Abstract
We will study a multi-sector discrete-time optimal growth model with neoclassical non-joint technology and show that any path on ann-dimensional flat supported by the optimal steady state price will converge to the optimal steady state and is optimal. Burmeister and Graham have proved a similar result in a continuous-time setting. Although their result is limited, it is a first challenge to generalize the global stability result obtained by Uzawa and Srinivasan in a two-sector optimal growth model. One prominent advantage of our approach is that due to the discrete-time model setting, we can apply the duality approach and introduce the so called "von Neumann facet" intensively studied by McKenzie, which plays a very important role in proving the saddle point stability.
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Takahashi, H. The von Neumann facet and a global asymptotic stability. Ann Oper Res 37, 273–282 (1992). https://doi.org/10.1007/BF02071060
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DOI: https://doi.org/10.1007/BF02071060