IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v28y2011i1-2p574-581.html
   My bibliography  Save this article

Endogenous discounting and the domain of the felicity function

Author

Listed:
  • Schumacher, Ingmar

Abstract

The objective is to show that endogenous discounting models should use a felicity function constrained to a positive domain. A variety of articles use the Mangasarian or Arrow and Kurz condition as a sufficient condition for optimality, which restricts felicity to a negative domain. Since the level of the felicity function shows up in the optimal path it leads to qualitatively different solutions when one uses a negative or positive felicity function. We suggest reasons why the domain should be positive. We furthermore derive sufficiency conditions for concavity of a transformed Hamiltonian if the felicity function is assumed to be positive.

Suggested Citation

  • Schumacher, Ingmar, 2011. "Endogenous discounting and the domain of the felicity function," Economic Modelling, Elsevier, vol. 28(1-2), pages 574-581, January.
    • Handle: RePEc:eee:ecmode:v:28:y:2011:i:1-2:p:574-581
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264-9993(10)00111-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Schumacher, Ingmar, 2009. "Endogenous discounting via wealth, twin-peaks and the role of technology," Economics Letters, Elsevier, vol. 103(2), pages 78-80, May.
    2. Hugh Richards & Ronald Barry, 1998. "U.S. Life Tables For 1990 By Sex, Race, And Education," Journal of Forensic Economics, National Association of Forensic Economics, vol. 11(1), pages 9-26, December.
    3. Gary S. Becker & Casey B. Mulligan, 1997. "The Endogenous Determination of Time Preference," The Quarterly Journal of Economics, Oxford University Press, vol. 112(3), pages 729-758.
    4. Becker, Robert A & Boyd, John H, III, 1992. "Recursive Utility and Optimal Capital Accumulation II: Sensitivity and Duality Theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(4), pages 547-563, October.
    5. N. Sagara, 2001. "Optimal Growth with Recursive Utility: An Existence Result without Convexity Assumptions," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 371-383, May.
    6. Le Kama, Alain Ayong & Schubert, Katheline, 2007. "A Note On The Consequences Of An Endogenous Discounting Depending On The Environmental Quality," Macroeconomic Dynamics, Cambridge University Press, vol. 11(2), pages 272-289, April.
    7. David Fielding & Sebastian Torres, 2009. "Health, Wealth, Fertility, Education, and Inequality," Review of Development Economics, Wiley Blackwell, vol. 13(1), pages 39-55, February.
    8. Karen Pittel, 2002. "Sustainability and Endogenous Growth," Books, Edward Elgar Publishing, number 2776.
    9. Obstfeld, Maurice, 1990. "Intertemporal dependence, impatience, and dynamics," Journal of Monetary Economics, Elsevier, vol. 26(1), pages 45-75, August.
    10. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    11. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-985, July.
    12. Epstein, Larry G & Hynes, J Allan, 1983. "The Rate of Time Preference and Dynamic Economic Analysis," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 611-635, August.
    13. Palivos, Theodore & Wang, Ping & Zhang, Jianbo, 1997. "On the Existence of Balanced Growth Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 205-224, February.
    14. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
    15. Becker, Robert A. & Boyd, John III & Sung, Bom Yong, 1989. "Recursive utility and optimal capital accumulation. I. Existence," Journal of Economic Theory, Elsevier, vol. 47(1), pages 76-100, February.
    16. Drugeon, Jean-Pierre, 1996. "Impatience and long-run growth," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 281-313.
    17. Nairay, Alain, 1984. "Asymptotic behavior and optimal properties of a consumption-investment model with variable time preference," Journal of Economic Dynamics and Control, Elsevier, vol. 7(3), pages 283-313, September.
    18. Epstein, Larry G., 1987. "A simple dynamic general equilibrium model," Journal of Economic Theory, Elsevier, vol. 41(1), pages 68-95, February.
    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. Schumacher, Ingmar, 2009. "Endogenous discounting via wealth, twin-peaks and the role of technology," Economics Letters, Elsevier, vol. 103(2), pages 78-80, May.
    2. Raouf Boucekkine & Blanca Martínez & J. Ramon Ruiz-Tamarit, 2018. "Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case," Lecture Notes in Economics and Mathematical Systems, in: Gustav Feichtinger & Raimund M. Kovacevic & Gernot Tragler (ed.), Control Systems and Mathematical Methods in Economics, pages 321-347, Springer.
    3. Wu, Ting & He, Linfeng & Zhang, Fan, 2021. "Endogenous discounting, investment and Tobin’s q," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    4. Camacho, Carmen & Saglam, Cagri & Turan, Agah, 2013. "Strategic interaction and dynamics under endogenous time preference," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 291-301.
    5. François Belle-Larant & Hugo Mauron & Pascal da Costa, 2021. "Climate Change and Degrowth: a Nordhaus' DICE Model Set of Simulations based on Endogenous Discounting," Working Papers hal-03146625, HAL.
    6. Kawagishi, Taketo, 2014. "Investment for patience in an endogenous growth model," Economic Modelling, Elsevier, vol. 42(C), pages 508-515.
    7. Can Askan Mavi, 2019. "Can harmful events be another source of environmental traps?," CEE-M Working Papers halshs-02141789, CEE-M, Universtiy of Montpellier, CNRS, INRA, Montpellier SupAgro.
    8. Schumacher, Ingmar, 2013. "Political stability, corruption and trust in politicians," Economic Modelling, Elsevier, vol. 31(C), pages 359-369.
    9. Mavi, Can Askan, 2020. "Can harmful events be another source of environmental traps?," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 29-46.
    10. Six, M. & Wirl, F., 2015. "Optimal pollution management when discount rates are endogenous," Resource and Energy Economics, Elsevier, vol. 42(C), pages 53-70.
    11. Can Askan Mavi, 2020. "Can harmful events be another source of environmental traps?," Post-Print hal-02880592, HAL.
    12. Bouché, Stéphane, 2017. "Learning by doing, endogenous discounting and economic development," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 34-43.
    13. Hirose, K. & Ikeda, Shinsuke, 2015. "Decreasing marginal impatience destabilizes multi-country economies," Economic Modelling, Elsevier, vol. 50(C), pages 237-244.
    14. Can Askan Mavi, 2019. "Can harmful events be another source of environmental traps?," Working Papers halshs-02141789, HAL.

