
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
expand_more
expand_more
format_list_bulleted
Question
Questions g) and h)
![4.13 CES indirect utility and expenditure functions
In this problem, we will use a more standard form of the CES utility function to derive indirect utility and expenditure
functions. Suppose utility is given by
U(x, y) = (x° +y®)'/8
[in this function the elasticity of substitution o = 1/(1 – 6)].
a. Show that the indirect utility function for the utility function just given is
V = I(p, + p,)¬/",
where r = 8/(ò – 1) = 1 – 0.
b. Show that the function derived in part (a) is homogeneous of degree zero in prices and income.
c. Show that this function is strictly increasing in income.
d. Show that this function is strictly decreasing in any price.
e. Show that the expenditure function for this case of CES utility is given by
E = V(p', + p,)''".
f. Show that the function derived in part (e) is homogeneous of degree one in the goods' prices.
g. Show that this expenditure function is increasing in each of the prices.
h. Show that the function is concave in each price.](https://content.bartleby.com/qna-images/question/b1776ef4-eb5a-42b4-8bd9-b41536cc546d/e519f3f8-6201-4da0-bbaf-b27202e9c84e/rch34tg_thumbnail.png)
Transcribed Image Text:4.13 CES indirect utility and expenditure functions
In this problem, we will use a more standard form of the CES utility function to derive indirect utility and expenditure
functions. Suppose utility is given by
U(x, y) = (x° +y®)'/8
[in this function the elasticity of substitution o = 1/(1 – 6)].
a. Show that the indirect utility function for the utility function just given is
V = I(p, + p,)¬/",
where r = 8/(ò – 1) = 1 – 0.
b. Show that the function derived in part (a) is homogeneous of degree zero in prices and income.
c. Show that this function is strictly increasing in income.
d. Show that this function is strictly decreasing in any price.
e. Show that the expenditure function for this case of CES utility is given by
E = V(p', + p,)''".
f. Show that the function derived in part (e) is homogeneous of degree one in the goods' prices.
g. Show that this expenditure function is increasing in each of the prices.
h. Show that the function is concave in each price.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps with 8 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Similar questions
- (dollars/16) 8= Ps 5 = P₁ 4= P₂ 0.1 = P4 016 а b g U.S. beef market Q3 Q₁ 113 120 125 (dollars/16) (thousand tons) Rises, L+m+n Falls, L Falls, o None of the above is correct 10=P₂ 7=P3 5-Pi 2= P6 k l Im Q4 Q5 74 76 Japan beef market 'S Q6 86 (thousand tons Refer to the above partial equilibrium model of trade (large country case). Assume the world price is $5 when reaching free-trade equilibrium. Moving from a closed situation to free trade, producer surplus in Japan______ byarrow_forwardNonearrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Principles of Economics (12th Edition)EconomicsISBN:9780134078779Author:Karl E. Case, Ray C. Fair, Sharon E. OsterPublisher:PEARSONEngineering Economy (17th Edition)EconomicsISBN:9780134870069Author:William G. Sullivan, Elin M. Wicks, C. Patrick KoellingPublisher:PEARSON
- Principles of Economics (MindTap Course List)EconomicsISBN:9781305585126Author:N. Gregory MankiwPublisher:Cengage LearningManagerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage LearningManagerial Economics & Business Strategy (Mcgraw-...EconomicsISBN:9781259290619Author:Michael Baye, Jeff PrincePublisher:McGraw-Hill Education


Principles of Economics (12th Edition)
Economics
ISBN:9780134078779
Author:Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:PEARSON

Engineering Economy (17th Edition)
Economics
ISBN:9780134870069
Author:William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:PEARSON

Principles of Economics (MindTap Course List)
Economics
ISBN:9781305585126
Author:N. Gregory Mankiw
Publisher:Cengage Learning

Managerial Economics: A Problem Solving Approach
Economics
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Cengage Learning

Managerial Economics & Business Strategy (Mcgraw-...
Economics
ISBN:9781259290619
Author:Michael Baye, Jeff Prince
Publisher:McGraw-Hill Education