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Optimal location of economic activity and population density: The role of the social welfare function

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Abstract

In this paper, we consider a spatiotemporal growth model where a social planner chooses the optimal location of economic activity across space by maximization of a spatiotemporal utilitarian social welfare function. Space and time are continuous, and capital law of motion is a parabolic partial differential diffusion equation. The production function is AK. We generalize previous work by considering a continuum of social welfare functions ranging from Benthamite to Millian functions. Using a dynamic programming method in infinite dimension, we can identify a closed-form solution to the induced HJB equation in infinite dimension and recover the optimal control for the original spatiotemporal optimal control problem. Optimal stationary spatial distributions are also obtained analytically. We prove that the Benthamite case is the unique case for which the optimal stationary detrended consumption spatial distribution is uniform. Interestingly enough, we also find that as the social welfare function gets closer to the Millian case, the optimal spatiotemporal dynamics amplify the typical neoclassical dilution population size effect, even in the long-run.

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  • Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "Optimal location of economic activity and population density: The role of the social welfare function," AMSE Working Papers 2003, Aix-Marseille School of Economics, France.
  • Handle: RePEc:aim:wpaimx:2003
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    References listed on IDEAS

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    1. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(1), pages 20-45, February.
    2. 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.
    3. 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.
    4. Robin Cubitt & Chris Starmer & Robert Sugden, 2001. "Discovered preferences and the experimental evidence of violations of expected utility theory," Journal of Economic Methodology, Taylor & Francis Journals, vol. 8(3), pages 385-414.
    5. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
    6. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    7. Raouf Boucekkine & Giorgio Fabbri, 2013. "Assessing Parfit’s Repugnant Conclusion within a canonical endogenous growth set-up," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(2), pages 751-767, April.
    8. Krugman, Paul, 1998. "What's New about the New Economic Geography?," Oxford Review of Economic Policy, Oxford University Press, vol. 14(2), pages 7-17, Summer.
    9. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    10. Treb Allen & Costas Arkolakis, 2014. "Trade and the Topography of the Spatial Economy," The Quarterly Journal of Economics, Oxford University Press, vol. 129(3), pages 1085-1140.
    11. Marc Nerlove & Assaf Razin & Efraim Sadka, 1985. "Population Size: Individual Choice and Social Optima," The Quarterly Journal of Economics, Oxford University Press, vol. 100(2), pages 321-334.
    12. Palivos, Theodore & Yip, Chong K., 1993. "Optimal population size and endogenous growth," Economics Letters, Elsevier, vol. 41(1), pages 107-110.
    13. 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.
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    Keywords

    spatiotemporal growth models; Benthamite vs Millian social welfare functions; imperfect altruism; diffusion; dynamic programming in infinite dimension;

    JEL classification:

    • R1 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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