Multiplier Effect Vs. Acceleration Effect
The acceleration effect is the phenomenon that a variable moves toward its desired value faster and faster with respect to time. Usually, the variable is the capital stock. In Keynesian models, fixed capital is not in consideration, so the accelerator coefficient becomes the reciprocal of the multiplier and the capital decision degenerates to investment decision. In more general theory, where the capital decision determines the desired level of capital stock (which includes fixed capital and working capital), and the investment decision determines the change of capital stock in a sequences of periods, the acceleration effect emerges as only the current period gap affects the current investment, so do the previous gaps. The Aftalion-Clark accelerator v has such a form, while the Keynesian multiplier m has such a form where c is the propensity to consume.
From the above, it can clearly be seen that the change of investment has a multiplier effect on income, but the point that the increase of income accelerates capital accumulation (the acceleration effect increase over time) can only be shown numerically.
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