Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Derivation of Profit Curve by Cubic Cost Function and Mathematical Verification of Industry Life Cycle: Focused on All Industries in Korea

3차 비용함수에 의한 이익곡선 도출과 산업 라이프사이클의 수리적 검증: 우리나라 전 산업을 중심으로

  • Hoo Seok Pai (Institute of World Maritime Development, Korea Maritime and Ocean University) ;
  • Chae Kwan Lim (Department of Distribution and Distribution, Tongmyong University)
  • 배후석 (한국해양대학교 세계해양발전연구소) ;
  • 임채관 (동명대학교 유통물류학과)
  • Received : 2023.08.31
  • Accepted : 2023.11.13
  • Published : 2023.12.31
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Abstract

Purpose: The main theme of this study is to derive a profit curve by a cubic cost function for nonlinear CVP analysis. According to the analytical approach to derive a nonlinear profit function in this study, it is possible with only the existing cost structure to calculate the profit maximization and downtime point sales unlike the classical CVP analysis. Furthermore, the profit curve by the mathematical model of this study could serve as a tool to quantify the qualitative evaluation of each stage of the industry life cycle. Methods: This study followed the mathematical approach from the cubic cost function model of microeconomics, and using real data of the Bank of Korea Results: The nonlinear profit function suggested by this study is as follows; ${\pi}(x)=-a\left(x-\frac{f}{1-v}\right)^3+(1-v)x-k$ where $a=\frac{1}{3}v\left(\frac{(1-v)}{f}\right)^2,k=f-a\left(1-\frac{f}{1-v \right)^3$ Conclusion: The process and results of this study would be able to contribute not only in practice of nonlinear CVP analysis required in the management accounting or financial management, but also in cost theory of microeconomics. Also, since the life cycle of all industries in Korea was verified to the growth or mature stage, decision makers should pay careful attention to determining life cycle stages and consider the profit curve by the average variable cost ratio over multi periods.

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References

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