Novel insights into the multiplier rule

Abstract

We present the Lagrange multiplier rule, one of the basic optimization methods, in a new way. Novel features include:• Explanation of the true source of the power of the rule: reversal of tasks, but not the use of multipliers.• A natural proof based on a simple picture, but not the usual technical derivation from the implicit function theorem.• A practical method to avoid the cumbersome second order conditions.• Applications from various areas of mathematics, physics, economics.• Some hnts on the use of the rule.bargaining;dynamical systems;economics;finance;multiplier rule;second order condition