The multiplier–accelerator model (also known as Hansen–Samuelson model) is a macroeconomic model which analyzes the business cycle.[1] This model was developed by Paul Samuelson, who credited Alvin Hansen for the inspiration.[1][2][3] This model is based on the Keynesian multiplier and the accelerator theory of investment.
Model
The multiplier–accelerator model can be stated as follows:[3]
where is national income, is government expenditure, is consumption expenditure, is induced private investment, and the subscript is time. Here we can rearrange these equations and rewrite them as a second order linear difference equation:[3][4]
Samuelson demonstrated that there are several kinds of solution path for national income to be derived from this second order linear difference equation.[3][4] This solution path changes its form, depending on the values of the roots of the equation or the relationships between the parameter and .[3][4]
References
- ^ a b Edward E. Leamer (2008). Macroeconomic Patterns and Stories. Springer Science & Business Media. p. 158.
- ^ Samuelson, P.A. (1939). "Interactions Between the Multiplier Analysis and the Principle of Acceleration". Review of Economic Statistics. 21 (2): 75–78. doi:10.2307/1927758.
{{cite journal}}: Invalid|ref=harv(help) - ^ a b c d e A. W. Mullineux (1984). The Business Cycle After Keynes: A Contemporary Analysis. Rowman & Littlefield. p. 11.
- ^ a b c Goldberg, Samuel (1958). Introduction to Difference Equations. New York: John Wiley & Sons. pp. 153–56.
Further reading
- Fellner, W. J. (1956). Trends and Cycles in Economic Activity. New York: Henry Holt. pp. 308–338.