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) = C/N 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: Y 2PC ¹/2 Hc = 0 (PN)" 1/2 H₂ = U (PC) HN E (Pc, PN,U) = Pc * Hc + PN * Hn = 2Ū(Pc * PN)¹/2 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
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) = C/N 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: Y 2PC ¹/2 Hc = 0 (PN)" 1/2 H₂ = U (PC) HN E (Pc, PN,U) = Pc * Hc + PN * Hn = 2Ū(Pc * PN)¹/2 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
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Please explain in detail part a to d.
![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 PN = $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:
\[
H_C = \bar{U} \left( \frac{P_N}{P_C} \right)^{1/2}
\]
\[
H_N = \bar{U} \left( \frac{P_C}{P_N} \right)^{1/2}
\]
\[
E(P_C, P_N, \bar{U}) = P_C * H_C + P_N * H_N = 2\bar{U}(P_C * P_N)^{1/2}
\]
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).
c. Now redraw your graph from part (b) and add the compensated demand function for boxes of croissants. Denote both CV and ΔCS on the graph. Identify the difference between CV and ΔCS and clearly label it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6850447-b244-442b-b92c-69f25b6856c2%2Fb1bb82e7-1546-4b41-a601-ded1c51133e5%2Ftj5v1b_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 PN = $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:
\[
H_C = \bar{U} \left( \frac{P_N}{P_C} \right)^{1/2}
\]
\[
H_N = \bar{U} \left( \frac{P_C}{P_N} \right)^{1/2}
\]
\[
E(P_C, P_N, \bar{U}) = P_C * H_C + P_N * H_N = 2\bar{U}(P_C * P_N)^{1/2}
\]
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).
c. Now redraw your graph from part (b) and add the compensated demand function for boxes of croissants. Denote both CV and ΔCS on the graph. Identify the difference between CV and ΔCS and clearly label it.
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