期刊名称：Economics Discussion Papers / Department of Economics, College of Management and Economics, University of Guelph
出版年度：2010
卷号：2010
期号：01
出版社：University of Guelph
摘要：Lagrange technique transforms a constrained optimization problem into an unconstrained optimization
problem. This is both mathematically incorrect, and in some contexts contrary to a basic understanding of
economic principles. In fact, as is probably understood by most instructors, solutions to the Lagrange
conditions for a constrained optimization problem are generally saddle points, an observation typically
included in advanced treatments of mathematical economics. At the introductory level, however,
instructors often ‘cut corners’ and emphasize that the first-order conditions associated with the method of
Lagrange multipliers are essentially the same as for an unconstrained optimization problem, hence leading
to an incorrect intuition. We propose an alternative intuition that introduces the Lagrangian function as a
perturbation of the original objective function. We characterize a constrained optimum as a point at which
all the derivatives of a suitable perturbation must vanish. The paper is both useful for instructors of
introductory courses in mathematical methods for economics and also can be used to provide enrichment to
students for this very important mathematical technique.
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