OPTIMIZATION WITH EQUALITY CONSTRAINTS

Vasileios Zikos

Chapter 5 in Essential Mathematics for Economics:A Student's Guide to Key Mathematical Techniques, 2026, pp 73-87 from World Scientific Publishing Co. Pte. Ltd.

Abstract: After completing this chapter, students will be able to:Use the Lagrange multiplier method to solve optimization problems with equality constraints.Understand the interpretation of the Lagrange multiplier.Apply the Lagrange multiplier method to various economic problems.In Chapter 4, we studied how to optimize a function in the absence of constraints. However, economic problems often involve various types of constraints: a consumer may maximize utility subject to a budget constraint or minimize expenditure while attaining a given level of utility. Similarly, a firm may seek to maximize profits or minimize costs under quantity constraints…

Keywords: Microeconomics; Applied Microeconomics; Optimization; First-order Conditions; Second-order Conditions; Equality Constraints; Inequality Constraints; Concavity; Convexity; Matrix Algebra; Determinants; Differential Calculus; Integral Calculus; First-order Linear Differential Equations; Utility Maximization; Profit Maximization; Research Applications (search for similar items in EconPapers)
JEL-codes: C01 C02 C61 D00 (search for similar items in EconPapers)
Date: 2026
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