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Young Women in Harmonic Analysis and PDE

December 2-4, 2016

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Laura Somorowsky (Trier University)

The Spatial Ramsey Model: Modeling the Nonlocal Impact of Direct Neighbors

The Ramsey model is one of the most popular neoclassical growth models in economics. First introduced by F.P. Ramsey in [3], it has been analyzed and varied a lot. The outstanding idea in this model is the lifetime utility optimization approach of the consuming sector. Combining this with the assumption of a gain maximization effort in the producing sector, leads to an equilibrium problem. The primary time-depending model has been extended by a spatial component in the last few years, meaning that capital accumulation is a process not only in time but in space as well which then yields an optimal control problem with PDE constraints of parabolic type.

In a new approach, we consider a Ramsey economy where the value of capital is influenced by the surrounding area. We adapt the spatial Ramsey model introduced by Brito in [1] including a nonlocal diffusion term in integral form. This leads to an optimal control problem with a PIDE constraint and volume constraints as defined by Du et al. in [2]. The numerical examples show that our nonlocal model is able to preserve heterogeneity in the initial capital distribution, which is a huge advantage compared to Brito's model, at least if myopic consumers are considered.

References

[1] P. Brito The dynamics of growth and distribution in a spatially heterogeneous world. Working Papers, Department of Economics, ISEG, WP13/2004/DE/UECE. (2004)
[2] Q. Du, Z. Huang and R.B. Lehoucq Nonlocal convection-diffusion volume-constrained problems and jump processes. Discrete and Continuous Dynamical Sytems Series B, Vol. 19, p. 961-977. (2014)
[3] F.P. Ramsey A Mathematical Theory of Saving. The Economic Journal, Vol. 38., Is. 152, p. 543-559. (1928)

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