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Constraint: 2x + py = m a) Show that the utility function is concave. b) Find the Lagrange multiplier. c) Derive the utility maximizing demand function for good y as a function of (p, m).

Constraint: 2x + py = m a) Show that the utility function is concave. b) Find the Lagrange multiplier. c) Derive the utility maximizing demand function for good y as a function of (p, m).

Advanced Engineering Mathematics
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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Utility function: U (x,y) = 2x +y (x 2 0,y 2 0) Constraint: 2x+py = m a) Show that the utility function is concave. b) Find the Lagrange multiplier. c) Derive the utility maximizing demand function for good y as a function of (p, m). d) Find the homogeneity of the function you derived above. e) Find aU/am and comment on your answer.
Transcribed Image Text:Utility function: U (x,y) = 2x +y (x 2 0,y 2 0) Constraint: 2x+py = m a) Show that the utility function is concave. b) Find the Lagrange multiplier. c) Derive the utility maximizing demand function for good y as a function of (p, m). d) Find the homogeneity of the function you derived above. e) Find aU/am and comment on your answer.
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