Q.Explain the key difference between the multiplier and the acceleration principle in terms of the direction of causation each describes.

The multiplier runs from a change in investment to a (larger) change in income; the accelerator runs the other way, from a change in output/income to induced investment.

The investment multiplier describes a causal chain that starts with a change in INVESTMENT and ends with a (larger) change in INCOME: an initial rise in investment spending becomes income for its recipients, who spend a fraction (MPC) of it further, generating income for a further round of recipients, and so on — the direction of causation is $\Delta I \rightarrow \Delta Y$, with the size of the eventual income change governed by the multiplier $k=1/(1-MPC)$.

The acceleration principle describes the OPPOSITE causal chain: it starts with a change in OUTPUT (or income/demand) and explains the resulting change in INVESTMENT. Because producing a given level of output requires capital in a roughly fixed proportion (the capital-output ratio), any change in the level of output that firms need to produce forces a corresponding, proportional change in the capital (and hence investment) they must acquire — the direction of causation here is $\Delta Q \rightarrow \Delta I_{\text{induced}}$, governed by the accelerator coefficient $v$. …

A common confusion is treating the multiplier and accelerator as simply "the same idea, applied to investment vs. income" — they are NOT the same mechanism viewed from two angles; they describe genuinely OPPOSITE directions of causation, and mixing up which variable is the CAU …