please only do: if you can teach explain steps A consumer has utility functionu(x₁, x2) = (x₁ - C₁) (x₂ - 0₂)where c₁ and ₂ are positive constants.(a) Are this consumer's preferences monotone?Solution: No. Differentiating gives = x2-02, which is negative for x2 < c₂.(b) Find this consumer's Hicksian demands and expenditure function if she must choose1₁ ≥ ₁ and 2₂ ≥ 02. Explain briefly how you would check that your solution is optimal(you do not actually have to check it).Solution: The expenditure minimization problem ismin p₁æ1+p2æ2 s.t (₁-₁)(x₂ - 0₂) ≥ u.Since preferences are monotone for x₁ ≥ c₁ and x₂ ≥ c2, the constraint binds. Thefirst-order conditions areand thereforeP1 = √(x₂ - 0₂)and p2= (₁-C₁).Dividing the two conditions gives21 C1P2X2 C2 P1Substituting back into the constraint givesP2 (x₂-0₂)² = uP1h₂(p, u) = c₂ +piùP2

Introduction One of the assumptions that aids customers in decision-making are "Completeness and…

A consumer has utility function u(T₁, 12) = (11 — C₁) (12 - 0₂) where c₁ and ₂ are positive constants. (a) Are this consumer's preferences monotone? Solution: No. Differentiating gives = 12 - C2, which is negative for 12 < €2. (b) Find this consumer's Hicksian demands and expenditure function if she must ch 1₁ ≥ 4₁ and 1₂ ≥ 0₂. Explain briefly how you would check that your solution is opti (you do not actually have to check it). Solution: The expenditure minimization problem is min p₁z₁+p2x2 st (₁-C₁) (12 - 0₂) ≥ u.

A consumer has utility function u(T₁, 12) = (11 — C₁) (12 - 0₂) where c₁ and ₂ are positive constants. (a) Are this consumer's preferences monotone? Solution: No. Differentiating gives = 12 - C2, which is negative for 12 < €2. (b) Find this consumer's Hicksian demands and expenditure function if she must ch 1₁ ≥ 4₁ and 1₂ ≥ 0₂. Explain briefly how you would check that your solution is opti (you do not actually have to check it). Solution: The expenditure minimization problem is min p₁z₁+p2x2 st (₁-C₁) (12 - 0₂) ≥ u.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.13P

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