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Andrea maximizes the following utility function: subject to the budget constraint u(x1, x2) = x ² x ² P1x1 + ₂x2 = I where p1, p2, x1, x2, I > 0 (a) Find the (x₁, x2) that maximizes u(x₁, x2). (b) Show that the maximizer x (P1, P2, I) is decreasing in p2 and increasing in I (Hint: Use the partial derivatives). (c) Does x (P1, P2, I) change if p₁ changes? (Hint: partial derivatives).

Andrea maximizes the following utility function: subject to the budget constraint u(x1, x2) = x ² x ² P1x1 + ₂x2 = I where p1, p2, x1, x2, I > 0 (a) Find the (x₁, x2) that maximizes u(x₁, x2). (b) Show that the maximizer x (P1, P2, I) is decreasing in p2 and increasing in I (Hint: Use the partial derivatives). (c) Does x (P1, P2, I) change if p₁ changes? (Hint: partial derivatives).

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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Andrea maximizes the following utility function: subject to the budget constraint 1 3 u(x₁, x₂) = x 1 x₂ P₁x₁ + P₂x2 = I where P1, 1, P2, X1, X2, I >0 (a) Find the (x₁, x2) that maximizes u(x₁, x2). (b) Show that the maximizer x*(p1, P2, I) is decreasing in på and increasing in I (Hint: Use the partial derivatives). (c) Does x (P1, P2, I) change if p₁ changes? (Hint: partial derivatives).
Transcribed Image Text:Andrea maximizes the following utility function: subject to the budget constraint 1 3 u(x₁, x₂) = x 1 x₂ P₁x₁ + P₂x2 = I where P1, 1, P2, X1, X2, I >0 (a) Find the (x₁, x2) that maximizes u(x₁, x2). (b) Show that the maximizer x*(p1, P2, I) is decreasing in på and increasing in I (Hint: Use the partial derivatives). (c) Does x (P1, P2, I) change if p₁ changes? (Hint: partial derivatives).
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