The Dynamics of a Spatial Economic Model with Bounded Population Growth
We investigate a spatial economic growth model with bounded population growth to obtain the asymptotic behavior of detrended capital in a continuous space. The formation of capital accumulation is expressed by a partial differential equation with corresponding boundary conditions. The capital accumu...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/9963437 |
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| Summary: | We investigate a spatial economic growth model with bounded population growth to obtain the asymptotic behavior of detrended capital in a continuous space. The formation of capital accumulation is expressed by a partial differential equation with corresponding boundary conditions. The capital accumulation interacts with the morphology to affect the optimal dynamics of economic growth. After redrafting the spatial growth model in the infinite dimensional Hilbert space, we identify the unique optimal control and value function when the bounded population growth is considered. With nonnegative initial distribution of capital, the explicit solution of the model is obtained. The time behavior of the explicit solution guarantees the convergence issue of the detrended capital level across space and time. |
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| ISSN: | 1026-0226 1607-887X |