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:

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**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
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
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