Accelerator

The accelerator ( lat. Accelerator "accelerator") is a key figure in economics that expresses the extent to which a certain change in aggregate demand leads to a certain investment volume .

overview

In addition to the multiplier process, the accelerator process is the most important mechanism by which economic impulses can build up. If, for example, consumer demand increases by a certain amount in the economic phase, companies try to increase their production capacities by investing to a certain extent, which is greater the greater the increase in demand. This increases the investment demand, so that the total demand, which is made up of consumer and investment demand, increases again, which in turn triggers a certain investment volume via the accelerator.

The accelerator works accordingly in the downturn. Together with the multiplier, it can lead to business cycle fluctuations within the framework of the Samuelson-Hicks model ( business cycle -theoretical variant of the Harrod-Domar model : multiplier-accelerator model ). Depending on the size of the accelerator and the multiplier it can come to the fact that the economic development

steadily growing
steadily shrinks
oscillates explosively (oscillates around an equilibrium path with ever larger amplitudes )
vibrates at a damped rate (i.e. gradually approaches the equilibrium path)
or in the borderline case has a constant oscillation.

history

The accelerator principle was already described by the economists Albert Aftalion and Arthur Spiethoff .

Roy F. Harrod and Evsey D. Domar believed explosive developments were possible.

Paul A. Samuelson and John Richard Hicks ( multiplier-accelerator model ) provided other Keynesian models .

Investment function with accelerator (discrete time)

Delay by one period: ${\ displaystyle I_ {t} = v \ cdot (Y_ {t-1} -Y_ {t-2})}$

Immediately: ${\ displaystyle I_ {t} = v \ cdot (Y_ {t} -Y_ {t-1})}$

I: investments
Y: production
v: accelerator

The new capital stock is obtained by adding the investments of the current period to the old capital stock at the beginning of the period:

                              $K_{t+1}=K_{t}+I_{t}$

Investment function with accelerator (continuous time)

If one moves from discrete time periods to infinitesimally small time segments, then one obtains the continuous version of the accelerator equation:

                         $I=v\cdot {\dot {Y}}$

The increase in the capital stock is again equal to the investments:

                         ${\dot {K}}=I$

Adjustment to desired capital stock

The accelerator principle can also be interpreted as an investment behavior in which the companies try to bring the actual size of the capital stock K to a desired value. So much is invested that the old capital stock plus the investments in the next period t + 1 is equal to the desired capital stock. Let the desired capital stock be equal to a certain multiple v of production Y, whereby the companies are based on the previous period: ${\ displaystyle K_ {t}}$ ${\ displaystyle I_ {t}}$

Desired capital stock: ${\ displaystyle K_ {t + 1} = v \ cdot Y_ {t}}$

The new capital stock results from the old capital stock plus the investments:

                              $K_{t+1}=K_{t}+I_{t}$

or

${\ displaystyle I_ {t} = K_ {t + 1} -K_ {t} = v \ cdot Y_ {t} -v \ cdot Y_ {t-1} = v \ cdot (Y_ {t} -Y_ {t -1})}$

This corresponds to the accelerator function (without a time delay).

On the basis of such accelerator functions, the investments can be estimated econometrically (see International Monetary Fund 2015, p. 118, footnote 15).

Remarks

↑ denotes the derivative of the variable with respect to time : thus are changing the variables at the time of. ${\ displaystyle {\ dot {X}} _ {t}}$ ${\ displaystyle X}$ ${\ displaystyle t}$ ${\ displaystyle {\ dot {X}} _ {t} = {\ frac {\ mathrm {d} X_ {t}} {\ mathrm {d} t}}}$ ${\ displaystyle {\ dot {X}} _ {t}}$ ${\ displaystyle X}$ ${\ displaystyle t}$

literature

Aiginger Karl: The different concepts of the accelerator - economic meaningfulness and empirical estimation possibilities. ( available online on the WIFO homepage ) In: Empirica. Journal of the Institute for Austrian Economic Research. 1975. page 3ff.
Roy GD Allen: Macroeconomic Theory. A Mathematical Treatment. Macmillan, London et al. 1968.
International Monetary Fund . 2015. World Economic Outlook: Uneven Growth — Short- and Long-Term Factors. Washington (April). P. 118, fn. 16. [1]

[1] tes the derivative of the variable with respect to time : thus are changing the variables at the time of. ${\ displaystyle {\ dot {X}} _ {t}}$ ${\ displaystyle X}$ ${\ displaystyle t}$ ${\ displaystyle {\ dot {X}} _ {t} = {\ frac {\ mathrm {d} X_ {t}} {\ mathrm {d} t}}}$ ${\ displaystyle {\ dot {X}} _ {t}}$ ${\ displaystyle X}$ ${\ displaystyle t}$