PEA 2026 PEA Q28 | ISI MSQE

PEAMCQModerate

2026 PEA Q28

Solow economy with $Y = K^{1/2} L^{1/2}$ , no depreciation, $n = 0.02$ , savings rate $s > 0$ . If the steady-state capital--labour ratio is $k^* = 9$ and the current ratio is $k = 1$ , then the growth rate of $y = Y/L$ at the current date is

Reveal answer and solution

Answer

Solution

1
Per-worker output is $y = k^{1/2}$ . The Solow law of motion (with no depreciation) is
2
$\dot k = s\,k^{1/2} - n\,k.$
3
Steady state: $s\,(k^*)^{1/2} = n\,k^* \Rightarrow s = n\,(k^*)^{1/2} = 0.02 \cdot 3 = 0.06$ .
4
Current growth rate of $k$ :
5
$\frac{\dot k}{k} = \frac{s}{\sqrt k} - n = \frac{0.06}{1} - 0.02 = 0.04.$
6
Since $y = k^{1/2}$ ,
7
$\frac{\dot y}{y} = \tfrac{1}{2}\cdot \frac{\dot k}{k} = \tfrac{1}{2}\cdot 0.04 = 0.02.$

Answer structure / marking notes

Don't forget the factor $1/2$ when converting from the growth rate of $k$ to that of $y = k^{1/2}$ .

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2026/ISI_MSQE_PEA_2026_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.