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Solving Optimal Timing Problems Elegantly

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  • 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
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    References listed on IDEAS

    as
    1. Fuente,Angel de la, 2000. "Mathematical Methods and Models for Economists," Cambridge Books, Cambridge University Press, number 9780521585293, January.
    2. Todorova, Tamara, 2010. "Problems Book to Accompany Mathematics for Economists," MPRA Paper 117866, University Library of Munich, Germany.
    3. 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.
    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)

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    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

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