Suppose U(x, y, z) = xy² z³ is the utility function of a person consuming x, y and z units of three commodities X, Y and Z. Suppose that X, Y and Z each costs €3 per unit. If a person has a budget of €90 then they can maximize their utility by consuming 5 units of good X, 10 units of good Y and 15 units of good Z to give a maximum utility of 1687,500. If the Lagrange multiplier for this problem is 112, 500 approximate the utility they would receive if their budget was €91. Briefly expalin your answer.
Suppose U(x, y, z) = xy² z³ is the utility function of a person consuming x, y and z units of three commodities X, Y and Z. Suppose that X, Y and Z each costs €3 per unit. If a person has a budget of €90 then they can maximize their utility by consuming 5 units of good X, 10 units of good Y and 15 units of good Z to give a maximum utility of 1687,500. If the Lagrange multiplier for this problem is 112, 500 approximate the utility they would receive if their budget was €91. Briefly expalin your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose
U (x, y, z) = xy² z³
is the utility function of a person consuming x, y and z units of three commodities
X, Y and Z. Suppose that X, Y and Z each costs €3 per unit. If a person has a
budget of €90 then they can maximize their utility by consuming 5 units of good X,
10 units of good Y and 15 units of good Z to give a maximum utility of 1687,500.
If the Lagrange multiplier for this problem is 112, 500 approximate the utility they
would receive if their budget was €91. Briefly expalin your answer.
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