Show that the two utility functions given below generate identical demand functions for goods X and YUCXY) log(X)+log(YC) UCxY) (XY05The demand function for good X and the demand function for good Y for both utility functions equalO A.X=and YPvPxО В.Х-and Y2PvОс.X Y=21PXPYO D.Х-and Y2P.2PyОЕ.X= Y=РХPY

Question
Asked Oct 23, 2019
109 views
Show that the two utility functions given below generate identical demand functions for goods X and Y
UCXY) log(X)+log(Y
C) UCxY) (XY05
The demand function for good X and the demand function for good Y for both utility functions equal
O A.
X=
and Y
Pv
Px
О В.
Х-
and Y
2Pv
Ос.
X Y=
21
PXPY
O D.
Х-
and Y
2P.
2Py
ОЕ.
X= Y=
РХPY
help_outline

Image Transcriptionclose

Show that the two utility functions given below generate identical demand functions for goods X and Y UCXY) log(X)+log(Y C) UCxY) (XY05 The demand function for good X and the demand function for good Y for both utility functions equal O A. X= and Y Pv Px О В. Х- and Y 2Pv Ос. X Y= 21 PXPY O D. Х- and Y 2P. 2Py ОЕ. X= Y= РХPY

fullscreen
check_circle

Expert Answer

Step 1

Two utility functions are given which are:

help_outline

Image Transcriptionclose

() U(X,Y) log(X)+ log(Y) (ii) U(X,Y) (XY)05

fullscreen
Step 2

Instead of using equation (ii), monotonic transformation of equation (ii) can be done as follows:

help_outline

Image Transcriptionclose

U (x,Y) (XY)0 Applying log. U(X,Y) log(XY)0.5 .(ii) =0.5log(X)+0.5log(Y) ..(i)

fullscreen
Step 3

Now, equations (i) and (iii) are identical equations, so their demand functions will also be identi...

help_outline

Image Transcriptionclose

For equation: U(X,Y) = alogX + blogY Demand function for X and Y are: b I , Y b P a ab P а I Putting values from equation (ii), I ,Y 0.5+0.5 P 0.5 0.5 I Х- 0.5+0.5 P I ,Y 2Px I X 2P

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Business

Economics

Related Economics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: NAME: Chapters 2 & 3 Problem 1 Remember to show all work and briefly discuss your results. Minutes N...

A: The opportunity cost is the best alternative use of a resource. It is the value of what one has to g...

question_answer

Q: List and explain 4 types of transactions that would not be included in GDP and why they should be om...

A: Hey, Thank you for the question. According to our policy we can only answer 1 question per session. ...

question_answer

Q: a. Based on these demand elasticity estimates, which fruit is most inelastically demanded? Which is ...

A: a.The item which is most in-elastically demanded is the one with the least elasticity of demand valu...

question_answer

Q: Firms in a perfectly competitive industry maximize profits by:     eliminating the competition...

A: The perfect competition is a market structure which is characterized by the presence of a large numb...

question_answer

Q: 7. LO 2, 4 Suppose that a consumer can earn a higher wage rate for working overtime. That is, for th...

A: Let the consumer has two goods to consume, consumption (C) and leisure (l). The consumer’s budget co...

question_answer

Q: explain on the impact of a drop in the discount rate on the supply of money in the market

A: Monetary Policy: It refers to the decision of the central bank regarding the amount of money supply ...

question_answer

Q: A case study in this chapter discusses the federal minimum-wage law. Suppose the minimum wage is ...

A: The aforementioned given statement can be used to draw the labor market graph as follows:

question_answer

Q: Consider the following graph of a production function when capital is constant. (The following is a ...

A: Marginal Product of Labor (MPL) represents the change in total output resulting from employing an ad...

question_answer

Q: 2. An economy has a production function:Yt = 3(squaredKt)(squaredLt). The economy has a saving rate ...

A: Click to see the answer