An Introduction to Lagrange Multipliers: Theory and Applications in Economics
DOI:
https://doi.org/10.61173/ch4v0m11Keywords:
Lagrange Multiplier Method, Constraints, Optimization, Economics, DerivativeAbstract
The purpose of this paper is to explore the basic applications of the Lagrange multiplier method in economics and to help beginners build their understanding of this mathematical tool. Tesla Inc. is used as a case study to examine how it maximizes profits by optimizing pricing and marketing expenses under given market conditions and constraints. The context of the study includes the importance of maintaining Tesla’s leadership position as the world’s leading electric car manufacturer in a competitive market. In this paper, the Lagrange multiplier method is used to incorporate specific market share and marketing expense constraints into the profit function and to find the extreme values by constructing the Lagrange function and solving for the derivatives. However, the results of the study show that the solutions obtained are extreme minima rather than the expected maxima. This result highlights the possible limitations of the Lagrange multiplier method in economic optimization problems. Nonetheless, this paper provides valuable lessons for understanding and applying the Lagrange multiplier method and points the way for further research on the application of optimization methods in economic decision making.References
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