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The present paper constructs a family of three-sector models of optimal endogenous growth, and conducts exact bifurcation analysis. In so doing, original six-dimensional equilibrium dynamics is decomposed into five-dimensional stationary autonomous dynamics and one-dimensional endogenously growing component. It is shown that the stationary dynamics thus decomposed undergoes supercritical Hopf bifurcation. It is inferred from the convex structure of our model that the dimension of a stable manifold of each closed orbit thus bifurcated in this five-dimensional dynamics should be two. [ABSTRACT FROM AUTHOR]

We study the two-sector Robinson-Shinkai-Leontief (RSL) model of discrete-time optimal economic growth for the case of capital-intensive consumption goods. We frame the model in the context of Nishimura's oeuvre, and more specifically, relate it to its neoclassical cousin: the Uzawa-Srinivasan continuous-time version studied in Haque, W. 1970. "Sceptical Notes on Uzawa's 'Optimal Growth in a Two-Sector Model of Capital Accumulation', and a Precise Characterization of the Optimal Path." The Review of Economic Studies 37: 377–394. We take Fujio's identification of the marginal rate of transformation ζ of capital goods today into capital goods tomorrow (Fujio, M. 2006. Optimal Transition Dynamics in the Leontief Two-Sector Growth Model. Ph.D. thesis, The Johns Hopkins University), and using a mix of the Bellman-Blackwell methods of dynamic programming and the value-loss approach of Brock-Mitra, pin down the optimal policy for a specific subset of the parameter space. We discern a bifurcation pattern with respect to the discount factor that echoes the results of Benhabib, J., and K. Nishimura. 1979. "The Hopf Bifurcation and the Structure and Stability of Closed Orbits with Heterogeneous Steady States in Multi-Sector Models of Optimal Growth." Journal of Economic Theory 21: 421–444 for the neoclassical model, and Khan, M. A., and T. Mitra. 2005. "On Choice of Technique in the Robinson-Solow-Srinivasan Model." International Journal of Economic Theory 1: 83–110 for the RSS model. We also study the optimal policy correspondence for a general parameter set. [ABSTRACT FROM AUTHOR]