PEA 2026 PEA Q25 | ISI MSQE

PEAMCQModerate

2026 PEA Q25

Two countries $H$ and $F$ produce single goods with outputs $Y_H, Y_F$ . Take $H$ 's good as numeraire and $p$ as the relative price of $F$ 's good. Consumers in country $i$ spend a fraction $1/4$ of their expenditure on the foreign good. $E_i$ denotes total expenditure of country $i$ measured in its own good. Given $Y_H = 120$ , $Y_F = 100$ , $E_H = 80$ and market clearing with $Y_H + p Y_F = E_H + p E_F$ , find $p$ .

Reveal answer and solution

Answer

Solution

1
By the Cobb--Douglas expenditure shares, each country spends $3/4$ on its own good and $1/4$ on the foreign good.
2
Market clearing for $H$ 's good (measured in units of $H$ 's good).
3
Demand by $H$ -consumers: $\tfrac{3}{4} E_H = \tfrac{3}{4}\cdot 80 = 60$ .
4
Demand by $F$ -consumers: a fraction $1/4$ of their total expenditure $p\,E_F$
5
expressed in $H$ -units, i.e.\ $\tfrac{1}{4}\,p\,E_F$ .
6
Total demand equals supply $Y_H$ :
7
$60 + \tfrac{1}{4}\,p\,E_F \;=\; 120 \quad\Longrightarrow\quad p\,E_F = 240.$
8
Budget identity. Total income $=$ total expenditure (in the same units):
9
$Y_H + p\,Y_F \;=\; E_H + p\,E_F \quad\Longrightarrow\quad 120 + 100 p \;=\; 80 + 240 \;=\; 320.$
10
Thus $100 p = 200$ , hence $p = 2$ .

Answer structure / marking notes

Keeping the units straight (own good vs.\ numeraire) is the only delicate step.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2026/ISI_MSQE_PEA_2026_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.