Lagrange: A Well-Behaved Function

Abstract

This paper outlines the biography and achievements of Joseph Louis Lagrange (1736-1813) and includes a detailed explanation, with examples, of the Lagrange Multiplier method for optimizing multivariate functions subject to constraint. The Lagrange Multiplier is widely used in chemistry, physics, and economics, in particular. The paper considers the origin of economics' use of the multiplier and provides a concrete example of how it is used in microeconomic theory. While the focus is on the multiplier's application to microeconomics, the intended audience includes all teachers and students who encounter any of Lagrange's contributions. Since Lagrange's contributions to mathematics are numerous, so too are those who might benefit from learning more about the man and his time. ABSTRACT FROM AUTHOR Copyright of Montana Mathematics Enthusiast is the property of Montana Mathematics Enthusiast and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts) This paper outlines the biography and achievements of Joseph Louis Lagrange (1736-1813) and includes a detailed explanation, with examples, of the Lagrange Multiplier method for optimizing multivariate functions subject to constraint. The Lagrange Multiplier is widely used in chemistry, physics, and economics, in particular. The paper considers the origin of economics' use of the multiplier and provides a concrete example of how it is used in microeconomic theory. While the focus is on the multiplier's application to microeconomics, the intended audience includes all teachers and students who encounter any of Lagrange's contributions. Since Lagrange's contributions to mathematics are numerous, so too are those who might benefit from learning more about the man and his time. ABSTRACT FROM AUTHOR Copyright of Montana Mathematics Enthusiast is the property of Montana Mathematics Enthusiast and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts)