a convex-concave technology) in order to stress the role that eventual poverty traps might play on both economic and environmental outcomes. We show that in the convex-concave technology framework, whenever rich regions are substantially rich diffusion can help poor regions to escape their poverty traps; if however they are not rich enough diffusion might condemn also rich regions to collapse. However, even if rich regions are particularly rich whenever the pollution externality is strong, the whole spatial economy mi...

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Section: The Ramsey-type Problemmentioning

confidence: 99%

Pollution diffusion and abatement activities across space and over time

Torre

Liuzzi

Marsiglio

2015

Mathematical Social Sciences

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“…Neto and Claeyssen [24] consider the stability of a spatial Solow model with labor mobility and prove that capital induced labor migration is a necessary condition for the spatiotemporal dynamics of the model. Capasso et al [25] prove the steady state of the classical Solow model with a nonconcave production function and analyze the convergence of a spatial Solow model with technological diffusion. In our paper, we generalize the classical Solow model in [25] and obtain the steady states of the generalized Solow model in a geographic structure.…”

Section: Introductionmentioning

confidence: 99%

“…Capasso et al [25] prove the steady state of the classical Solow model with a nonconcave production function and analyze the convergence of a spatial Solow model with technological diffusion. In our paper, we generalize the classical Solow model in [25] and obtain the steady states of the generalized Solow model in a geographic structure. In open regions, we prove the existence and uniqueness of solution for a partial differential equation with corresponding boundary conditions, which is different from convergence analysis in [25].…”

Section: Introductionmentioning

confidence: 99%

“…In our paper, we generalize the classical Solow model in [25] and obtain the steady states of the generalized Solow model in a geographic structure. In open regions, we prove the existence and uniqueness of solution for a partial differential equation with corresponding boundary conditions, which is different from convergence analysis in [25].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spatial Dynamics for a Generalized Solow Growth Model

Zhong

Huang

2018

Discrete Dynamics in Nature and Society

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The existence of nontrivial equilibrium and poverty traps for a generalized Solow growth model with concave and nonconcave production functions is investigated. The explicit solutions of the growth model, which is expressed by a differential equation with corresponding boundary conditions, are employed to illustrate the spatial dynamics of the model in different economic regions. Numerical method is used to justify the validity of the theoretical analysis.

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“…We will give some numerical examples for the reconstruction of the production function (see [8,9]). We assume we have the given data k ε i ∈ [0, 1] × [0, T] with i = 1, 2, 3 (figures 2, 4 and 5) with the respective noise level…”

Section: (I) Constant Technological Levelmentioning

confidence: 99%

Inverse problems in geographical economics: parameter identification in the spatial Solow model

Engbers

Burger

Capasso

2014

Phil. Trans. R. Soc. A.

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The identification of production functions from data is an important task in the modelling of economic growth. In this paper, we consider a non-parametric approach to this identification problem in the context of the spatial Solow model which allows for rather general production functions, in particular convex–concave ones that have recently been proposed as reasonable shapes. We formulate the inverse problem and apply Tikhonov regularization. The inverse problem is discretized by finite elements and solved iteratively via a preconditioned gradient descent approach. Numerical results for the reconstruction of the production function are given and analysed at the end of this paper.

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On a spatial Solow model with technological diffusion and nonconcave production function

Cited by 47 publications

References 19 publications

Pollution diffusion and abatement activities across space and over time

Pollution diffusion and abatement activities across space and over time

Spatial Dynamics for a Generalized Solow Growth Model

Inverse problems in geographical economics: parameter identification in the spatial Solow model

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