Multiplier-accelerator model

The Multiplier–accelerator model is a macroeconomic model which explains what might cause cycles. This model was developed by Paul Samuelson in Samuelson, P.A. (1939). This model is based on Keynesian multiplier and accelerator theory of investment.

Model

See also: Multiplier (economics) § Keynesian and Hansen-Samuelson multipliers

The multiplier–accelerator model can be stated as follows:

$Y_{t}=g_{t}+C_{t}+I_{t}$

$C_{t}=\alpha Y_{t-1}$

$I_{t}=\beta \mid C_{t}-C_{t-1}\mid$

$g_{t}=1$

where $Y_{t}$ is national income, $g_{t}$ is government expenditure, $C_{t}$ is consumption expenditure, $I_{t}$ is induced private investment, and the subscript $t$ is time. Here we can rearrange these equations and rewrite them as a second order linear difference equation:

$Y_{t}=1+\alpha (1+\beta )Y_{t-1}-\alpha \beta Y_{t-2}$

Samuelson demonstrated that there are several kinds of solution path for national income to be derived from this second order linear difference equation. This solution path changes its form, depending on the values of the roots of the equation or the relationships between the parameter $\alpha$ and $\beta$.

References

• Samuelson, P.A. (1939). "Interactions between the multiplier analysis and the principle of acceleration". Review of Economic Statistics 21: 75–78. {{cite journal}}: Invalid |ref=harv (help)