Optimal location of economic activity and population density: The role of the social welfare function
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7 février 2020
- handle: 10670/1.oih4h7
- halshs: halshs-02472772
info:eu-repo/semantics/OpenAccess
Mots-clés
Spatiotemporal growth models Benthamite vs Millian social welfare functions imperfect altruism diffusion dynamic programming in infinite dimension R - Urban, Rural, Regional, Real Estate, and Transportation Economics/R.R1 - General Regional Economics O - Economic Development, Innovation, Technological Change, and Growth/O.O4 - Economic Growth and Aggregate Productivity C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C61 - Optimization Techniques • Programming Models • Dynamic AnalysisSujets proches
Social welfare Social work Social service agencies Relief stations (for the poor) Philanthropy Benevolent institutions Social reform Social welfare Reform, Social Public welfare--Government policy Welfare (Public assistance) Social welfare Poor relief Public welfare reform Relief (Aid) Welfare reform Public assistance Benevolent institutions Public relief Public charities Social welfare Philanthropy Human welfare Institutions, Charitable and philanthropic Social welfare Endowed charities Charitable institutions Poor relief Alms and almsgiving Relief (Aid) Philanthropy Benevolent institutions Private nonprofit social work Charities--Societies, etcCiter ce document
Raouf Boucekkine et al., « Optimal location of economic activity and population density: The role of the social welfare function », HAL-SHS : économie et finance, ID : 10670/1.oih4h7
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Résumé
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.