PEA 2023 PEA Q1 | ISI MSQE

PEAMCQModerate

2023 PEA Q1

A consumer's budgetary allocation for two commodities $x$ and $y$ is $m$ . Her demand for $x$ is

x(p_x,p_y,m)=\frac{2m}{5p_x}.

Initially $m=1000$ , $p_y=20$ , $p_x=5$ . The price of $x$ falls from $5$ to $4$ . The substitution effect of the price change is:

Reveal answer and solution

Answer

Solution

1
Original demand: $x^0=\dfrac{2(1000)}{5\cdot 5}=80$ , with $y^0=\dfrac{3m}{5p_y}=\dfrac{3000}{100}=30$
2
(since the Cobb--Douglas-like demands sum to $m$ : shares $2/5$ and $3/5$ ).
3
Slutsky compensation. To isolate the substitution effect we keep the original bundle affordable at the new prices. Required compensated income:
4
$m'=p_x^{\text{new}}x^0+p_y y^0=4(80)+20(30)=320+600=920.$
5
Compensated demand for $x$ :
6
$x^{s}=\frac{2 m'}{5 p_x^{\text{new}}}=\frac{2(920)}{5(4)}=\frac{1840}{20}=92.$
7
So the substitution effect moves demand from $80$ to $92$ .

Answer structure / marking notes

Option (C) ``80 to 90'' arises from Hicksian compensation done incorrectly. Slutsky compensation (holding the original bundle feasible) is the standard convention in ISI PEA and yields 92.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2023/ISI_MSQE_PEA_2023_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.