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2024 PEA Q22

Solow economy with Y=K1/3L2/3Y=K^{1/3}L^{2/3}, no population growth or technological change, δ=0.05\delta=0.05, s=0.2s=0.2. What is the steady-state capital--labour ratio?

Reveal answer and solution

Answer

B

Solution

  1. 1

    Intensive form: y=k1/3y=k^{1/3}. Steady-state condition sf(k∗)=δk∗sf(k^{*})=\delta k^{*}:

  2. 2
    0.2 k1/3=0.05 k ⟹ k2/3=0.20.05=4 ⟹ k∗=43/2=8. 0.2\,k^{1/3}=0.05\,k\ \Longrightarrow\ k^{2/3}=\frac{0.2}{0.05}=4\ \Longrightarrow\ k^{*}=4^{3/2}=8.

Answer structure / marking notes

No major trap beyond standard calculation care.

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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.