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Examples of the Lagrangian and Lagrange multiplier technique in action.

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In mathematical optimization, the method of Lagrange multipliers (or method of Lagrange’s undetermined multipliers, named after Joseph-Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).

In macroeconomics, a multiplier is a factor of proportionality that measures how much an endogenous variable changes in response to a change in some exogenous variable. For example, suppose variable x changes by 1 unit, which causes another variable y to change by M units. Then the multiplier is M

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