THE ACCELERATION PRINCIPLE
Suppose that there is a given ratio between the level of output Y_{t} at any time t, and the capital stock required to produce it K_{t} and that this ratio is equal to α, hence:
K_{t} =αY_{t}
The coefficient is the capital-output ratio, α, = ^{K}/_{Y} and is called the accelerator co-efficient.
If there is an autonomous increase in investment, ?I this through the multiplier process will lead to increased employment resulting in an overall increase in income, ?Y. This may lead to further investment called Induced Investment in the production of goods and services. This process is called acceleration.
The ratio of induced investment to the increase in income resulting from an initial autonomous increase in investment is called the accelerator. Thus, if the included investment is denoted by ?I^{1}, and the accelerator by β, then:
?I^{1}
^{ ---------------- }= β, ΔI^{1} = βΔY
?Y
Thus another way of looking at the accelerator is as the factor by which the increase in income resulting from an initial autonomous increase in investment is multiplied by the induced investment.
From the Keynesian model ?Y = ?1.^{1}/_{s } we c an write
Δ1^{1} = β, Δ1^{1 }.^{1}/_{s }
Thus, the higher the multiplier and the higher the accelerator, the higher will be the level of induced investment from an initial autonomous increase.