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Necessary And Sufficient Conditions For Dynamic Optimization

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  • Coşar, A. Kerem
  • Green, Edward J.

Abstract

We characterize the necessary and sufficient conditions for optimality in discrete-time, infinite-horizon optimization problems with a state space of finite or infinite dimension. It is well known that the challenging task in this problem is to prove the necessity of the transversality condition. To do this, we follow a duality approach in an abstract linear space. Our proof resembles that of Kamihigashi (2003), but does not explicitly use results from real analysis. As an application, we formalize Sims's argument that the no-Ponzi constraint on the government budget follows from the necessity of the tranversality condition for optimal consumption.

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  • Coşar, A. Kerem & Green, Edward J., 2016. "Necessary And Sufficient Conditions For Dynamic Optimization," Macroeconomic Dynamics, Cambridge University Press, vol. 20(3), pages 667-684, April.
    • Handle: RePEc:cup:macdyn:v:20:y:2016:i:03:p:667-684_00
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    Cited by:

    1. Marco Bassetto & Thomas J. Sargent, 2020. "Shotgun Wedding: Fiscal and Monetary Policy," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 659-690, August.
    2. Marco Bassetto & Christopher Phelan, 2012. "Speculative runs on interest rate pegs the frictionless case," Working Paper Series WP-2012-16, Federal Reserve Bank of Chicago.

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