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In mathematical optimization, the method of Lagrange multipliers (named after Joseph Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints.or this to be a probability distribution the sum of the probabilities at each point must equal 1, so our constraint is: We use Lagrange multipliers to find the point of maximum entropy, , across all discrete probability distributions on.
ECONOMIC APPLICATIONS OF LAGRANGE MULTIPLIERSMaximization of a function with a constraint is common in economic situations. The ï¬rst section consid-ers the problem in consumer theory of maximization of the utility function with a ï¬xed amount of wealth tospend on the commodities.he equations givenby the Lagrange multiplier method areâUâx i = Î»p i for 1 â¤ i â¤ nw 0 = p 1 x 1 +Â·Â·Â·+p n x n .A solution satisï¬esÎ» =1p i âUâx i for all i.Thus, the ratio of the marginal utility to price is the same for each commodity.