Problem 3. Consider the same setup as Problem 3 from last week's problem set. Look carefully through the solutions to that problem, including diagrams, before you get started! Preferences are represented by the Cobb-Douglas utility function with a = 1 u(x1,x2) = √x1x2 Suppose that initially m = = $40, p₁ = $2, p₂ = $5. In this problem we consider the impact of a (potential) price change where the price of good 2 increases to p2 = $10. a) Write down the indirect utility function. Find our consumer's utility levels u before (under the original prices and income) and u after (after the price of good 2 increases). after b) Write down the expenditure function. Find the Compensating Variation associated with this price change: If this price change has already happened (p af after = $2, P₂ = = $10), how much income do we need to give the consumer to reach their original level of utility, u before? c) Compare the answer you got to part b) above to the answer to Problem 3b) on last week's problem set. Which one is larger and why? d) Find the Equivalent Variation associated with this price change: Before the price change occurs before = $2, P2 $5), how much income would the consumer be willing to give up to before = (p₁₂ prevent it from happening? e) Illustrate your answers to parts b) and d) on two diagrams similar to slides 9 and 10 of Notes #8 from class. Clearly label the old ("before") and new ("after") budget lines and indifference curves on each diagram.
Problem 3. Consider the same setup as Problem 3 from last week's problem set. Look carefully through the solutions to that problem, including diagrams, before you get started! Preferences are represented by the Cobb-Douglas utility function with a = 1 u(x1,x2) = √x1x2 Suppose that initially m = = $40, p₁ = $2, p₂ = $5. In this problem we consider the impact of a (potential) price change where the price of good 2 increases to p2 = $10. a) Write down the indirect utility function. Find our consumer's utility levels u before (under the original prices and income) and u after (after the price of good 2 increases). after b) Write down the expenditure function. Find the Compensating Variation associated with this price change: If this price change has already happened (p af after = $2, P₂ = = $10), how much income do we need to give the consumer to reach their original level of utility, u before? c) Compare the answer you got to part b) above to the answer to Problem 3b) on last week's problem set. Which one is larger and why? d) Find the Equivalent Variation associated with this price change: Before the price change occurs before = $2, P2 $5), how much income would the consumer be willing to give up to before = (p₁₂ prevent it from happening? e) Illustrate your answers to parts b) and d) on two diagrams similar to slides 9 and 10 of Notes #8 from class. Clearly label the old ("before") and new ("after") budget lines and indifference curves on each diagram.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Transcribed Image Text:Problem 3.
Consider the same setup as Problem 3 from last week's problem set. Look carefully through the
solutions to that problem, including diagrams, before you get started! Preferences are represented by
the Cobb-Douglas utility function with a =
1
u(x1,x2) = √x1x2
Suppose that initially m = = $40, p₁ = $2, p₂
= $5. In this problem we consider the impact of a
(potential) price change where the price of good 2 increases to p2 = $10.
a) Write down the indirect utility function. Find our consumer's utility levels u before (under the
original prices and income) and u after (after the price of good 2 increases).
after
b) Write down the expenditure function. Find the Compensating Variation associated with this
price change: If this price change has already happened (p af
after
= $2, P₂
=
= $10), how
much income do we need to give the consumer to reach their original level of utility, u before?
c) Compare the answer you got to part b) above to the answer to Problem 3b) on last week's
problem set. Which one is larger and why?
d) Find the Equivalent Variation associated with this price change: Before the price change occurs
before = $2, P2
$5), how much income would the consumer be willing to give up to
before
=
(p₁₂
prevent it from happening?
e) Illustrate your answers to parts b) and d) on two diagrams similar to slides 9 and 10 of Notes #8
from class. Clearly label the old ("before") and new ("after") budget lines and indifference
curves on each diagram.
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