IDEAS home Printed from https://ideas.repec.org/p/zbw/cegedp/222.html
   My bibliography  Save this paper

A closed-form solution for the health capital model

Author

Listed:
  • Strulik, Holger

Abstract

This paper provides a closed-form solution for the health capital model of health demand. The results are exploited in order to prove analytically the comparative dynamics of the model. Results are derived for the so called pure investment model, the pure consumption model and a combination of both types of models. Given the plausible assumptions that (i) health declines with age and that (ii) the health capital stock at death is lower than the health capital stock needed for eternal life, it is shown that the optimal solution always implies eternal life. This outcome occurs independently from the initial stock of health, the impact of health on productivity, and the importance of health for utility and it is robust against the introduction of a finite age-dependent rate of health depreciation.

Suggested Citation

  • Strulik, Holger, 2014. "A closed-form solution for the health capital model," University of Göttingen Working Papers in Economics 222, University of Goettingen, Department of Economics.
    • Handle: RePEc:zbw:cegedp:222
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/103879/1/804405212.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cropper, M L, 1977. "Health, Investment in Health, and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 85(6), pages 1273-1294, December.
    2. Anne Case & Angus S. Deaton, 2005. "Broken Down by Work and Sex: How Our Health Declines," NBER Chapters, in: Analyses in the Economics of Aging, pages 185-212, National Bureau of Economic Research, Inc.
    3. Galama, Titus & Kapteyn, Arie, 2011. "Grossman’s missing health threshold," Journal of Health Economics, Elsevier, vol. 30(5), pages 1044-1056.
    4. Kuhn, Michael & Wrzaczek, Stefan & Prskawetz, Alexia & Feichtinger, Gustav, 2015. "Optimal choice of health and retirement in a life-cycle model," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 186-212.
    5. Strulik, Holger, 2011. "Health and Education: Understanding the Gradient," Hannover Economic Papers (HEP) dp-487, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    6. Havranek, Tomas & Horvath, Roman & Irsova, Zuzana & Rusnak, Marek, 2015. "Cross-country heterogeneity in intertemporal substitution," Journal of International Economics, Elsevier, vol. 96(1), pages 100-118.
    7. Wagstaff, Adam, 1986. "The demand for health : Some new empirical evidence," Journal of Health Economics, Elsevier, vol. 5(3), pages 195-233, September.
    8. Carl-Johan Dalgaard & Holger Strulik, 2014. "Optimal Aging And Death: Understanding The Preston Curve," Journal of the European Economic Association, European Economic Association, vol. 12(3), pages 672-701, June.
    9. Robert E. Hall & Charles I. Jones, 2007. "The Value of Life and the Rise in Health Spending," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(1), pages 39-72.
    10. Meier, Volker, 2000. "On the demand for preventive care," Munich Reprints in Economics 19191, University of Munich, Department of Economics.
    11. Ehrlich, Isaac & Chuma, Hiroyuki, 1990. "A Model of the Demand for Longevity and the Value of Life Extension," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 761-782, August.
    12. Audrey Laporte & Brian Ferguson, 2007. "Investment in health when health is stochastic," Journal of Population Economics, Springer;European Society for Population Economics, vol. 20(2), pages 423-444, April.
    13. Eisenring, Christoph, 1999. "Comparative dynamics in a health investment model," Journal of Health Economics, Elsevier, vol. 18(5), pages 653-658, October.
    14. Jacobson, Lena, 2000. "The family as producer of health -- an extended grossman model," Journal of Health Economics, Elsevier, vol. 19(5), pages 611-637, September.
    15. Grossman, Michael, 1972. "On the Concept of Health Capital and the Demand for Health," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 223-255, March-Apr.
    16. Grossman, Michael, 2000. "The human capital model," Handbook of Health Economics, in: A. J. Culyer & J. P. Newhouse (ed.), Handbook of Health Economics, edition 1, volume 1, chapter 7, pages 347-408, Elsevier.
    17. Carl-Johan Dalgaard & Holger Strulik, 2017. "The Genesis of the Golden Age: Accounting for the Rise in Health and Leisure," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 24, pages 132-151, March.
    18. Ried, Walter, 1998. "Comparative dynamic analysis of the full Grossman model," Journal of Health Economics, Elsevier, vol. 17(4), pages 383-425, August.
