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2023 PEA Q11

Y=KˉαL1−αY=\bar K^\alpha L^{1-\alpha}, 0<α<10<\alpha<1. Perfectly competitive. Find LdL^d as a function of real wage W/PW/P.

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

C

Solution

  1. 1

    Profit max ⇒\Rightarrow WP=MPL=(1−α)KˉαL−α\dfrac{W}{P}=MPL=(1-\alpha)\bar K^\alpha L^{-\alpha}. Solve for LL:

  2. 2
    Lα=(1−α)Kˉα(WP)−1  ⟹  Ld=Kˉ (1−α)1/α(WP)−1/α. L^\alpha=(1-\alpha)\bar K^\alpha\Bigl(\tfrac{W}{P}\Bigr)^{-1} \;\Longrightarrow\; L^d=\bar K\,(1-\alpha)^{1/\alpha}\Bigl(\tfrac{W}{P}\Bigr)^{-1/\alpha}.

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.