This essay presents a complete characterization of undiscounted optimal policy in a Leontief two-sector growth model. We work with the precise technological specification used in Nishimura and Yano [Nishimura, K., Yano, M., 1995. Non-linear dynamics and chaos in optimal growth: an example. Econometrica 63, 981-1001; Nishimura, K., Yano, M., 1996. Chaotic solutions in dynamic linear programming. Chaos Solitons & Fractals 7, 1941-1953; Nishimura, K., Yano, M., 2000. Non-linear dynamics and chaos in optimal growth: a constructive exposition. In: Majumdar, M., Mitra, T. (Eds.), Optimization and Chaos. Springer-Verlag, Berlin, pp. 258-295] and employ a geometric method developed by Khan and Mitra [Khan, M.A., Mitra. T., in press. Optimal growth in a two-sector model without discounting: a geometric investigation. Japanese Economic Review]. Our analysis uncovers rich transition dynamics. Monotonic convergence emerges only under a non-negligible set of parameters with two special features; impossibility of full utilization of factors and convergence in a finite number of periods. Moving beyond this special case, full utilization is not always optimal even if it is feasible. Furthermore, with 'large enough' capital stock the optimal policy becomes a constant.
