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Monetary equilibrium and the differentiability of the value function

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Author Info

  • Aliprantis, C.D.
  • Camera, G.
  • Ruscitti, F.

Abstract

In this study we offer a new approach to proving the differentiability of the value function, which complements and extends the literature on dynamic programming. This result is then applied to the analysis of equilibrium in the recent class of monetary economies developed in [Lagos, R., Wright, R., 2005. A unified framework for monetary theory and policy analysis. Journal of Political Economy 113, 463-484]. For this type of environments we demonstrate that the value function is differentiable and this guarantees that the marginal value of money balances is well defined.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 33 (2009)
Issue (Month): 2 (February)
Pages: 454-462

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Handle: RePEc:eee:dyncon:v:33:y:2009:i:2:p:454-462

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Web page: http://www.elsevier.com/locate/jedc

Related research

Keywords: Value function Optimal plans Money;

References

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  1. Ricardo Lagos & Randall Wright, 2002. "A unified framework for monetary theory and policy analysis," Working Paper 0211, Federal Reserve Bank of Cleveland.
  2. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
  3. Aleksander Berentsen & Gabriele Camera & Christopher Waller, . "The Distribution of Money Balances and the Non-Neutrality of Money," IEW - Working Papers 220, Institute for Empirical Research in Economics - University of Zurich.
  4. Camera, Gabriele & Corbae, Dean, 1999. "Money and Price Dispersion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(4), pages 985-1008, November.
  5. Maria Luisa Gota & Luigi Montrucchio, 1999. "On Lipschitz continuity of policy functions in continuous-time optimal growth models," Economic Theory, Springer, vol. 14(2), pages 479-488.
  6. Miguel Molico, 2006. "The Distribution Of Money And Prices In Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(3), pages 701-722, 08.
  7. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-32, May.
  8. Edward J. Green & Ruilin Zhou, 2000. "Dynamic monetary equilibrium in a random-matching economy," Working Paper Series WP-00-1, Federal Reserve Bank of Chicago.
  9. Aleksander Berentsen & Gabriele Camera & Christopher Waller, . "The Distribution of Money and Prices in an Equilibrium with Lotteries," IEW - Working Papers 174, Institute for Empirical Research in Economics - University of Zurich.
  10. Aliprantis, C.D. & Camera, Gabriele & Puzzello, D., 2005. "Anonymous Markets and Monetary Trading," Purdue University Economics Working Papers 1179, Purdue University, Department of Economics.
  11. Blume, Lawrence & Easley, David & O'Hara, Maureen, 1982. "Characterization of optimal plans for stochastic dynamic programs," Journal of Economic Theory, Elsevier, vol. 28(2), pages 221-234, December.
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