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On locally optimal programs in the Robinson–Solow–Srinivasan model

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Abstract

In the context of a model due to Robinson, Solow and Srinivasan (the RSS model), we report results on the existence and characterization of locally optimal programs, a concept taken from theoretical physics. In particular, we propose a (new) transversality condition under which all locally optimal programs are good. An extended introduction places our theorems in the context of previous work on the existence question, including that on agreeable programs. It appears that there is no completely rational way to attack [the] problem without considering development programmes over an infinite horizon (Gale in Rev Econ Stud 34:1–8, 1967). The analysis of simple models is essential if we are to understand the corresponding situation for more complex models of the economy (Mirrlees and Stern in J Econ Theory 4:268–288, 1972). The technical convenience, for clear and quantitative results, of using an infinite time horizon is rather great (Hammond and Mirrlees in Models of economic growth, Wiley, New York, pp 283–299, 1973).

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References

  • Arkin VI, Evstigneev IV (1987) Stochastic models of control and economic dynamics. Academic Press, New York

    Google Scholar 

  • Atsumi H (1965) Neoclassical growth and the efficient program of capital accumulation. Rev Econ Stud 32: 127–136

    Article  Google Scholar 

  • Aubry S, Le Daeron PY (1983) The discrete Frenkel–Kontorova model and its extensions I. Physica D 8: 381–422

    Article  Google Scholar 

  • Braun OM, Kivshar YS (2004) The Frenkel–Kontorova model: concepts, methods and applications. Springer, Berlin

    Google Scholar 

  • Brock WA (1970) On existence of weakly maximal programmes in a multi-sector economy. Rev Econ Stud 37: 275–280

    Article  Google Scholar 

  • Carlson DA, Haurie AB, Leizarowitz A (1991) Infinite horizon optimal control: deterministic and stichastic systems. Springer, New York

    Google Scholar 

  • Coleman BD, Marcus M, Mizel VJ (1992) On the thermodynamics of periodic phases. Arch Ration Mech Anal 117: 321–347

    Article  Google Scholar 

  • Fujio M (2008) Undiscounted optimal growth in the Leontief two-sector model with circulating capital and a labor-intensive consumption goods sector. J Econ Behav Org 66: 420–436

    Article  Google Scholar 

  • Gale D (1967) On optimal development in a multi-sector economy. Rev Econ Stud 34: 1–18

    Article  Google Scholar 

  • Hammond PJ (1974) Consistent planning and intertemporal welfare economics. Unpublished Ph.D. dissertation, University of Cambridge, Cambridge, England

  • Hammond PJ (1975) Agreeable plans with many capital goods. Rev Econ Stud 42: 1–14

    Article  Google Scholar 

  • Hammond PJ, Kennan J (1979) Uniformly optimal infinite horizon plans. Int Econ Rev 20: 283–296

    Article  Google Scholar 

  • Hammond PJ, Mirrlees JA (1973) Agreeable plans. In: Mirrlees J, Stern NH (eds) Models of economic growth. Wiley, New York, pp 283–299

    Google Scholar 

  • Khan MA, Mitra T (2005) On choice of technique in the Robinson–Solow–Srinivasan model. Int J Econ Theory 1: 83–110

    Article  Google Scholar 

  • Khan MA, Mitra T (2006a) Optimal growth in the two-sector RSS model: a continuous time analysis. In: Proceedings of the seventh Portugese conference on automatic control, Electronic publication

  • Khan MA, Mitra T (2006b) Undiscounted optimal growth under irreversible investment: a synthesis of the value-loss approach and dynamic programming. Econ Theory 29: 341–362

    Article  Google Scholar 

  • Khan MA, Mitra T (2007) Optimal growth in a two-sector model without discounting: a geometric investigation. Jpn Econ Rev 58: 191–225

    Article  Google Scholar 

  • Khan MA, Piazza A (2009a) On uniform convergence of undiscounted optimal programs in the Mitra–Wan forestry model: the strictly concave case. Publicación Técnica CMM 222: 1–15

    Google Scholar 

  • Khan MA, Piazza A (2009b) On the Mitra–Wan forestry model: a unified analysis. Publicación Técnica CMM 226: 1–22

    Google Scholar 

  • Khan MA, Zaslavski AJ (2007) On a uniform turnpike of the third kind in the Robinson–Solow–Srinivasan model. J Econ 92: 137–166

    Article  Google Scholar 

  • Khan MA, Zaslavski AJ (2008) On two classical turnpike results for the Robinson–Solow–Srinivasan (RSS) model. Johns Hopkins University, Mimeo, pp 1–50

    Google Scholar 

  • Khan MA, Zaslavski AJ (2009) On existence of optimal programs: the RSS model without concavity assumptions on felicities. J Math Econ 46:1–14 (available online 13 May 2008)

    Google Scholar 

  • Koopmans TC (1965) On the concept of optimal economic growth. Pontif Acad Sci Scr Varia 28: 225–300

    Google Scholar 

  • Koopmans TC (1967) Intertemporal distribution and “optimal” aggregate economic growth. In: Fellner W et al (eds) Ten economic studies in the tradition of Irving Fisher. Wiley, New York, pp 95–126

    Google Scholar 

  • Leizarowitz A, Mizel VJ (1989) One dimensional infinite horizon variational problems arising in continuum mechanics. Arch Ration Mech Anal 106: 161–194

