Indicating consumption sider an agent who want to maximize her duty function, 6₁, 62) - ₁2 subject to budge respectively, while p>0 and w>0 are exogenously given parameters, indicating the relative price of good 2 and the relative wealth in term of good 1's price. Decide whether the following claims are true or false. W The value of the Lagrange multiplier is λ = 2p O False O True The value function u(w) is equal to u(w) = w² 4p O True O False (w) measures the approximate change in utility that can be obtained from an increase/decrease in wealth w. O True O False modity and

Economics For Today
10th Edition
ISBN:9781337613040
Author:Tucker
Publisher:Tucker
Chapter6: Consumer Choice Theory
Section: Chapter Questions
Problem 23SQ
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Consider an agent who want to maximize her utility function, u (C₁, C₂) = C₁ C₂ subject to the budget constraint, c₁ + pc₂ = w with C₁, C₂ > 0 indicating consumption of commodity 1 and 2,
respectively, while p>0 and w>0 are exogenously given parameters, indicating the relative price of good 2 and the relative wealth in term of good 1's price.
Decide whether the following claims are true or false.
W
• The value of the Lagrange multiplier is λ =
2p
False
True
w²
• The value function u(w) is equal to u(w) =
4p
True
False
• λ(w) measures the approximate change in utility that can be obtained from an increase/decrease in wealth w.
True
False
Transcribed Image Text:Consider an agent who want to maximize her utility function, u (C₁, C₂) = C₁ C₂ subject to the budget constraint, c₁ + pc₂ = w with C₁, C₂ > 0 indicating consumption of commodity 1 and 2, respectively, while p>0 and w>0 are exogenously given parameters, indicating the relative price of good 2 and the relative wealth in term of good 1's price. Decide whether the following claims are true or false. W • The value of the Lagrange multiplier is λ = 2p False True w² • The value function u(w) is equal to u(w) = 4p True False • λ(w) measures the approximate change in utility that can be obtained from an increase/decrease in wealth w. True False
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