    19. Muurinen, Jaana-Marja, 1982. "Demand for health: A generalised Grossman model," Journal of Health Economics, Elsevier, vol. 1(1), pages 5-28, May.
    20. van Kippersluis, Hans & Galama, Titus J., 2014. "Wealth and health behavior: Testing the concept of a health cost," European Economic Review, Elsevier, vol. 72(C), pages 197-220.
    21. Forster, Martin, 2001. "The meaning of death: some simulations of a model of healthy and unhealthy consumption," Journal of Health Economics, Elsevier, vol. 20(4), pages 613-638, July.
    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. Holger Strulik & Volker Grossmann, 2022. "Life Cycle Economics with Infectious and Chronic Diseases," CESifo Working Paper Series 10141, CESifo.
    2. D. Dragone & H. Strulik, 2017. "Human Health and Aging over an Infinite Time Horizon," Working Papers wp1104, Dipartimento Scienze Economiche, Universita' di Bologna.
    3. Carl-Johan Dalgaard & Holger Strulik, 2017. "The Genesis of the Golden Age: Accounting for the Rise in Health and Leisure," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 24, pages 132-151, March.
    4. Schünemann, Johannes & Strulik, Holger & Trimborn, Timo, 2017. "Going from bad to worse: Adaptation to poor health health spending, longevity, and the value of life," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 130-146.
    5. Strulik, Holger, 2019. "An economic theory of depression and its impact on health behavior and longevity," Journal of Economic Behavior & Organization, Elsevier, vol. 158(C), pages 269-287.
    6. Strulik, Holger, 2018. "The return to education in terms of wealth and health," The Journal of the Economics of Ageing, Elsevier, vol. 12(C), pages 1-14.
    7. Caputo, Michael R., 2021. "New insights in the canonical model of health capital," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 23-33.
    8. Kristian Bolin & Michael R. Caputo, 2024. "Specification of the health production function and its behavioral implications," Health Economics, John Wiley & Sons, Ltd., vol. 33(11), pages 2671-2684, November.
    9. Volker Grossmann, 2021. "Medical Innovations and Ageing: A Health Economics Perspective," CESifo Working Paper Series 9387, CESifo.
    10. Bolin, Kristian & Caputo, Michael R., 2020. "Consumption and investment demand when health evolves stochastically," Journal of Economic Dynamics and Control, Elsevier, vol. 114(C).
    11. Schünemann, Johannes & Strulik, Holger & Trimborn, Timo, 2017. "The gender gap in mortality: How much is explained by behavior?," Journal of Health Economics, Elsevier, vol. 54(C), pages 79-90.
    12. Titus Galama, 2011. "A Contribution to Health Capital Theory," Working Papers WR-831, RAND Corporation.
    13. Dragone, Davide & Strulik, Holger, 2020. "Negligible senescence: An economic life cycle model for the future," Journal of Economic Behavior & Organization, Elsevier, vol. 171(C), pages 264-285.
    14. Strulik, Holger & Grossmann, Volker, 2024. "The economics of aging with infectious and chronic diseases," Economics & Human Biology, Elsevier, vol. 52(C).
    15. Carl‐Johan Dalgaard & Casper Worm Hansen & Holger Strulik, 2021. "Fetal origins—A life cycle model of health and aging from conception to death," Health Economics, John Wiley & Sons, Ltd., vol. 30(6), pages 1276-1290, June.
    16. Jochen Hartwig & Jan-Egbert Sturm, 2018. "Testing the Grossman model of medical spending determinants with macroeconomic panel data," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 19(8), pages 1067-1086, November.
    17. Strulik, Holger, 2015. "Frailty, mortality, and the demand for medical care," The Journal of the Economics of Ageing, Elsevier, vol. 6(C), pages 5-12.
    18. Strulik, Holger, 2018. "Smoking kills: An economic theory of addiction, health deficit accumulation, and longevity," Journal of Health Economics, Elsevier, vol. 62(C), pages 1-12.
    19. Trimborn, Timo & Schünemann, Johannes & Strulik, Holger, 2016. "Disentangling the Gender Gap in Longevity," VfS Annual Conference 2016 (Augsburg): Demographic Change 145570, Verein für Socialpolitik / German Economic Association.
    20. Michael Grossman, 2022. "The demand for health turns 50: Reflections," Health Economics, John Wiley & Sons, Ltd., vol. 31(9), pages 1807-1822, September.
    21. Edouard Ribes, 2022. "Financial planning & optimal retirement timing for physically intensive occupations," Working Papers hal-03219182, HAL.
    22. Edouard A. Ribes, 2022. "Financial planning and optimal retirement timing for physically intensive occupations," SN Business & Economics, Springer, vol. 2(8), pages 1-28, August.

