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Growth Models with Externalities on Networks

Author

Listed:
  • Giorgio Fabbri

    (Univ.Grenoble Alpes, CNRS, INRIA, Grenoble INP, GAEL, Grenoble, France)

  • Silvia Faggian

    (Department of Economics, Ca' Foscari University of Venice)

  • Giuseppe Freni

    (Department of Business and Economics, University of Naples "Parthenope", Naples, Italy.)

Abstract

This study examines the dynamics of capital stocks distributed among several nodes, representing different sites of production and connected via a weighted, directed network.The network represents the externalities or spillovers that the production in each node generates on the capital stock of other nodes. A regulator decides to designate some of the nodes for the production of a consumption good to maximise a cumulative utility from consumption. It is demonstrated how the optimal strategies and stocks depend on the productivity of the resource sites and the structure of the connections between the sites. The best locations to host production of the consumption good are identified per the model's parameters and correspond to the least central (in the sense of eigenvector centrality) nodes of a suitably redefined network that combines both flows between nodes and the nodes' productivity.

Suggested Citation

  • Giorgio Fabbri & Silvia Faggian & Giuseppe Freni, 2023. "Growth Models with Externalities on Networks," Working Papers 2023: 23, Department of Economics, University of Venice "Ca' Foscari".
    • Handle: RePEc:ven:wpaper:2023:23
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    References listed on IDEAS

    as
    1. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    2. Le Van, Cuong & Vailakis, Yiannis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Journal of Economic Theory, Elsevier, vol. 123(2), pages 187-209, August.
    3. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
    4. Jess Benhabib & Qinglai Meng & Kazuo Nishimura, 2012. "Indeterminacy Under Constant Returns to Scale in Multisector Economies," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 403-412, Springer.
    5. Sanchirico, James N. & Wilen, James E., 2005. "Optimal spatial management of renewable resources: matching policy scope to ecosystem scale," Journal of Environmental Economics and Management, Elsevier, vol. 50(1), pages 23-46, July.
    6. Calvia, Alessandro & Gozzi, Fausto & Leocata, Marta & Papayiannis, Georgios I. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2024. "An optimal control problem with state constraints in a spatio-temporal economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    7. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    8. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
    9. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 2024. "On competition for spatially distributed resources in networks," Theoretical Economics, Econometric Society, vol. 19(2), May.
    10. Giorgio Fabbri & Silvia Faggian & Giuseppe Freni, 2022. "On competition for spatially distributed resources in networks: an extended version," Working Papers 2022:03, Department of Economics, University of Venice "Ca' Foscari".
    11. Fabbri, Giorgio, 2016. "Geographical structure and convergence: A note on geometry in spatial growth models," Journal of Economic Theory, Elsevier, vol. 162(C), pages 114-136.
    12. Dolmas, Jim, 1996. "Endogenous Growth in Multisector Ramsey Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 403-421, May.
    13. Calvia, Alessandro & Gozzi, Fausto & Leocata, Marta & Papayiannis, Georgios I. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2024. "An optimal control problem with state constraints in a spatio-temporal economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    14. Cuong Le Van & Yiannis Vailakis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Post-Print halshs-00101201, HAL.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Capital allocation; Production externalities; Network spillovers; Economic centrality measures.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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