2. [This question shows that our marginal utility calculations for consumer behav- ior essentially do not depend on which utility we use to represent preferences, even though the marginal utilities themselves do.] Suppose u: X → R is differentiable at some x € X, with strictly positive marginal utilities. Let f: R→ R be a function with strictly positive derivative; let u fou. (In particular, u and u represent the same preferences because f is strictly increasing.) = (a) Show by example that the marginal utility for good 1 could be different under u and under u. (b) Show that the ratio MU is the same for utility u as it is for utility u. MU₂(1)
2. [This question shows that our marginal utility calculations for consumer behav- ior essentially do not depend on which utility we use to represent preferences, even though the marginal utilities themselves do.] Suppose u: X → R is differentiable at some x € X, with strictly positive marginal utilities. Let f: R→ R be a function with strictly positive derivative; let u fou. (In particular, u and u represent the same preferences because f is strictly increasing.) = (a) Show by example that the marginal utility for good 1 could be different under u and under u. (b) Show that the ratio MU is the same for utility u as it is for utility u. MU₂(1)
Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section: Chapter Questions
Problem 3SQP
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Question
![2. [This question shows that our marginal utility calculations for consumer behav-
ior essentially do not depend on which utility we use to represent preferences,
even though the marginal utilities themselves do.]
Suppose u: X→ R is differentiable at some r E X, with strictly positive
marginal utilities. Let f: R→ R be a function with strictly positive derivative;
let u fou. (In particular, u and u represent the same preferences because f
is strictly increasing.)
=
(a) Show by example that the marginal utility for good 1 could be different
under u and under u.
(b) Show that the ratio MU() is the same for utility u as it is for utility u.
MU₂ (1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd86cda1-af2d-4585-b012-7ab18b7ef9b3%2F2a15b48a-19e3-45d5-bc10-4ecaa5d627fa%2Fxr89pd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. [This question shows that our marginal utility calculations for consumer behav-
ior essentially do not depend on which utility we use to represent preferences,
even though the marginal utilities themselves do.]
Suppose u: X→ R is differentiable at some r E X, with strictly positive
marginal utilities. Let f: R→ R be a function with strictly positive derivative;
let u fou. (In particular, u and u represent the same preferences because f
is strictly increasing.)
=
(a) Show by example that the marginal utility for good 1 could be different
under u and under u.
(b) Show that the ratio MU() is the same for utility u as it is for utility u.
MU₂ (1)
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