IDEAS home Printed from https://ideas.repec.org/p/hhs/umnees/0830.html
   My bibliography  Save this paper

On Envelope Theorems in Economics: Inspired by a Revival of a Forgotten Lecture

Author

Listed:
  • Löfgren, Karl-Gustaf

    (Department of Economics, Umeå University)

Abstract

This paper studies how envelope theorems have been used in Economics, their history and also who first introduced them. The existing literature is full of them and the reason is that all families of optimal value functions can produce them. The paper is driven by curiosity, but hopefully it will give the reader some new insights.

Suggested Citation

  • Löfgren, Karl-Gustaf, 2011. "On Envelope Theorems in Economics: Inspired by a Revival of a Forgotten Lecture," Umeå Economic Studies 830, Umeå University, Department of Economics.
    • Handle: RePEc:hhs:umnees:0830
    as

    Download full text from publisher

    File URL: http://www.econ.umu.se/DownloadAsset.action?contentId=166976&languageId=3&assetKey=ues830
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Seierstad, Atle, 1982. "Differentiability properties of the optimal value function in control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 303-310, November.
    2. Li, Chuan-Zhong & Löfgren, Karl-Gustaf, 2009. "Genuine Saving under Stochastic Growth," Umeå Economic Studies 779, Umeå University, Department of Economics.
    3. Thomas Aronsson & Karl-Gustaf Löfgren & Kenneth Backlund, 2004. "Welfare Measurement in Imperfect Markets," Books, Edward Elgar Publishing, number 2494.
    4. LaFrance, Jeffrey T. & Barney, L. Dwayne, 1991. "The envelope theorem in dynamic optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 355-385, April.
    5. Caputo, Michael R., 1990. "How to do comparative dynamics on the back of an envelope in optimal control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 14(3-4), pages 655-683, October.
    6. Michael R. Caputo, 1990. "Comparative Dynamics via Envelope Methods in Variational Calculus," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(4), pages 689-697.
    7. Silberberg, Eugene, 1974. "A revision of comparative statics methodology in economics, or, how to do comparative statics on the back of an envelope," Journal of Economic Theory, Elsevier, vol. 7(2), pages 159-172, February.
    8. Torsten Schmidt, 2004. "Really Pushing the Envelope: Early Use of the Envelope Theorem by Auspitz and Lieben," History of Political Economy, Duke University Press, vol. 36(1), pages 103-129, Spring.
    9. Aronsson, Thomas & Löfgren, Karl-Gustaf & Nyström, Kaj, 2003. "Stochastic Cost Benefit Rules: A Back-of-a-Lottery-Ticket Calculation Method," Umeå Economic Studies 606, Umeå University, Department of Economics.
    10. repec:bla:germec:v:9:y:2008:i::p:1-16 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    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. Caputo, Michael R. & Wilen, James E., 1995. "Optimality conditions and comparative statics for horizon and endpoint choices in optimal control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 351-369.
    2. Caputo, Michael R., 2003. "The comparative dynamics of closed-loop controls for discounted infinite horizon optimal control problems," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1335-1365, June.
    3. Chuan‐Zhong Li & Karl‐Gustaf Löfgren, 2008. "Evaluating Projects in a Dynamic Economy: Some New Envelope Results," German Economic Review, Verein für Socialpolitik, vol. 9(1), pages 1-16, February.
    4. Caputo, Michael R. & Ling, Chen, 2013. "The intrinsic comparative dynamics of locally differentiable feedback Nash equilibria of autonomous and exponentially discounted infinite horizon differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 37(10), pages 1982-1994.
    5. repec:bla:germec:v:9:y:2008:i::p:1-16 is not listed on IDEAS
    6. LaFrance, Jeffrey T., 1992. "Do Increased Commodity Prices Lead To More Or Less Soil Degradation?," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 36(1), pages 1-26, April.
    7. Barney, L. Jr., 1997. "Uncertainty and the comparative dynamics of stock price," International Review of Economics & Finance, Elsevier, vol. 6(4), pages 405-419.
    8. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585, Elsevier.
    9. Krysiak, Frank C., 2006. "Stochastic intertemporal duality: An application to investment under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 30(8), pages 1363-1387, August.
    10. Constadina Passa & Anastasios Xepapadeas, 2008. "Regulation of Farming Activities: An Evolutionary Approach," Working Papers 0811, University of Crete, Department of Economics.
    11. Michael Caputo, 1994. "The Slutsky matrix and homogeneity in intertemporal consumer theory," Journal of Economics, Springer, vol. 60(3), pages 255-279, October.
    12. Shumway, C. Richard, 1995. "Recent Duality Contributions In Production Economics," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 20(1), pages 1-17, July.
    13. Ngo Long & Horst Siebert, 1992. "A model of the socialist firm in transition to a market economy," Journal of Economics, Springer, vol. 56(1), pages 1-21, February.
    14. Yuntong Wang, 2014. "Envelope Theorem without Differentiability," Working Papers 1404, University of Windsor, Department of Economics.
    15. Anglin, Paul M., 2006. "Value and liquidity under changing market conditions," Journal of Housing Economics, Elsevier, vol. 15(4), pages 293-304, December.
    16. Thomas Aronsson & Kenneth Backlund & Karl-Gustav Löfgren, 2001. "International Cooperation over Green Taxes: On the Impossibility of Achieving a Probability-One Gain," CESifo Working Paper Series 567, CESifo.
    17. M. R. Caputo, 1998. "Economic Characterization of Reciprocal Isoperimetric Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 325-350, August.
    18. Micahel Caputo, 2011. "Optimal Control and Resources," Working Papers 2011-07, University of Central Florida, Department of Economics.
    19. Favard, Pascal & Karp, Larry, 2004. "How many cake-eaters? Chouette, on a du monde a diner !," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 801-815, January.
    20. Butterfield, David W., 2003. "Resource depletion under uncertainty: implications for mine depreciation, Hartwick's Rule and national accounting," Resource and Energy Economics, Elsevier, vol. 25(3), pages 219-238, August.
    21. Aronsson, Thomas & Löfgren, Karl-Gustaf & Nyström, Kaj, 2003. "Stochastic Cost Benefit Rules: A Back-of-a-Lottery-Ticket Calculation Method," Umeå Economic Studies 606, Umeå University, Department of Economics.

    More about this item

    Keywords

    Envelope theorems; names and history; value functions;
    All these keywords.

    JEL classification:

    • B16 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Quantitative and Mathematical
    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • B40 - Schools of Economic Thought and Methodology - - Economic Methodology - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hhs:umnees:0830. 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: David Skog (email available below). General contact details of provider: https://edirc.repec.org/data/inumuse.html .

    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.