4. Consider the general multiplicatively separable utility function given by u (x1,x2) = pu1 (x1) u2 (x2), and budget constraint given by pič1 + P2X2 = w. (a) Find the wealth effect for good 1. Show that, for a "well-behaved" utility function of this form (i.e., > 0, i = 1,2; and * < 0, i = Explain intuitively why this should be so. 1, 2), good 1 must be a normal good. (b) Find the own price effect for good 1. (c) Show that good 1 being a normal good is a sufficient condition for good 1 not being a Giffen good.

Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section: Chapter Questions
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4. Consider the general multiplicatively separable utility function given by u (x1, x2) = µu1 (x1) u2 (x2),
and budget constraint given by p1x1+P2X2 = W.
(a) Find the wealth effect for good 1. Show that, for a "well-behaved" utility function of this
г —
a2 u
form (i.e.,
ди
> 0, i = 1,2; and < 0, i =
1, 2), good 1 must be a normal good.
Explain intuitively why this should be so.
(b) Find the own price effect for good 1.
(c) Show that good 1 being a normal good is a sufficient condition for good 1 not being a
Giffen good.
Transcribed Image Text:4. Consider the general multiplicatively separable utility function given by u (x1, x2) = µu1 (x1) u2 (x2), and budget constraint given by p1x1+P2X2 = W. (a) Find the wealth effect for good 1. Show that, for a "well-behaved" utility function of this г — a2 u form (i.e., ди > 0, i = 1,2; and < 0, i = 1, 2), good 1 must be a normal good. Explain intuitively why this should be so. (b) Find the own price effect for good 1. (c) Show that good 1 being a normal good is a sufficient condition for good 1 not being a Giffen good.
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