Discounted optimal growth in a two-sector RSS model: a further geometric investigation
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The geometric apparatus of Khan–Mitra (Adv. Math. Econ. 8:349–381, 2006; Jpn. Econ. Rev. 58:191–225, 2007) enables an identification of a tripartite (inside-borderline-outside) distinction for discounted Ramseyian optimality in the 2-sector RSS model and to obtain the following results: (a) parametric ranges of the discount factor for which the check-map is the optimal policy function, (b) necessary and sufficient conditions for the existence of stable optimal 2-period cycles, (c) absence of 3-period cycles in the borderline case, and (d) existence of unstable 3-period cycles in a canonical instance of the outside case. The geometry is shown to have more general interest and relevance for future work.
Key words3-period convergence 3-period cycles Attracting 2-period cycles McKenzie bifurcation Optimal policy correspondence RSS model Trapezium Trapping square Tripartite categorical distinction
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