A three good utility function is given by the following equation. U(X,Y,Z) = 10X-6Y•'Z³ %3D Write the Lagrangean Function and the first-order conditions for utility maximization of this function. Now solve this equation for the X,Y, and Z as a function of the prices. Px, Py, and Pz and income, I. Economics 4100 Page 2 II. Write your answers on this test I. What type of utility function is used in this problem? (cont.) 1) Suppose the demand for Q is the quantity of DVRS demand television. How much does the qu Would your demand functions be different if the utility function were squared? A) drops by 2,500 DVRS Raised to the ½ power? B) increases by 4,000 DVRS rdrops by 10,000 DVRS Transformed by taking a natural logarithm? D) increases by 16,000 DVRS SHOW ALL WORK-No work no credit! What is the own price elasticity of demand for X? 2) When import restrictior increases, the demand curve for A) be unaffected BYshift rightward. C) shift leftward. D) become steeper. What is the cross price elasticity of demand for X with respect to the Price of Y? With respect to the Price of Z? What is the income elasticity of demand for X? What is the sum of the own price elasticity of demand for X, the cross price elasticities, and the income elasticity of demand for X? Does this hold only for the given type of utility function or all well behaved utility functions? _3)The figure below shows barrel, what is the price elastici A) -500 B) -10 What does this mean? D) -.02 What type of real world data and/or empirical evidence would lead you to accept or reject the above functional form of the utility function? Give at least 3 reasons including whether goods are necessities, luxury goods, or inferior, whether goods can be complements or substitutes, or whether goods can be price elastic or price inelastic.
A three good utility function is given by the following equation. U(X,Y,Z) = 10X-6Y•'Z³ %3D Write the Lagrangean Function and the first-order conditions for utility maximization of this function. Now solve this equation for the X,Y, and Z as a function of the prices. Px, Py, and Pz and income, I. Economics 4100 Page 2 II. Write your answers on this test I. What type of utility function is used in this problem? (cont.) 1) Suppose the demand for Q is the quantity of DVRS demand television. How much does the qu Would your demand functions be different if the utility function were squared? A) drops by 2,500 DVRS Raised to the ½ power? B) increases by 4,000 DVRS rdrops by 10,000 DVRS Transformed by taking a natural logarithm? D) increases by 16,000 DVRS SHOW ALL WORK-No work no credit! What is the own price elasticity of demand for X? 2) When import restrictior increases, the demand curve for A) be unaffected BYshift rightward. C) shift leftward. D) become steeper. What is the cross price elasticity of demand for X with respect to the Price of Y? With respect to the Price of Z? What is the income elasticity of demand for X? What is the sum of the own price elasticity of demand for X, the cross price elasticities, and the income elasticity of demand for X? Does this hold only for the given type of utility function or all well behaved utility functions? _3)The figure below shows barrel, what is the price elastici A) -500 B) -10 What does this mean? D) -.02 What type of real world data and/or empirical evidence would lead you to accept or reject the above functional form of the utility function? Give at least 3 reasons including whether goods are necessities, luxury goods, or inferior, whether goods can be complements or substitutes, or whether goods can be price elastic or price inelastic.
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.8P
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Question
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I have solved the equations for X, Y and Z.
I need help with the questions on the second page.
Transcribed Image Text:A three good utility function is given by the following equation.
U(X,Y,Z) = 10X-6Y•'Z³
%3D
Write the Lagrangean Function and the first-order conditions for utility maximization of this function.
Now solve this equation for the X,Y, and Z as a function of the prices. Px, Py, and Pz and income, I.
Transcribed Image Text:Economics 4100
Page 2
II. Write your answers on this test
I.
What type of utility function is used in this problem?
(cont.)
1) Suppose the demand for
Q is the quantity of DVRS demand
television. How much does the qu
Would your demand functions be different if the utility function were squared?
A) drops by 2,500 DVRS
Raised to the ½ power?
B) increases by 4,000 DVRS
rdrops by 10,000 DVRS
Transformed by taking a natural logarithm?
D) increases by 16,000 DVRS
SHOW ALL WORK-No work no credit!
What is the own price elasticity of demand for X?
2) When import restrictior
increases, the demand curve for
A) be unaffected
BYshift rightward.
C) shift leftward.
D) become steeper.
What is the cross price elasticity of demand for X with respect to the Price of Y? With respect to the Price of
Z?
What is the income elasticity of demand for X?
What is the sum of the own price elasticity of demand for X, the cross price elasticities, and the income
elasticity of demand for X?
Does this hold only for the given type of utility function or all well behaved utility functions?
_3)The figure below shows
barrel, what is the price elastici
A) -500
B) -10
What does this mean?
D) -.02
What type of real world data and/or empirical evidence would lead you to accept or reject the above
functional form of the utility function? Give at least 3 reasons including whether goods are necessities,
luxury goods, or inferior, whether goods can be complements or substitutes, or whether goods can be price
elastic or price inelastic.
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