PEA 2025 PEA Q30 | ISI MSQE

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2025 PEA Q30

Two consumers, same preferences, same endowments. Strictly convex preferences. Then the economy has:

Reveal answer and solution

Answer

Solution

1
With identical preferences and identical endowments, the no-trade allocation is the unique competitive equilibrium: at any candidate price, the symmetric demand of each agent equals the endowment (any common excess demand would require an equal opposite supply, impossible with identical agents). Strict convexity guarantees uniqueness of demand at any price, hence the equilibrium allocation is unique. (The set of Pareto-efficient allocations is a continuum --- the contract curve --- so (C) is false; (A) is clearly false; (B) is false because the symmetric equilibrium is unique.)

Answer structure / marking notes

Unique CE'' should not be confused with unique Pareto-efficient allocation'': the contract curve is large, but only the symmetric no-trade point is supported as an equilibrium here.

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Review Flags

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The following questions involve subtleties that the candidate should be aware of, although the final answers are verified:

\begin{itemize}[leftmargin=*]

Q1: The production function $Y=KN$ as printed yields a degenerate steady state under the standard $\dot K = sY - \delta K$ law. The intended intensive-form interpretation ( $\bar k = s^2/\delta^2$ , $\bar y = s/\delta$ ) matches option (C).
Q4--Q5: Exact numerical multiplier depends on the consumption MPC, which is taken as the canonical $0.5$ from the Blanchard two-country model. Answers (B) and (D) match the textbook calibration.
Q12: The question asks which independence claim is false. Statement (B), $A \perp G$ , is false because $G \subseteq A$ .
Q26: The tie-breaking under lexicographic preferences at $p_a = p_b$ requires careful handling --- statement III fails at the boundary.
Q29: Under a literal reading with $p_x = p_y$ , the boundary optimum gives $x = 0$ . The conventional answer matches the interior interpretation (C). \end{itemize}

Content note

Imported from public/resources/isi/msqe/solutions/pea/2025/ISI_MSQE_PEA_2025_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.