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Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects

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  • Majumdar, Mukul
  • Mitra, Tapan

Abstract

We examine a discrete-time aggregative model of discounted dynamic optimization where the felicity function depends on both consumption and capital stock. The need for studying such models has been stressed in the theory of optimal growth and also in the economics of natural resources. We identify conditions under which the optimal program is monotone. In our framework, the optimal program can exhibit cyclic behavior for all discount factors close to one. We also present an example to show that our model can exhibit optimal behavior which is chaotic in both topological and ergodic senses.

Suggested Citation

  • Majumdar, Mukul & Mitra, Tapan, 1994. "Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 649-676, August.
    • Handle: RePEc:spr:joecth:v:4:y:1994:i:5:p:649-76
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    Citations

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    Cited by:

    1. Baierla, Gary & Nishimura, Kazuo & Yano, Makoto, 1998. "The role of capital depreciation in multi-sectoral models," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 467-479, January.
    2. Joshi, Sumit, 2003. "The stochastic turnpike property without uniformity in convex aggregate growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1289-1315, May.
    3. Katrin Erdlenbruch & Alain Jean-Marie & Michel Moreaux & Mabel Tidball, 2013. "Optimality of impulse harvesting policies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(2), pages 429-459, March.
    4. Mitra, Tapan & Nishimura, Kazuo, 2001. "Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 256-293, January.
    5. Richard M. H. Suen, 2014. "Time Preference And The Distributions Of Wealth And Income," Economic Inquiry, Western Economic Association International, vol. 52(1), pages 364-381, January.
    6. Santanu Roy, 2010. "On sustained economic growth with wealth effects," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 29-45, March.
    7. Olson, Lars J. & Roy, Santanu, 1996. "On Conservation of Renewable Resources with Stock-Dependent Return and Nonconcave Production," Journal of Economic Theory, Elsevier, vol. 70(1), pages 133-157, July.
    8. Khan, M. Ali & Piazza, Adriana, 2011. "Classical turnpike theory and the economics of forestry," Journal of Economic Behavior & Organization, Elsevier, vol. 79(3), pages 194-210, August.
    9. Anjan Mukherji, 2003. "Competitive Equilibria: Convergence, Cycles or Chaos," ISER Discussion Paper 0591, Institute of Social and Economic Research, Osaka University.
    10. de Hek, Paul A., 1998. "An aggregative model of capital accumulation with leisure-dependent utility," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 255-276, September.
    11. Gregory Amacher & Markku Ollikainen & Mikko Puhakka, 2018. "Renewable Resource Use and Nonseparable Amenity Benefits," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 69(4), pages 637-659, April.
    12. Kopel, M. & Dawid, H. & Feichtinger, G., 1998. "Periodic and chaotic programs of intertemporal optimization models with non-concave net benefit function," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 435-447, January.
    13. Araújo, Aloísio Pessoa de & Maldonado, Wilfredo Fernando Leiva, 2001. "A note on learning chaotic sunspot equilibrium," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 423, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    14. Olson, Lars J. & Roy, Santanu, 2000. "Dynamic Efficiency of Conservation of Renewable Resources under Uncertainty," Journal of Economic Theory, Elsevier, vol. 95(2), pages 186-214, December.
    15. Ali Khan, M. & Piazza, Adriana, 2011. "Optimal cyclicity and chaos in the 2-sector RSS model: An anything-goes construction," Journal of Economic Behavior & Organization, Elsevier, vol. 80(3), pages 397-417.
    16. Horan, Richard D. & Bulte, Erwin H., 2001. "Resource Or Nuisance? Managing African Elephants As A Multi-Use Species," 2001 Annual meeting, August 5-8, Chicago, IL 20440, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    17. Lars Olson & Santanu Roy, 2008. "Controlling a biological invasion: a non-classical dynamic economic model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(3), pages 453-469, September.

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