IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v33y2009i2p454-462.html
   My bibliography  Save this article

Monetary equilibrium and the differentiability of the value function

Author

Listed:
  • 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.

Suggested Citation

  • Aliprantis, C.D. & Camera, G. & Ruscitti, F., 2009. "Monetary equilibrium and the differentiability of the value function," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 454-462, February.
  • Handle: RePEc:eee:dyncon:v:33:y:2009:i:2:p:454-462
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(08)00130-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Aleksander Berentsen & Gabriele Camera & C hristopher W aller, 2005. "The Distribution Of Money Balances And The Nonneutrality Of Money," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(2), pages 465-487, May.
    2. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    3. 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 727-732, May.
    4. D. Aliprantis, C. & Camera, G. & Puzzello, D., 2007. "Anonymous markets and monetary trading," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 1905-1928, October.
    5. 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, August.
    6. Ricardo Lagos & Randall Wright, 2005. "A Unified Framework for Monetary Theory and Policy Analysis," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 463-484, June.
    7. 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.
    8. Aleksander Berentsen & Gabriele Camera & Christopher Waller, 2006. "The distribution of money and prices in an equilibrium with lotteries," Studies in Economic Theory, in: Charalambos D. Aliprantis & Nicholas C. Yannelis & Gabriele Camera (ed.), Recent Developments on Money and Finance, pages 173-193, Springer.
    9. Maria Luisa Gota & Luigi Montrucchio, 1999. "On Lipschitz continuity of policy functions in continuous-time optimal growth models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 479-488.
    10. Edward J. Green & Ruilin Zhou, 2002. "Dynamic Monetary Equilibrium in a Random Matching Economy," Econometrica, Econometric Society, vol. 70(3), pages 929-969, May.
    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.
    12. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, January.
    13. Ken-ichi Inada, 1963. "On a Two-Sector Model of Economic Growth: Comments and a Generalization," Review of Economic Studies, Oxford University Press, vol. 30(2), pages 119-127.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Leo Ferraris & Makoto Watanabe, 2012. "Liquidity Constraints In A Monetary Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 255-277, February.
    2. Valerie R. Bencivenga & Gabriele Camera, 2011. "Banking in a Matching Model of Money and Capital," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(s2), pages 449-476, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Aliprantis, C.D. & Camera, G. & Ruscitti, F., 2007. "Monetary Equilibrium and the Differentiability of the Value Function," Purdue University Economics Working Papers 1199, Purdue University, Department of Economics.
    2. Kim, Young Sik & Lee, Manjong, 2010. "A model of debit card as a means of payment," Journal of Economic Dynamics and Control, Elsevier, vol. 34(8), pages 1359-1368, August.
    3. Menzio, Guido & Shi, Shouyong & Sun, Hongfei, 2013. "A monetary theory with non-degenerate distributions," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2266-2312.
    4. Young Sik Kim & Manjong Lee, 2009. "Wealth Distribution, Inflation Tax, and Societal Benefits of Illiquid Bonds," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(5), pages 809-830, August.
    5. Berentsen, Aleksander & Camera, Gabriele & Waller, Christopher, 2007. "Money, credit and banking," Journal of Economic Theory, Elsevier, vol. 135(1), pages 171-195, July.
    6. Irina A. Telyukova & Randall Wright, 2008. "A Model of Money and Credit, with Application to the Credit Card Debt Puzzle," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 629-647.
    7. Pidong Huang & Young Sik Kim & Manjong Lee, 2014. "Optimal Allocation of Social Cost for Electronic Payment System: A Ramsey Approach," Discussion Paper Series 1402, Institute of Economic Research, Korea University.
    8. D. Aliprantis, C. & Camera, G. & Puzzello, D., 2007. "Anonymous markets and monetary trading," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 1905-1928, October.
    9. Rocheteau, Guillaume & Weill, Pierre-Olivier & Wong, Tsz-Nga, 2021. "An heterogeneous-agent New-Monetarist model with an application to unemployment," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 64-90.
    10. Lee, Manjong, 2013. "Coexistence and welfare cost of inflation," Journal of Macroeconomics, Elsevier, vol. 36(C), pages 23-32.
    11. Choi, Hyung Sun & Kwon, Ohik & Lee, Manjong, 2016. "Inflation, credit, and indexed unit of account," International Review of Economics & Finance, Elsevier, vol. 41(C), pages 144-154.
    12. Guillaume Rocheteau & Pierre-Olivier Weill & Tsz-Nga Wong, 2015. "Working through the Distribution: Money in the Short and Long Run," NBER Working Papers 21779, National Bureau of Economic Research, Inc.
    13. Boel, Paola & Camera, Gabriele, 2009. "Financial sophistication and the distribution of the welfare cost of inflation," Journal of Monetary Economics, Elsevier, vol. 56(7), pages 968-978, October.
    14. Rocheteau, Guillaume & Weill, Pierre-Olivier & Wong, Russell, 2018. "A tractable model of monetary exchange with ex-post heterogeneity," Theoretical Economics, Econometric Society, vol. 13(3), September.
    15. Yann Algan & Edouard Challe & Xavier Ragot, 2011. "Incomplete markets and the output–inflation tradeoff," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 55-84, January.
    16. Scott J. Dressler, 2011. "Money Holdings, Inflation, And Welfare In A Competitive Market," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(2), pages 407-423, May.
    17. Shouyong Shi, 2006. "A Microfoundation of Monetary Economics," Working Papers tecipa-211, University of Toronto, Department of Economics.
    18. Jean, Kasie & Rabinovich, Stanislav & Wright, Randall, 2010. "On the multiplicity of monetary equilibria: Green-Zhou meets Lagos-Wright," Journal of Economic Theory, Elsevier, vol. 145(1), pages 392-401, January.
    19. Stephen D. Williamson & Randall Wright, 2010. "New monetarist economics: methods," Review, Federal Reserve Bank of St. Louis, vol. 92(May), pages 265-302.
    20. Guillaume Rocheteau & Peter Rupert & Randall Wright, 2007. "Inflation and Unemployment in General Equilibrium," Scandinavian Journal of Economics, Wiley Blackwell, vol. 109(4), pages 837-855, December.

    More about this item

    Keywords

    Value function Optimal plans Money;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:33:y:2009:i:2:p:454-462. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.