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Output Maximization Subject to a Nonlinear Constraint

Author

Listed:
  • Jamal NazrulIslam

    (Research Centre for Mathematical and Physical Sciences, University of Chittagong, Bangladesh)

  • Haradhan Kumar Mohajan
  • Pahlaj Moolio

Abstract

The main aim of this paper is to derive the mathematical formulation to device an optimal purchasing policy for the service providing agency. An attempt has been made to maximize the output function of an agency subject to a nonlinear budget constraint by assuming that the agency gets price discounts for purchasing larger quantities of other inputs. Such quantity discounts alter the linear budget constraint and result in a nonlinear (convex type) budget constraint. We use the method of Lagrange multipliers and apply the firstorder necessary conditions as well as the second-order sufficient conditions for maximization. We also use comparative static analysis and study the behavior of the agency when prices of inputs undergo change, besides providing useful interpretation of the Lagrange multipliers in this specific case. Illustrating an explicit example, we show that the optimization problems play an important role in the real world.

Suggested Citation

  • Jamal NazrulIslam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2011. "Output Maximization Subject to a Nonlinear Constraint," KASBIT Business Journals (KBJ), Khadim Ali Shah Bukhari Institute of Technology (KASBIT), vol. 4, pages 116-128, December.
    • Handle: RePEc:ksb:journl:v:4:y:2011:p:116-128
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    References listed on IDEAS

    as
    1. Jamal Nazrul Islam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2010. "Utility Maximization Subject to Multiple Constraints," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 4(1), pages 15-29, December.
    2. Jamal Nazrul Islam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2009. "Preference of Social Choice in Mathematical Economics," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 3(1), pages 18-38, June.
    3. Pahlaj Moolio & Jamal Nazrul Islam, 2008. "Cost Minimization of a Competitive Firm," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 2(2), pages 148-160, December.
    4. Pahlaj Moolio & Jamal Nazrul Islam & Haradhan Kumar Mohajan, 2009. "Output Maximization of an Agency," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 3(1), pages 39-51, June.
    5. Joseph S. Desalvo & Mobinul Huq, 2002. "Introducing Nonlinear Pricing into Consumer Choice Theory," The Journal of Economic Education, Taylor & Francis Journals, vol. 33(2), pages 166-179, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Maximization; Nonlinear Constraint; Interpretation of Lagrange Multiplier;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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