We will study a multi-sector discrete-time optimal growth model with neoclassical non-joint technology and show that any path on an n-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.
