Consider the utility function и (х, х2) %3D х, + 3x; a) Find the demand functions for goods 1 and 2 as a function of prices and income. Note these demands will look like x, (pup2,m) = {72 (P1» P2» m) m > h(Pı, P2) l92(P1, P2, m) m < h(P,,P2) for some functions f2, 92, and h; your job is to find these functions. b) Explain why these demand functions do not necessarily satisfy the typical "MRS equals relative price" condition. Include a graph in your answer. c) "Income expansion paths are curves in (x1, x2) space along which MRS is constant." Is this statement true for these preferences? If so, what does it imply about the shape of the income expansion paths for these preferences? Include a graph in your answer.

Consider the utility function и (х, х2) %3D х, + 3x; a) Find the demand functions for goods 1 and 2 as a function of prices and income. Note these demands will look like x, (pup2,m) = {72 (P1» P2» m) m > h(Pı, P2) l92(P1, P2, m) m < h(P,,P2) for some functions f2, 92, and h; your job is to find these functions. b) Explain why these demand functions do not necessarily satisfy the typical "MRS equals relative price" condition. Include a graph in your answer. c) "Income expansion paths are curves in (x1, x2) space along which MRS is constant." Is this statement true for these preferences? If so, what does it imply about the shape of the income expansion paths for these preferences? Include a graph in your answer.

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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