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PEAMCQModerate

2022 PEA Q12

mm identical firms with C(q)=q2+1C(q) = q^2 + 1. Industry demand D(P)=a−bPD(P) = a - bP, a,b>0a,b > 0. Short-run equilibrium output per firm?

Reveal answer and solution

Answer

B

Solution

  1. 1

    Firm's MC: C′(q)=2qC'(q) = 2q, so the supply per firm is q=P/2q = P/2 and aggregate supply

  2. 2

    S(P)=mP/2S(P) = mP/2.

  3. 3

    Setting D=SD = S:

  4. 4
    a−bP=mP2⟹P=2am+2b. a - bP = \frac{mP}{2} \quad \Longrightarrow \quad P = \frac{2a}{m + 2b}.
  5. 5

    Therefore,

  6. 6
    q∗=P2=am+2b. q^* = \frac{P}{2} = \frac{a}{m + 2b}.

Answer structure / marking notes

Use P=MCP = MC for each firm and equate aggregate supply with demand.

Content note

Imported from public/resources/isi/msqe/solutions/pea/2022/ISI_MSQE_PEA_2022_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.