    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. Ingmar, SCHUMACHER, 2006. "On optimality, endogeneous discounting and wealth accumulation," Discussion Papers (ECON - Département des Sciences Economiques) 2006058, Université catholique de Louvain, Département des Sciences Economiques.
    2. Schumacher, Ingmar, 2009. "Endogenous discounting via wealth, twin-peaks and the role of technology," Economics Letters, Elsevier, vol. 103(2), pages 78-80, May.
    3. Strulik, Holger, 2016. "Limited self-control and long-run growth," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 1-8.
    4. Das, Mausumi, 2003. "Optimal growth with decreasing marginal impatience," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1881-1898, August.
    5. Kawagishi, Taketo, 2014. "Investment for patience in an endogenous growth model," Economic Modelling, Elsevier, vol. 42(C), pages 508-515.
    6. Strulik, Holger, 2015. "Hyperbolic discounting and endogenous growth," Economics Letters, Elsevier, vol. 126(C), pages 131-134.
    7. Strulik, Holger, 2012. "Patience and prosperity," Journal of Economic Theory, Elsevier, vol. 147(1), pages 336-352.
    8. Bouché, Stéphane, 2017. "Learning by doing, endogenous discounting and economic development," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 34-43.
    9. Yanase, Akihiko, 2011. "Impatience, pollution, and indeterminacy," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1789-1799, October.
    10. Le Kama, Alain Ayong & Schubert, Katheline, 2007. "A Note On The Consequences Of An Endogenous Discounting Depending On The Environmental Quality," Macroeconomic Dynamics, Cambridge University Press, vol. 11(2), pages 272-289, April.
    11. Chu, Hsun & Lai, Ching-chong & Liao, Chih-hsing, 2016. "A Note On Environment-Dependent Time Preferences," Macroeconomic Dynamics, Cambridge University Press, vol. 20(6), pages 1652-1667, September.
    12. Wei-Bin Zhang, 2013. "Dynamic Interactions among Growth, Environmental Change, Habit Formation, and Preference Change," The International Journal of Economic Behavior - IJEB, Faculty of Business and Administration, University of Bucharest, vol. 3(1), pages 3-25, December.
    13. Harashima, Taiji, 2016. "The Cause of the Great Recession: What Caused the Downward Shift of the GDP Trend in the United States?," MPRA Paper 69215, University Library of Munich, Germany.
    14. Evangelos V. Dioikitopoulos & Sarantis Kalyvitis, 2015. "Optimal Fiscal Policy with Endogenous Time Preference," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(6), pages 848-873, December.
    15. ZHANG, Wei-Bin, 2013. "Habit Formation And Preference Change In A Twosector Growth Model With Elastic Labor Supply," Academica Science Journal, Economica Series, Dimitrie Cantemir University, Faculty of Economical Science, vol. 1(2), pages 3-20, May.
    16. Zhang Wei-Bin, 2013. "Habit Formation and Preference Change with Capital and Renewable Resources," Business Systems Research, Sciendo, vol. 4(2), pages 108-125, December.
    17. Ken-Ichi Hirose & Shinsuke Ikeda, 2015. "Decreasing Marginal Impatience and Capital Accumulation in a Two-Country World Economy," Metroeconomica, Wiley Blackwell, vol. 66(3), pages 474-507, July.
    18. Pittel Karen, 2005. "Diskontraten: Endogen oder nicht endogen? / Disounting: Endogenous or not Endogenous?: Eine umweltrelevante Fragestellung / Implications for the Environment," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 225(4), pages 441-458, August.
    19. Six, M. & Wirl, F., 2015. "Optimal pollution management when discount rates are endogenous," Resource and Energy Economics, Elsevier, vol. 42(C), pages 53-70.
    20. Wei-Bin ZHANG, 2012. "Habits, Saving Propensity, And Economic Growth," Scientific Bulletin - Economic Sciences, University of Pitesti, vol. 11(2), pages 3-15.

    More about this item

    Keywords

    Endogenous time preference Optimality Recursive utility Felicity;

    JEL classification:

    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    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:ecmode:v:28:y:2011:i:1-2:p:574-581. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    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/inca/30411 .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.