PEA 2024 PEA Q25 | ISI MSQE

PEAMCQModerate

2024 PEA Q25

Two countries $A$ and $B$ produce wheat and television respectively, with $Y_A=200$ and $Y_B=250$ . The TV price is normalised to $1$ , the relative price of wheat is $p$ . Let $E_A$ (in wheat units) and $E_B$ (in TV units) denote total expenditures. The income identity is $pY_A+Y_B=pE_A+E_B$ . Initially $E_A=100$ ; $A$ reduces $E_A$ to $70$ . Suppose $1/3$ of each country's expenditure is on wheat. What happens to the equilibrium $p$ ?

Reveal answer and solution

Answer

Solution

1
Country $A$ 's total expenditure in TV units is $pE_A$ ; spending $1/3$ on wheat yields wheat demand $\dfrac{pE_A/3}{p}=\dfrac{E_A}{3}$ . Country $B$ 's wheat demand is $\dfrac{E_B/3}{p}$ . World wheat market clearing:
2
$\frac{E_A}{3}+\frac{E_B}{3p}=Y_A=200. \quad (\star)$
3
Combined with the income identity $200p+250=pE_A+E_B$ , we can solve:
4
Before ( $E_A=100$ ): $(\star)\Rightarrow E_B=3p(200-100/3)=p(600-100)=500p$ . Income identity: $200p+250=100p+500p=600p\Rightarrow p=\dfrac{250}{400}=\dfrac{5}{8}$ .
5
After ( $E_A=70$ ): $(\star)\Rightarrow E_B=3p(200-70/3)=p(600-70)=530p$ . Income identity: $200p+250=70p+530p=600p\Rightarrow p=\dfrac{5}{8}$ .
6
The relative price is unchanged. This is the classical neutrality of transfers result: when both countries have identical homothetic preferences (here Cobb--Douglas shares), a transfer or change in expenditure between them does not affect the terms of trade.

Answer structure / marking notes

With identical expenditure shares across countries, the transfer problem becomes neutral.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2024/ISI_MSQE_PEA_2024_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.