    Article  Google Scholar 

  • Marcus M, Zaslavski AJ (1999) The structure of extremals of a class of second order variational problems. Ann Inst H Poincare/Anal Non Lineare 16: 593–629

    Article  Google Scholar 

  • Majumdar M (1988) Decentralization in infinite horizon economies: an introduction. J Econ Theory 45: 217–227

    Article  Google Scholar 

  • Majumdar M (1991) On attaining Ramsey–Weizsäcker optimality in a decentralized economy: an impossibility theorem. In: Banerjee D (eds) Economic analysis and policy. Oxford University Press, Delhi, pp 69–87

    Google Scholar 

  • McKenzie LW (1968) Accumulation programs of maximum utulity and the von Neumann facet. In: Wolfe JN (eds) Value, capital and growth. Edinburgh University Press, Edinburgh, pp 353–383

    Google Scholar 

  • McKenzie LW (1976) Turnpike theory. Econometrica 44: 841–866

    Article  Google Scholar 

  • McKenzie LW (1983) A primal route to the turnpike and Lyapunov stability. J Econ Theory 30: 330–352

    Article  Google Scholar 

  • McKenzie LW (1986) Optimal economic growth, turnpike theorems and comparative dynamics. In: Arrow KJ, Intrilligator M (eds) Handbook of mathematical economics, vol 3. North-Holland, New York, pp 1281–1355

    Google Scholar 

  • McKenzie LW (2002) Classical general equilibrium. MIT Press, Cambridge

    Google Scholar 

  • Mirrlees JA, Stern N (1972) Fairly good plans. J Econ Theory 4: 268–288

    Article  Google Scholar 

  • Mitra T (2000) Introduction to dynamic optimization theory. In: Majumdar M, Mitra T, Nishimura K (eds) Optimization and chaos. Springer, Berlin, pp 31–108

    Google Scholar 

  • Mitra T (2005) Intergenerational equity and the forest management problem. In: Kant S, Berry RA (eds) Economics, sustainability, and natural resources: economics of sustainable forest management. Springer, Berlin, pp 137–173

    Chapter  Google Scholar 

  • Mitra T (2006) Notes on a model of forestry: the undiscounted case. Mimeo, Cornell University, 10 June 2006

  • Mitra T, Wan HW Jr (1986) On the Faustmann solution to the forest management problem. J Econ Theory 40: 229–249

    Article  Google Scholar 

  • Nishimura K, Yano M (1995) Nonlinear dynamics and chaos in optimal growth: an example. Econometrica 63: 981–1001

    Article  Google Scholar 

  • Nishimura K, Yano M (1996) Chaotic solutions in dynamic linear programming. Chaos Solitons Fract 7: 1941–1953

    Article  Google Scholar 

  • Osumi K (1986) Economic planning and agreeability. Kyushu University Press, Tokyo

    Google Scholar 

  • Ramsey F (1928) A mathematical theory of savings. Econ J 38: 543–559

    Article  Google Scholar 

  • Samuelson PA (1965) A catenary turnpike theorem involving consumption and the golden rule. Am Econ Rev 55: 486–496

    Google Scholar 

  • Samuelson PA (1976) The periodic turnpike theorem. Nonlinear Anal Theory Methods Appl 1: 3–13

    Article  Google Scholar 

  • Samuelson PA, Solow RM (1956) A complete capital model involving heterogeneous capital goods. Q J Econ LXX: 537–562

    Article  Google Scholar 

  • Stiglitz JE (1968) A note on technical choice under full employment in a socialist economy. Econ J 78: 603–609

    Article  Google Scholar 

  • von Weizsäcker CC (1965) Existence of optimal programs of accumulation for an infinite horizon. Rev Econ Stud 32: 85–104

    Article  Google Scholar 

  • Zaslavski AJ (1987) Ground states in Frenkel–Kontorova model. Math USSR Izvestiya 29: 323–354

    Article  Google Scholar 

  • Zaslavski AJ (1996) Structure of extremals for one-dimensional variational problems arising in continuum mechanics. J Math Anal Appl 198: 893–921

    Article  Google Scholar 

  • Zaslavski AJ (2005) Turnpike properties in the calculus of variations and optimal control. Springer, New York

    Google Scholar 

  • Zaslavski AJ (2006a) Good programs in the RSS model with a nonconcave utility function. J Ind Manage Optim 2: 399–423

    Google Scholar 

  • Zaslavski AJ (2006b) Optimal programs in the continuous time RSS model. In: Proceedings of the seventh Portugese conference on automatic control, Electronic publication

  • Zaslavski AJ (2007) Turnpike results for discrete-time optimal control systems arising in economic dynamics. Nonlinear Anal 67: 2024–2049

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Economics, The Johns Hopkins University, Baltimore, MD, 21218, USA

    M. Ali Khan

  2. Department of Economics, University of Queensland, Brisbane, QLD, 4072, Australia

    M. Ali Khan

  3. Department of Mathematics, The Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Alexander J. Zaslavski

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  1. M. Ali Khan
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  2. Alexander J. Zaslavski
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Correspondence to M. Ali Khan.

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Khan, M.A., Zaslavski, A.J. On locally optimal programs in the Robinson–Solow–Srinivasan model. J Econ 99, 65–92 (2010). https://doi.org/10.1007/s00712-009-0102-y

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  • DOI: https://doi.org/10.1007/s00712-009-0102-y

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