Mary can consume two goods X₁ and X2, where X₁ and X₂ are the quantities of two goods purchased. From the consumption of these two goods, Mary gains utility according to the function U (X₁, X₂) = X6 X9.4. The price of X₁, noted as P₁, is £12, and the price of X₂, noted as P2, is £4. Mary's weekly budget is £40. By using the Lagrangean method, find the quantities of X₁ and X2 that Mary should buy each week in order to maximise her utility. Give an economic interpretation of the Lagrange multiplier.

Mary can consume two goods X₁ and X2, where X₁ and X₂ are the quantities of two goods purchased. From the consumption of these two goods, Mary gains utility according to the function U (X₁, X₂) = X6 X9.4. The price of X₁, noted as P₁, is £12, and the price of X₂, noted as P2, is £4. Mary's weekly budget is £40. By using the Lagrangean method, find the quantities of X₁ and X2 that Mary should buy each week in order to maximise her utility. Give an economic interpretation of the Lagrange multiplier.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Mary can consume two goods X₁ and X2, where X₁ and X₂ are
the quantities of two goods purchased. From the consumption
of these two goods, Mary gains utility according to the function
U(X₁, X₂) = X0.6 X0.4. The price of X₁, noted as P₁, is £12, and
the price of X₂, noted as P2, is £4. Mary's weekly budget is £40.
By using the Lagrangean method, find the quantities of X₁ and X₂
that Mary should buy each week in order to maximise her utility.
Give an economic interpretation of the Lagrange multiplier.

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