Spatial dynamics and convergence: The spatial AK model

Boucekkine, Raouf; Camacho, Carmen; Fabbri, Giorgio

doi:10.1016/j.jet.2013.09.013

Cited by 102 publications

(119 citation statements)

References 12 publications

(22 reference statements)

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“…It is well known that systems similar to ours cannot be solved analytically (with the exception of the linear production function case, as in Boucekkine et al, 2013b). Thus, in order to analyze the behavior of capital and pollution we need to rely on numerical simulations.…”

Section: Spatio-temporal Dynamicsmentioning

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: Spatio-temporal Dynamicsmentioning

confidence: 99%

Pollution diffusion and abatement activities across space and over time

Torre

Liuzzi

Marsiglio

2015

Mathematical Social Sciences

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“…In a simpli…ed set-up, consider a large number of …rms which occupy a spatial domain O; sell a homogeneous output at an exogenous price, face quadratic adjustment costs with respect to net investment, and experience knowledge spillovers which generate spatial interactions among them. The RE and SO problems can be written as: 1 2 An interesting paper by Boucekkine et al (2010) studies optimal dynamic social welfare, e.g., an analog of our SO problem in an AK type model with a trade balance on a circular space where capital is mobile across space and growth occurs. It would be interesting to model the e¤ect of introducing spillover externalities like ours as well as introducing growth and trends like Boucekkine et al (2010) and comparing the solutions for SO and RE as we do in our paper.…”

Section: Discussion Extensions and Concluding Remarksmentioning

confidence: 99%

“…leads to a reformulation of the instantaneous budget constraint in a static 3 We assume that the agent (or the site) has discounted future income greater than any desired borrowing at any point in time. Thus the capitalized, at the rate r; sum of the site's future income is large enough to pay o¤ the debt incurred by borrowing.…”

Section: Hmentioning

confidence: 99%

Optimal agglomerations in dynamic economics

Brock¹,

Xepapadeas²,

Yannacopoulos³

2014

Journal of Mathematical Economics

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We study rational expectations equilibrium problems and social optimum problems in in…nite horizon spatial economies in the context of a Ramsey type capital accumulation problem with geographical spillovers. We identify su¢ cient local and global conditions for the emergence (or not) of optimal agglomeration, using techniques from monotone operator theory and spectral theory in in…nite dimensional Hilbert spaces. Our analytical methods can be used to systematically study optimal potential agglomeration and clustering in dynamic economics.

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“…LP n (x) = n (n + 1) P n (x). 4 We use this property in the solution of the model. The term D (T (t)) LT (x; t) models therefore the heat ‡ux associated with the temperature anomaly.…”

Section: Temperature Dynamics and Heat Transportmentioning

confidence: 99%

Spatial Heat Transport, Polar Amplification and Climate Change Policy

Brock

Xepapadeas

2016

SSRN Journal

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This paper is, to our knowledge, the …rst paper in climate economics to consider the combination of spatial heat transport and polar ampli…cation.We simpli…ed the problem by stratifying the Earth into latitude belts and assuming, as in North et al. (1981), that the two hemispheres were symmetric. Our results suggest that it is possible to build climate economic models that include the very real climatic phenomena of heat transport and polar ampli…cation and still maintain analytical tractability. We derive optimal fossil fuel paths under heat transport with and without polar ampli…cation.We show that the optimal tax function depends not only on the distribution of welfare weights but also on the distribution of population across latitudes, the distribution of marginal damages across latitudes and cross latitude interactions of marginal damages, and climate dynamics. We also determine optimal taxes per unit of emission and show that, in contrast to the standard results suggesting spatially uniform emission taxes, poorer latitudes should be taxed less per unit emissions than richer latitudes.JEL Classi…cation: Q54, Q58, C61

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Spatial dynamics and convergence: The spatial AK model

Cited by 102 publications

References 12 publications

Pollution diffusion and abatement activities across space and over time

Pollution diffusion and abatement activities across space and over time

Optimal agglomerations in dynamic economics

Spatial Heat Transport, Polar Amplification and Climate Change Policy

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