Lagrange Multiplier Problems in Economics
Several surprises are in store for the mathematics student who looks
for the first time at nontrivial constrained optimization problems in economics. The
usual constrained problem in a mathematics course has only one or two critical points
and the selection of the absolute maximum is clear from the geometric nature of the
problem. Mathematics texts often ignore sufficient conditions (involving bordered
Hessian determinants) for relative extrema and provide no interpretation of the Lagrange
multiplier leaving the student with the impression that has no significance beyond
providing an extra variable which magically transforms the constrained problem into an
unconstrained higher dimensional problem.
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