Andrew is a deeply committed lover of croissants. Assume his preferences are Cobb-Douglas over croissants (denoted by D on the x-axis) and a numeraire good (note: we use the notion of a numeraire good to represent spending on all other consumption goods-in this example, that means everything other than croissants - its price is normalized such that P = $1). Assuming Andrew's utility function is given by U(C, N) = CN and his income is $64 a year, his Marshallian demand for croissants will be Dc (Pc, Pn, Y) = The expenditure minimization problem yields his compensated (Hicksian) demand for croissants, his compensated (Hicksian) 2PC demand for the numeraire good and his expenditure function:
Andrew is a deeply committed lover of croissants. Assume his preferences are Cobb-Douglas over croissants (denoted by D on the x-axis) and a numeraire good (note: we use the notion of a numeraire good to represent spending on all other consumption goods-in this example, that means everything other than croissants - its price is normalized such that P = $1). Assuming Andrew's utility function is given by U(C, N) = CN and his income is $64 a year, his Marshallian demand for croissants will be Dc (Pc, Pn, Y) = The expenditure minimization problem yields his compensated (Hicksian) demand for croissants, his compensated (Hicksian) 2PC demand for the numeraire good and his expenditure function:
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
b-d please!!
![**1. Economic Analysis of Andrew's Preference for Croissants**
Andrew is a deeply committed lover of croissants. Assume his preferences are Cobb-Douglas over croissants (denoted by \( D \) on the x-axis) and a numeraire good (note: we use the notion of a numeraire good to represent spending on all other consumption goods—in this example, that means everything other than croissants—its price is normalized such that \( P_N = \$1 \)). Assuming Andrew’s utility function is given by \( U(C, N) = C^{\frac{1}{2}}N^{\frac{1}{2}} \) and his income is $64 a year, his Marshallian demand for croissants will be \( D_C(P_C, P_N, Y) = \frac{Y}{2P_C} \).
The expenditure minimization problem yields his compensated (Hicksian) demand for croissants, his compensated (Hicksian) demand for the numeraire good, and his expenditure function:
\[
H_C = \overline{U}\left(\frac{P_N}{P_C}\right)^{\frac{1}{2}}
\]
\[
H_N = \overline{U}\left(\frac{P_C}{P_N}\right)^{\frac{1}{2}}
\]
\[
E(P_C, P_N, \overline{U}) = P_C \cdot H_C + P_N \cdot H_N = 2\overline{U}(P_C \cdot P_N)^{\frac{1}{2}}
\]
*Note: There is a side note stating "No need to derive these for the assignment, but you can solve for them on your own if you want extra practice!"*
**a.** You’ve been hired by a government official considering a proposed piece of legislation that would increase the price of croissants from $1 to $4 while leaving incomes unchanged. Find the original level of utility Andrew achieved before the price increase, then compute the Compensating Variation for this price increase, that is, the minimum amount that Andrew would need to be paid so that he’s no worse off after the price for a box of croissants rises to $4.
**b.** Draw a rough graph of the Marshallian demand and show the loss of Consumer Surplus that would be associated with this price increase. Set](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad5f8718-b822-43a6-888a-6d9b997f8030%2F248277e2-54ff-45f5-987b-4e11ab3443c8%2Fzx68zje_processed.png&w=3840&q=75)
Transcribed Image Text:**1. Economic Analysis of Andrew's Preference for Croissants**
Andrew is a deeply committed lover of croissants. Assume his preferences are Cobb-Douglas over croissants (denoted by \( D \) on the x-axis) and a numeraire good (note: we use the notion of a numeraire good to represent spending on all other consumption goods—in this example, that means everything other than croissants—its price is normalized such that \( P_N = \$1 \)). Assuming Andrew’s utility function is given by \( U(C, N) = C^{\frac{1}{2}}N^{\frac{1}{2}} \) and his income is $64 a year, his Marshallian demand for croissants will be \( D_C(P_C, P_N, Y) = \frac{Y}{2P_C} \).
The expenditure minimization problem yields his compensated (Hicksian) demand for croissants, his compensated (Hicksian) demand for the numeraire good, and his expenditure function:
\[
H_C = \overline{U}\left(\frac{P_N}{P_C}\right)^{\frac{1}{2}}
\]
\[
H_N = \overline{U}\left(\frac{P_C}{P_N}\right)^{\frac{1}{2}}
\]
\[
E(P_C, P_N, \overline{U}) = P_C \cdot H_C + P_N \cdot H_N = 2\overline{U}(P_C \cdot P_N)^{\frac{1}{2}}
\]
*Note: There is a side note stating "No need to derive these for the assignment, but you can solve for them on your own if you want extra practice!"*
**a.** You’ve been hired by a government official considering a proposed piece of legislation that would increase the price of croissants from $1 to $4 while leaving incomes unchanged. Find the original level of utility Andrew achieved before the price increase, then compute the Compensating Variation for this price increase, that is, the minimum amount that Andrew would need to be paid so that he’s no worse off after the price for a box of croissants rises to $4.
**b.** Draw a rough graph of the Marshallian demand and show the loss of Consumer Surplus that would be associated with this price increase. Set
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 now
This is a popular solution!
Step by step
Solved in 5 steps with 5 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.
Recommended textbooks for you
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 (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