Consider two consumers 1 and 2 with wealth w₁ and we respectively. There are two goods 1 and 2. u₁(11.21) = 211 +221, U₂(F12, F22) = 212 +22. Assume that pi #p2- a) Prove or disprove that the aggregate demand can be written as (p, w₁ + ₂). b) Consider a Bergson-Samuelson social welfare function W(u₁, 1₂) = log u₁ +log u₂. Under what condition, can these two consumers be represented by a normative representative consumer with respect to this social welfare function?
Consider two consumers 1 and 2 with wealth w₁ and we respectively. There are two goods 1 and 2. u₁(11.21) = 211 +221, U₂(F12, F22) = 212 +22. Assume that pi #p2- a) Prove or disprove that the aggregate demand can be written as (p, w₁ + ₂). b) Consider a Bergson-Samuelson social welfare function W(u₁, 1₂) = log u₁ +log u₂. Under what condition, can these two consumers be represented by a normative representative consumer with respect to this social welfare function?
Chapter1: Making Economics Decisions
Section: Chapter Questions
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![Consider two consumers 1 and 2 with wealth w₁ and we respectively. There are two goods 1 and
2. u₁(11,221) = 11 + 21, u2(x12,22) = 12 +22. Assume that pi #p2.
a) Prove or disprove that the aggregate demand can be written as (p, w₁ + w₂).
b) Consider a Bergson-Samuelson social welfare function W (u₁. uz) = log u₁ + log u₂. Under what
condition, can these two consumers be represented by a normative representative consumer with
respect to this social welfare function?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10124bda-3ce9-4d24-b35c-9e6026078af4%2F41cfb5a5-c277-44cd-b83a-ed307cada6e0%2F9325zk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider two consumers 1 and 2 with wealth w₁ and we respectively. There are two goods 1 and
2. u₁(11,221) = 11 + 21, u2(x12,22) = 12 +22. Assume that pi #p2.
a) Prove or disprove that the aggregate demand can be written as (p, w₁ + w₂).
b) Consider a Bergson-Samuelson social welfare function W (u₁. uz) = log u₁ + log u₂. Under what
condition, can these two consumers be represented by a normative representative consumer with
respect to this social welfare function?
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