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Output Maximization Subject to a Nonlinear Constraint


Author Info

  • Jamal NazrulIslam

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

  • Haradhan Kumar Mohajan
  • Pahlaj Moolio


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.

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Bibliographic Info

Article provided by Khadim Ali Shah Bukhari Institute of Technology (KASBIT) in its journal KASBIT Bussiness Journal.

Volume (Year): 4 (2011)
Issue (Month): (December)
Pages: 116-128

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Handle: RePEc:ksb:journl:v:4:y:2011:p:116-128

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Keywords: Maximization; Nonlinear Constraint; Interpretation of Lagrange Multiplier;

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  1. Pahlaj, Moolio & Islam, Jamal & Mohajan, Haradhan, 2008. "Output Maximization of an Agency," MPRA Paper 50666, University Library of Munich, Germany, revised 20 Jan 2009.
  2. 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.
  3. 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, January.
  4. Islam, Jamal & Mohajan, Haradhan & Moolio, Pahlaj, 2008. "Preference of Social Choice in Mathematical Economics," MPRA Paper 50665, University Library of Munich, Germany, revised 20 Nov 2009.
  5. 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.
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