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PEAMCQModerate Needs review

2023 PEA Q8

Unit mass of consumers, valuation θ∼F\theta\sim F on [θ‾,θ‾][\underline\theta,\overline\theta]. Each buys 11 unit iff θ≥p\theta\ge p. Inverse demand p(q)p(q). Find p′(q)p'(q).

The available source text does not include a full option block for this item, so the question is marked needsReview.
Reveal answer and solution

Answer

B

Solution

  1. 1

    Aggregate demand at price pp: q=1−F(p)q=1-F(p), i.e.\ F(p(q))=1−qF(p(q))=1-q. Differentiating w.r.t.\ qq:

  2. 2
    F′(p(q))⋅p′(q)=−1  ⟹  p′(q)=−1F′(p(q)). F'\bigl(p(q)\bigr)\cdot p'(q)=-1 \;\Longrightarrow\; p'(q)=-\frac{1}{F'(p(q))}.

Answer structure / marking notes

Needs review: source TeX does not provide a full four-option MCQ block.

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.