IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/47591.html
   My bibliography  Save this paper

Solving Optimal Timing Problems Elegantly

Author

Listed:
  • Todorova, Tamara

Abstract

Few textbooks in mathematical economics cover optimal timing problems. Those which cover them do it scantly or in a rather clumsy way, making it hard for students to understand and apply the concept of optimal time in new contexts. Discussing the plentiful illustrations of optimal timing problems, we present an elegant and simple method of solving them. Whether the present value function is exponential or logarithmic, a convenient way to solve it is to convert the base to the exponential number e, thus making it easy to differentiate the new objective function with respect to time t. This convenient method of base conversion allows to find a second-order derivative and to use the second-order condition as a proof of optimum.

Suggested Citation

  • Todorova, Tamara, 2013. "Solving Optimal Timing Problems Elegantly," MPRA Paper 47591, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:47591
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/47591/1/MPRA_paper_47591.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Todorova, Tamara, 2010. "Problems Book to Accompany Mathematics for Economists," MPRA Paper 117866, University Library of Munich, Germany.
    2. Pindyck, Robert S., 2002. "Optimal timing problems in environmental economics," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1677-1697, August.
    3. Fuente,Angel de la, 2000. "Mathematical Methods and Models for Economists," Cambridge Books, Cambridge University Press, number 9780521585293.
    4. Samuelson, Paul A, 1976. "Economics of Forestry in an Evolving Society," Economic Inquiry, Western Economic Association International, vol. 14(4), pages 466-492, December.
    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. Todorova, Tamara, 2013. "An Easy Way to Teach First-order Linear Differential and Difference Equations with a Constant Term and a Constant Coefficient," MPRA Paper 48187, University Library of Munich, Germany.
    2. Millock, Katrin & Xabadia, Angels & Zilberman, David, 2012. "Policy for the adoption of new environmental monitoring technologies to manage stock externalities," Journal of Environmental Economics and Management, Elsevier, vol. 64(1), pages 102-116.
    3. Sinha, Ankur & Rämö, Janne & Malo, Pekka & Kallio, Markku & Tahvonen, Olli, 2017. "Optimal management of naturally regenerating uneven-aged forests," European Journal of Operational Research, Elsevier, vol. 256(3), pages 886-900.
    4. Agliardi, Elettra & Sereno, Luigi, 2012. "Environmental protection, public finance requirements and the timing of emission reductions," Environment and Development Economics, Cambridge University Press, vol. 17(6), pages 715-739, December.
    5. Pindyck, Robert S., 2012. "Uncertain outcomes and climate change policy," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 289-303.
    6. Terstiege, Stefan, 2013. "Precontractual Investigation and Sequential Screening," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 429, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    7. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2017. "Uniqueness of Nash Equilibrium in Continuous Weighted Potential Games," CSEF Working Papers 471, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 18 Jun 2017.
    8. Yuri Biondi, 2009. "Capital budgeting under relational contracting: optimal ranking and duration criteria for schemes of concession, project-financing and public-private partnership," Post-Print hal-00404305, HAL.
    9. Klaus Mittenzwei & David S. Bullock & Klaus Salhofer, 2012. "Towards a theory of policy timing," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 56(4), pages 583-596, October.
    10. Newbold, Stephen C. & Johnston, Robert J., 2020. "Valuing non-market valuation studies using meta-analysis: A demonstration using estimates of willingness-to-pay for water quality improvements," Journal of Environmental Economics and Management, Elsevier, vol. 104(C).
    11. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    12. Couture, Stéphane & Reynaud, Arnaud, 2011. "Forest management under fire risk when forest carbon sequestration has value," Ecological Economics, Elsevier, vol. 70(11), pages 2002-2011, September.
    13. Jin, Wei & Zhang, ZhongXiang, 2016. "On the mechanism of international technology diffusion for energy technological progress," Resource and Energy Economics, Elsevier, vol. 46(C), pages 39-61.
    14. Lin, Tyrone T. & Huang, Shio-Ling, 2011. "Application of the modified Tobin's q to an uncertain energy-saving project with the real options concept," Energy Policy, Elsevier, vol. 39(1), pages 408-420, January.
    15. Jagjit S. Chadha, 2009. "Monetary Policy Analysis: An Undergraduate Toolkit," Palgrave Macmillan Books, in: Giuseppe Fontana & Mark Setterfield (ed.), Macroeconomic Theory and Macroeconomic Pedagogy, chapter 3, pages 55-75, Palgrave Macmillan.
    16. Ahlvik, Lassi & Iho, Antti, 2018. "Optimal geoengineering experiments," Journal of Environmental Economics and Management, Elsevier, vol. 92(C), pages 148-168.
    17. Mario E Niklitschek & Eugenio Bobenrieth, 1992. "Incentivos Económicos para una Explotación Eficiente del Bosque," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 29(88), pages 463-480.
    18. Vercammen, James, 2014. "The Welfare Impacts of a Conservation Easement," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 169813, Agricultural and Applied Economics Association.
    19. Xu, Ying & Amacher, Gregory S. & Sullivan, Jay, 2016. "Optimal forest management with sequential disturbances," Journal of Forest Economics, Elsevier, vol. 24(C), pages 106-122.
    20. Asante, Patrick & Armstrong, Glen W. & Adamowicz, Wiktor L., 2011. "Carbon sequestration and the optimal forest harvest decision: A dynamic programming approach considering biomass and dead organic matter," Journal of Forest Economics, Elsevier, vol. 17(1), pages 3-17, January.

    More about this item

    Keywords

    optimization of functions of one variable; continuous time; optimal timing; discounted present value; future value;
    All these keywords.

    JEL classification:

    • A22 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Undergraduate
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation

    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:pra:mprapa:47591. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.