Multiplier-accelerator model: Difference between revisions

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{{Short description|Economic model}}

The '''multiplier–accelerator model''' (also known as '''Hansen–Samuelson model''') is a [[macroeconomic model]] which analyzes the [[business cycle]].<ref name="Edward 2008">{{Cite book|author=Edward E. Leamer |year=2008 |title=Macroeconomic Patterns and Stories |publisher=Springer Science & Business Media |page=158 |isbn=9783540463894 |url=https://books.google.com/books?id=XObELQuIWv8C&pg=PA158 }}</ref> This model was developed by [[Paul Samuelson]], who credited [[Alvin Hansen]] for the inspiration.<ref name="Edward 2008" /><ref>{{Cite journal|author=Samuelson, P.A.|date=1939|title=Interactions Between the Multiplier Analysis and the Principle of Acceleration |journal=[[Review of Economic Statistics]] |volume=21 |issue=2 |pages=75–78 |ref=harv |doi=10.2307/1927758 |jstor=1927758 }}</ref><ref name="Mullineux 1984" /> This model is based on the Keynesian [[multiplier (economics)|multiplier]], which is a consequence of assuming that consumption intentions depend on the level of economic activity, and the [[Accelerator effect|accelerator theory of investment]], which assumes that investment intentions depend on the pace of growth in economic activity.

== Model ==

{{seealso|Multiplier (economics)#Keynesian and Hansen–Samuelson multipliers}}

The multiplier–accelerator model can be stated for a closed economy as follows:<ref name="Mullineux 1984">{{Cite book|author=A. W. Mullineux |year=1984 |title=The Business Cycle After Keynes: A Contemporary Analysis |publisher=Rowman & Littlefield |page=11 |isbn=9780389204534 |url=https://books.google.com/books?id=237spXDRlwYC&pg=PA10 }}</ref> First, the market-clearing level of economic activity is defined as that at which production exactly matches the total of government spending intentions, households' consumption intentions and firms' investing intentions.

:<math>Y_{t} = g_{t} + C_{t} + I_{t}</math>;

then an equation to express the idea that households' consumption intentions depend upon some measure of economic activity, possibly with a lag:

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and finally a statement that government spending intentions are not influenced by any of the other variables in the model. For example, the level of government spending could be used as the unit of account:

:<math>g_{t} = 1</math>

where <math>Y_{t}</math> is national income, <math>g_{t}</math> is government expenditure, <math>C_{t}</math> is consumption expenditure, <math>I_{t}</math> is induced private investment, and the subscript <math>t</math> is time. Here we can rearrange these equations and rewrite them as a second-order linear [[difference equation]]:<ref name="Mullineux 1984" /><ref name="Goldberg1958">{{cite book |last=Goldberg |first=Samuel |title=Introduction to Difference Equations |url=https://archive.org/details/introductiontodi00gold_0 |url-access=registration |___location=New York |publisher=John Wiley & Sons |year=1958 |pages=[https://archive.org/details/introductiontodi00gold_0/page/153 153–56] }}</ref><ref>{{cite book |first=Giancarlo |last=Gandolfo |authorlinkauthor-link=Giancarlo Gandolfo |title=Economic Dynamics |___location=Berlin |publisher=Springer |edition=Third |year=1996 |chapter=Second-order Difference Equations in Economic Models |pages=71–81 |chapterurlisbn=9783540627609 |chapter-url=https://books.google.com/books?id=ZMwXi67nhHQC&pg=PA71 }}</ref>

:<math>Y_{t} = 1 + \alpha (1+ \beta)Y_{t-1} - \alpha \beta Y_{t-2}</math>

Samuelson demonstrated that there are several kinds of solution path for national income to be derived from this second order linear difference equation.<ref name="Mullineux 1984" /><ref name="Goldberg1958" /> This solution path changes its form, depending on the values of the roots of the equation or the relationships between the parameter <math>\alpha</math> and <math>\beta</math>.<ref name="Mullineux 1984" /><ref name="Goldberg1958" />

== Criticism ==

[[Jay Wright Forrester]] argues<ref>{{cite journal |doi=10.1002/sdr.1490 |title=Economic theory for the new millennium |author=Jay W. Forrester |date=2003}}</ref> that the Accelerator-Multiplier Theory cannot create the assumed business cycle but instead is a major contributor to the economic [[Kondratiev_wave|long wave]].

== References ==

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== Further reading ==

* {{cite book |first=E. C. |last=Bratt |title=Business Cycles and Forecasting |___location=Homewood |publisher=Irwin |edition=Fifth |year=1961 |chapter=Multiplier-Accelerator Models |pages=188–211 |chapterurlchapter-url=https://books.google.com/books?id=7pheNrBNeKUC&pg=PA188 }}

* {{cite book |first=J. A. |last=Estey |title=Business Cycles: Their Nature, Cause, and Control |___location=Englewood Cliffs |publisher=Prentice-Hall |edition=Third |year=1956 |chapter=The Multiplier-Accelerator Interaction |pages=275–287 |chapterurlchapter-url=https://books.google.com/books?id=qTBZAAAAYAAJ&pg=PA275 }}

* {{cite book |first=W. J. |last=Fellner |authorlinkauthor-link=William Fellner |title=Trends and Cycles in Economic Activity |___location=New York |publisher=Henry Holt |year=1956 |pages=308–338 |url=https://books.google.com/books?id=9LW3AAAAIAAJ&pg=PA308 }}

[[Category:Business cycle theories]]

[[Category:Keynesian economics]]