Lagrange’s ‘method of undetermined multipliers’ applies to a function of several variables subject to constraints, for which a maximum is required. Lagrange’s procedure avoids the arbitrary distinction between independent and dependent variables. The method involves further variables, the ‘multipliers’ associated with the constraints, which have importance in application to economic problems. Beside the value obtainable from a given resource, one might also wish to know the ‘marginal value’ obtainable when a unit of it is added. The Lagrangian method is therefore a natural tool of the ‘marginalist revolution’, and the multiplier concept underlies ‘shadow price’, ‘implicit value’ and similar expressions.
KeywordsChain rule Convex programming Implicit function theorem Kuhn–Tucker conditions Lagange multipliers Lagrangian function Marginal revolution Separating hyperplane theorem
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