The accelerator (lat. "“Accelerator"”) is an index, which expresses, in which measure a certain change of the overall economic demand to a certain investment volume leads.

The accelerator process is apart from the multiplicator process the most important mechanism, by which it can come to a Aufschaukeln of economic impulses. Increases itself for example in upward pulse phase consumer demand around certain amount, to increase try enterprises their production capacities, by it in certain extent invest, which is the larger, the failed more largely the Thereby the investment demand rises so that the total demand, which consists of consumer and investment demand, rises again, which releases a certain investment volume by accelerator again.

The accelerator works however accordingly in the wing over. Together with the multiplicator it can in the context of the Samuelson Hicks model (economic situation-theoretical variant of the Harrod Domar model: Multiplicator accelerator model) to business fluctuations lead. Depending upon size of the accelerator and the multiplicator it can come to the fact that the economic development

• constantly grows
• constantly shrinks
• explosively swings (around an equilibrium path swings with ever larger amplitudes)
• absorbed swings (thus gradually the equilibrium path approximates)
• or in the border line a constant oscillation exhibits.

Investment function with accelerator (discrete time):

Delay around one period: I_t = v \ cdot (Y_ {T-1} - Y_ {t-2})

Instantaneously: I_t = v \ cdot (Y_ {t} - Y_ {T-1})

• I: Investments
• Y: Production
• v: Accelerator

The new capital stick results in the case of by adding the old capital stick at the beginning of the period the investments of the current period:

                             K_ {t+1} = K_ {t} + I_t 

Investment function with accelerator (constant time):

If one turns into from discrete time periods on infinitesimally small time periods, then one receives the constant version of the accelerator equation:

                        I = v \ \ DOT Y cdot 

The increase of the capital stick is thereby again equal to the investments:

                        \ DOT K = I 

Adjustment at desired capital stick:

The accelerator principle can be also interpreted as an investment behavior, with which the enterprises try to advance the actual extent of the capital stick K to a desired value. It is as much invested that the old capital stick is K_t plus the investments I_t in the next period t+1 equal to the desired capital stick. The desired capital stick is equal a certain multiples v of production Y, whereby the enterprises orient themselves on the preliminary period:

Desired capital stick: K_ {t+1} = v \ cdot Y_ {t}

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

                             K_ {t+1} = K_ {t} + I_t 

or

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 temporal delay).

History

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

Roy F. Harrod and Evsey D. Domar considered even explosive developments possible.

Further keynesianisch coined/shaped models supplied Paul A. Samuelson and John R. Hicks (multiplicator accelerator model).

Literature

• Everything, R.G.D.: Macro Economic Theory: A Mathematical Treatment. - London, Melbourne, Toronto: Macmillan, 1968.

Articles in category "Accelerator"

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