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Rationalizing Policy Functions by Dynamic Optimization

Author

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  • Tapan Mitra
  • Gerhard Sorger

Abstract

The authors derive necessary and sufficient conditions for a pair of functions to be the optimal policy function and the optimal value function of a dynamic maximization problem with convex constraints and concave objective functional. It is shown that every Lipschitz continuous function can be the solution of such a problem. If the maintained assumptions include free disposal and monotonicity, then the authors obtain a complete characterization of all optimal policy and optimal value functions. This is the case, e.g., in the standard aggregative optimal growth model.

Suggested Citation

  • Tapan Mitra & Gerhard Sorger, 1999. "Rationalizing Policy Functions by Dynamic Optimization," Econometrica, Econometric Society, vol. 67(2), pages 375-392, March.
    • Handle: RePEc:ecm:emetrp:v:67:y:1999:i:2:p:375-392
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    Citations

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    Cited by:

    1. Sorger, Gerhard, 2004. "Consistent planning under quasi-geometric discounting," Journal of Economic Theory, Elsevier, vol. 118(1), pages 118-129, September.
    2. Bosi, Stefano & Magris, Francesco & Venditti, Alain, 2005. "Competitive equilibrium cycles with endogenous labor," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 325-349, April.
    3. Kazuo Nishimura & Alain Venditti & Makoto Yano, 2014. "Destabilization effect of international trade in a perfect foresight dynamic general equilibrium model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 357-392, February.
    4. Sorger, Gerhard, 2009. "Some notes on discount factor restrictions for dynamic optimization problems," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 435-448, July.
    5. Sorger, Gerhard, 2009. "Some notes on discount factor restrictions for dynamic optimization problems," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 435-448, July.
    6. Makoto Yano & Yuichi Furukawa, 2021. "Two-Dimensional Constrained Chaos and Industrial Revolution Cycles with Mathemetical Appendices," KIER Working Papers 1057, Kyoto University, Institute of Economic Research.
    7. Ghiglino, Christian & Venditti, Alain, 2007. "Wealth inequality, preference heterogeneity and macroeconomic volatility in two-sector economies," Journal of Economic Theory, Elsevier, vol. 135(1), pages 414-441, July.
    8. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    9. YANO Makoto & FURUKAWA Yuichi, 2019. "Two-dimensional Constrained Chaos and Time in Innovation: An analysis of industrial revolution cycles," Discussion papers 19008, Research Institute of Economy, Trade and Industry (RIETI).
    10. Guerrero-Luchtenberg, C.L., 2000. "A uniform neighborhood turnpike theorem and applications," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 329-357, November.
    11. Klaus Reiner Schenk-Hopp�, "undated". "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
    12. Hosoya, Yuhki, 2014. "Identification and testable implications of the Ramsey–Cass–Koopmans model," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 63-68.
    13. Sorger, Gerhard, 2024. "Discounted dynamic optimization and Bregman divergence," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    14. Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2020. "Exact parametric restrictions for 3-cycles in the RSS model: A complete and comprehensive characterization," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 48-56.

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