A consumer has utility function u(x₁, x₂) = (x₁ - C₁) (x₂-0₂) where c₁ and c₂ are positive constants. (a) Are this consumer's preferences monotone? (b) Find this consumer's Hicksian demands and expenditure function if she must choose ₁ ≥ ₁ and ₂ ≥ 0₂. Explain briefly how you would check that your solution is optimal (you do not actually have to check it). (c) Using your answer from Part (b), calculate this consumer's Marshallian demands without solving the utility maximization problem (again assuming ₁ ≥ ₁ and ₂ ≥ ₂).
A consumer has utility function u(x₁, x₂) = (x₁ - C₁) (x₂-0₂) where c₁ and c₂ are positive constants. (a) Are this consumer's preferences monotone? (b) Find this consumer's Hicksian demands and expenditure function if she must choose ₁ ≥ ₁ and ₂ ≥ 0₂. Explain briefly how you would check that your solution is optimal (you do not actually have to check it). (c) Using your answer from Part (b), calculate this consumer's Marshallian demands without solving the utility maximization problem (again assuming ₁ ≥ ₁ and ₂ ≥ ₂).
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:A consumer has utility function
u(x₁, x₂) = (x₁ - C₁) (x2 - C₂)
where c₁ and ₂ are positive constants.
(a) Are this consumer's preferences monotone?
(b) Find this consumer's Hicksian demands and expenditure function if she must choose
2₁ ≥ ₁ and ₂ ≥ ₂2. Explain briefly how you would check that your solution is optimal
(you do not actually have to check it).
(c) Using your answer from Part (b), calculate this consumer's Marshallian demands without
solving the utility maximization problem (again assuming ₁ ≥ ₁ and ₂ ≥ 0₂).
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