Answer all 3 Utility representationsFor each of the pairs of utility functions over X = R2, state whether they represent thesame preferences. If so, please find a monotone transformation that relates them (i.e., find afunction f: R→ R increasing such that f(U₁(x)) = U₂(x) or f(U₂(x)) = U₁(x) for all x). Ifnot, find a pair of outcomes which the two utility functions rank differently (i.e., find x andx' such that U₁(x) > U₁(x) and U₂(x) < U₂(x') ).1. U₁(x) = xx and U₂(x) = ln x₁ + ln x2-2. U₁(x) = x₁ + 2x2 and U₂(x) = x + 2x3. U₁(x) = x₁ - 1 and U₂(x) = (x₁ − 1)²

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ility representations = of the pairs of utility functions over X R2, state whether they erences. If so, please find a monotone transformation that relates ther f: RR increasing such that f(U₁(x)) = U₂(x) or f(U₂(x)) = U₁(x) a pair of outcomes which the two utility functions rank differently (i. at U₁(x) > U₁(x) and U₂(x) < U₂(x')). r) = xx and U₂(x) = ln x₁ + ln x₂ r) = x₁ + 2x₂ and U₂(x) = x² + 2x r) = x₁ - 1 and U₂(x) = (x₁ - 1)²

ility representations = of the pairs of utility functions over X R2, state whether they erences. If so, please find a monotone transformation that relates ther f: RR increasing such that f(U₁(x)) = U₂(x) or f(U₂(x)) = U₁(x) a pair of outcomes which the two utility functions rank differently (i. at U₁(x) > U₁(x) and U₂(x) < U₂(x')). r) = xx and U₂(x) = ln x₁ + ln x₂ r) = x₁ + 2x₂ and U₂(x) = x² + 2x r) = x₁ - 1 and U₂(x) = (x₁ - 1)²

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.10P

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