    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. Strulik, Holger, 2015. "Frailty, mortality, and the demand for medical care," The Journal of the Economics of Ageing, Elsevier, vol. 6(C), pages 5-12.
    2. Burggraf, Christine, 2017. "Russian demand for dietary quality: Nutrition transition, diet quality measurement, and health investment theory," Studies on the Agricultural and Food Sector in Transition Economies 269539, Institute of Agricultural Development in Transition Economies (IAMO).
    3. repec:zbw:iamost:269539 is not listed on IDEAS
    4. Schünemann, Johannes & Strulik, Holger & Trimborn, Timo, 2017. "The gender gap in mortality: How much is explained by behavior?," Journal of Health Economics, Elsevier, vol. 54(C), pages 79-90.
    5. Burggraf, Christine, 2017. "Russian demand for dietary quality: Nutrition transition, diet quality measurement, and health investment theory," Studies on the Agricultural and Food Sector in Transition Economies, Leibniz Institute of Agricultural Development in Transition Economies (IAMO), volume 86, number 86.
    6. Titus Galama & Arie Kapteyn & Raquel Fonseca & Pierre‐Carl Michaud, 2013. "A Health Production Model With Endogenous Retirement," Health Economics, John Wiley & Sons, Ltd., vol. 22(8), pages 883-902, August.
    7. Trimborn, Timo & Schünemann, Johannes & Strulik, Holger, 2016. "Disentangling the Gender Gap in Longevity," VfS Annual Conference 2016 (Augsburg): Demographic Change 145570, Verein für Socialpolitik / German Economic Association.
    8. Galama, Titus & Kapteyn, Arie, 2011. "Grossman’s missing health threshold," Journal of Health Economics, Elsevier, vol. 30(5), pages 1044-1056.
    9. Julien Hugonnier & Florian Pelgrin & Pascal St‐Amour, 2020. "Closing down the shop: Optimal health and wealth dynamics near the end of life," Health Economics, John Wiley & Sons, Ltd., vol. 29(2), pages 138-153, February.
    10. Galama, T. & Hullegie, P. & Meijer, E. & Outcault, S., 2012. "Empirical evidence for decreasing returns to scale in a health capital model," Health, Econometrics and Data Group (HEDG) Working Papers 12/05, HEDG, c/o Department of Economics, University of York.
    11. Gjerde, Jon & Grepperud, Sverre & Kverndokk, Snorre, 2009. "On adaptation, life-extension possibilities and the demand for health," HERO Online Working Paper Series 2001:7, University of Oslo, Health Economics Research Programme.
    12. Titus J. Galama & Patrick Hullegie & Erik Meijer & Sarah Outcault, 2012. "Is There Empirical Evidence For Decreasing Returns To Scale In A Health Capital Model?," Health Economics, John Wiley & Sons, Ltd., vol. 21(9), pages 1080-1100, September.
    13. Bolin, Kristian & Lindgren, Björn, 2016. "Non-monotonic health behaviours – implications for individual health-related behaviour in a demand-for-health framework," Journal of Health Economics, Elsevier, vol. 50(C), pages 9-26.
    14. Strulik, Holger, 2018. "The return to education in terms of wealth and health," The Journal of the Economics of Ageing, Elsevier, vol. 12(C), pages 1-14.
    15. Strulik, Holger, 2022. "A health economic theory of occupational choice, aging, and longevity," Journal of Health Economics, Elsevier, vol. 82(C).
    16. Bolin, Kristian & Caputo, Michael R., 2020. "Consumption and investment demand when health evolves stochastically," Journal of Economic Dynamics and Control, Elsevier, vol. 114(C).
    17. Gabriella Conti, 2013. "The Developmental Origins of Health Inequality," Research on Economic Inequality, in: Health and Inequality, volume 21, pages 285-309, Emerald Group Publishing Limited.
    18. Dragone, Davide & Strulik, Holger, 2020. "Negligible senescence: An economic life cycle model for the future," Journal of Economic Behavior & Organization, Elsevier, vol. 171(C), pages 264-285.
    19. Johannes Schuenemann & Holger Strulik & Timo Trimborn, 2020. "The Marriage Gap: Optimal Aging and Death in Partnerships," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 36, pages 158-176, April.
    20. Volker Grossmann & Holger Strulik, 2019. "Optimal Social Insurance and Health Inequality," German Economic Review, Verein für Socialpolitik, vol. 20(4), pages 913-948, November.
    21. Jon Gjerde & Sverre Grepperud & Snorre Kverndokk, 2005. "On adaptation and the demand for health," Applied Economics, Taylor & Francis Journals, vol. 37(11), pages 1283-1301.

    More about this item

    Keywords

    longevity; health; health care demand;
    All these keywords.

    JEL classification:

    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • J17 - Labor and Demographic Economics - - Demographic Economics - - - Value of Life; Foregone Income
    • J26 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Retirement; Retirement Policies
    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior

    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:zbw:cegedp:222. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/cdgoede.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.