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 PN = $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)=zPC The expenditure minimization problem yields his compensated (Hicksian) demand for croissants, his compensated (Hicksian) demand for the numeraire good, and his expenditure function: 1/2 Hc = U (PN) ² 1/2 Hy = U (Pc) ¹ No need to derive th for the assignment, I you can solve for the
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 PN = $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)=zPC The expenditure minimization problem yields his compensated (Hicksian) demand for croissants, his compensated (Hicksian) demand for the numeraire good, and his expenditure function: 1/2 Hc = U (PN) ² 1/2 Hy = U (Pc) ¹ No need to derive th for the assignment, I you can solve for the
Chapter10: Consumer Choice Theory
Section: Chapter Questions
Problem 9P
Related questions
Question
![1. 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)
demand for the numeraire good, and his expenditure function:
2PC
Hc = U
C.
1/2
HN = U
(PN) ²
1/2
= 0 (Pc) ¹/²
E (PC, PN,U)= Pc* Hc + PN * HN = 2Ū(Pc * PN)¹/2
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 up the integral that you would use to calculate the loss (no need to
actually solve for the area).
Now redraw your graph from part (b) and add the compensated demand function for boxes of croissants.
Denote both CV and ACS on the graph Identify the difference between CV and ACS and clearly label it.
d. What factor causes the divergence between CV and ACS to be large or small? Is the divergence between the
two significant in this situation? Support your answer with, at most, two sentences and the numerical values
of the elasticity version of the Slutsky equation (ε = ɛ* — §0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad5f8718-b822-43a6-888a-6d9b997f8030%2F26b6e16a-8f20-41e5-a75a-c7fee6dd12f9%2Flduyo2e_processed.png&w=3840&q=75)
Transcribed Image Text:1. 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)
demand for the numeraire good, and his expenditure function:
2PC
Hc = U
C.
1/2
HN = U
(PN) ²
1/2
= 0 (Pc) ¹/²
E (PC, PN,U)= Pc* Hc + PN * HN = 2Ū(Pc * PN)¹/2
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 up the integral that you would use to calculate the loss (no need to
actually solve for the area).
Now redraw your graph from part (b) and add the compensated demand function for boxes of croissants.
Denote both CV and ACS on the graph Identify the difference between CV and ACS and clearly label it.
d. What factor causes the divergence between CV and ACS to be large or small? Is the divergence between the
two significant in this situation? Support your answer with, at most, two sentences and the numerical values
of the elasticity version of the Slutsky equation (ε = ɛ* — §0).
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