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Lagrangean method is a way of locating local optimum subject to constraints. Suppose we have an objective function f(x,y) and we want to find an optimum of this function subject to the constraint g(x,y) =c. In order to find optimum, form a lagrangean function L(x,y,λ; c) = f(x,y) + λ(c-g(x,y)), where λ is the lagrangean multiplier.
In this series of videos, we formally derive the first order conditions and second order conditions of lagrangean method. Then, to support our formal proof, we provide some example of how lagrangean method works in practice
Lagrangean Multiplier Method First order conditions
Lagrangean method second order conditions
Consumer equlibrium using Lagrangean method
