PEA 2024 PEA Q21 | ISI MSQE

PEAMCQModerate

2024 PEA Q21

Consider an economy with $y=Ak$ (per-capita form), saving rate $s\in(0,1)$ , population growth rate $n>0$ and depreciation rate $\delta\in(0,1)$ . Assume parameters ensure positive long-run growth of $y$ . Which of the following is incorrect?

Reveal answer and solution

Answer

Solution

1
With $y=Ak$ , capital--labour accumulation gives
2
$\dot k = sy - (n+\delta)k = sAk - (n+\delta)k\ \Longrightarrow\ \frac{\dot k}{k}=sA-(n+\delta).$
3
A: matches the growth rate of $k$ . True.
4
B: $I>\delta K\Rightarrow\dot K=I-\delta K>0$ , hence $K$ and $Y=AK$ grow. True.
5
C: Because $\dot k/k$ is a constant (independent of $k$ ), every variable grows at a constant rate at all times --- the economy is permanently on its balanced growth path. True.
6
D: The growth rate of $y$ equals $\dot k/k=sA-(n+\delta)$ , which is strictly increasing in $s$ . Hence raising $s$ does affect the long-run growth rate. Incorrect.

Answer structure / marking notes

The AK model differs from Solow: $s$ does permanently affect growth.

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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.