IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v54y2019i2d10.1007_s10614-018-9841-6.html

Computational Approach for the Firm’s Cost Minimization Problem Using the Selective Infimal Convolution Operator

Author

Listed:
  • L. Bayón

    (University of Oviedo)

  • P. Fortuny Ayuso

    (University of Oviedo)

  • R. García-Rubio

    (University of Salamanca)

  • J. M. Grau

    (University of Oviedo)

  • M. M. Ruiz

    (University of Oviedo)

Abstract

The Infimal Convolution operator is well known in the context of convex analysis. This operator admits a very precise micro-economic interpretation: if several production units produce the same output, the Infimal Convolution of their cost functions represents the joint cost function distributing the production among all of them in the most efficient possible way. The drawback of this operator is that it does not discriminate whether one of some of the production units is not profitable (in the sense that it would be preferable to do without it).This is the motivating idea for the present work, in which we introduce a new operator: the Selective Infimal Convolution. We give not just its definition and basic properties but also an algorithm for its exact computation. Using this, we avoid the combinatorial blowing-up of other classical methods used for solving similar problems. Even more, our approach solves a one-parameter family of problems, not just a single one. We provide an application to the Firm’s Cost Minimization Problem, one of the most important problems in Microeconomics.

Suggested Citation

  • L. Bayón & P. Fortuny Ayuso & R. García-Rubio & J. M. Grau & M. M. Ruiz, 2019. "Computational Approach for the Firm’s Cost Minimization Problem Using the Selective Infimal Convolution Operator," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 535-549, August.
    • Handle: RePEc:kap:compec:v:54:y:2019:i:2:d:10.1007_s10614-018-9841-6
    DOI: 10.1007/s10614-018-9841-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-018-9841-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-018-9841-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, vol. 66(2), pages 409-426, March.
    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. Datta, Manjira & Mirman, Leonard J. & Reffett, Kevin L., 2002. "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Journal of Economic Theory, Elsevier, vol. 103(2), pages 377-410, April.
    2. John Stachurski & Cuong Le Van, 2004. "Parametric continuity of stationary distributions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03331313, HAL.
    3. Manuel S. Santos & Adrian Peralta-Alva, 2012. "Analysis of Numerical Errors," Working Papers 2012-6, University of Miami, Department of Economics.
    4. Manjira Datta & Kevin L. Reffett, 2005. "Isotone Recursive Methods: the Case of Homogeneous Agents," Tinbergen Institute Discussion Papers 05-012/2, Tinbergen Institute.
    5. Giovanni, Domenico De & Lamantia, Fabio & Pezzino, Mario, 2019. "A behavioral model of evolutionary dynamics and optimal regulation of tax evasion," Structural Change and Economic Dynamics, Elsevier, vol. 50(C), pages 79-89.
    6. Raahauge, Peter, 2006. "Upper Bounds on Numerical Approximation Errors," Working Papers 2004-4, Copenhagen Business School, Department of Finance.
    7. Cuong Le Van & Lisa Morhaim, 2006. "On optimal growth models when the discount factor is near 1 or equal to 1," Post-Print halshs-00096034, HAL.
    8. John Stachurski, 2008. "Continuous State Dynamic Programming via Nonexpansive Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 141-160, March.
    9. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    10. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    11. Lohano, Heman Das, 2002. "A Stochastic Dynamic Programming Analysis of Farmland Investment and Financial Management," Faculty and Alumni Dissertations 309035, University of Minnesota, Department of Applied Economics.
    12. Zhen Sun & Yang Xie, 2013. "Error Analysis and Comparison of Two Algorithms Measuring Compensated Income," Computational Economics, Springer;Society for Computational Economics, vol. 42(4), pages 433-452, December.
    13. Grüne, Lars & Semmler, Willi & Stieler, Marleen, 2015. "Using nonlinear model predictive control for dynamic decision problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 112-133.
    14. Stephanie Becker & Lars Grüne & Willi Semmler, 2007. "Comparing accuracy of second-order approximation and dynamic programming," Computational Economics, Springer;Society for Computational Economics, vol. 30(1), pages 65-91, August.
    15. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2014. "Lower Bounds on Approximation Errors: Testing the Hypothesis That a Numerical Solution Is Accurate?," BYU Macroeconomics and Computational Laboratory Working Paper Series 2014-06, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    16. Wilfredo Leiva Maldonado & Benar Fux Svaiter, 2001. "On the accuracy of the estimated policy function using the Bellman contraction method," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-8.
    17. Domenico De Giovanni & Fabio Lamantia & Mario Pezzino, 2018. "Evolutionary Tax Evasion and Optimal Regulation," Economics Discussion Paper Series 1814, Economics, The University of Manchester.
    18. Felix Kubler & Karl Schmedders, 2003. "Approximate Versus Exact Equilibria," Discussion Papers 1382, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Manjira Datta & Leonard Mirman & Olivier Morand & Kevin Reffett, 2002. "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Annals of Operations Research, Springer, vol. 114(1), pages 117-144, August.
    20. Geweke, John F. & Horowitz, Joel L. & Pesaran, M. Hashem, 2006. "Econometrics: A Bird's Eye View," IZA Discussion Papers 2458, IZA Network @ LISER.

    More about this item

    Keywords

    ;
    ;
    ;

    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:kap:compec:v:54:y:2019:i:2:d:10.1007_s10614-018-9841-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.