The Acceleration Principle

While the multiplier explains how a change in INVESTMENT causes a (larger) change in INCOME, the acceleration principle explains the REVERSE causal direction: how a change in the level of OUTPUT (or income/demand) induces a change in the volume of INVESTMENT.

The logic is straightforward: producing a given level of output requires a certain amount of capital (machinery, equipment) in a roughly fixed proportion — the capital-output ratio. If output needs to RISE, firms must acquire ADDITIONAL capital in proportion to that increase (this additional capital acquisition IS induced investment, referred to earlier). Formally, if $v$ is the capital-output ratio (the "accelerator coefficient"), then the induced investment required for a given change in output $\Delta Q$ is:

A key feature of the acceleration principle is that induced investment depends on the CHANGE (the rate of increase) in output, not on the absolute LEVEL of output itself — this is precisely why even a SLOWDOWN in the rate of growth of output (output still rising, just more slowly than before) can cause induced investment to FALL, well before output itself ever actually declines, a phenomenon often cited to help explain the sharpness of swings in investment spending over the business cycle. …