Question
Can the value of APS be negative? If yes, when.

Answer

Yes, the value of APS can be negative, at very low level of income when consumption expenditure exceeds income, e.g., at an income level of ₹ 200, when the consumption expenditure is ₹ 240, the saving is (-) 40.
So, $\text{APS}=\frac{\text{S}}{\text{Y}}=\frac{-40}{200}=-0.2$

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