Multiplier-accelerator model: Difference between revisions

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

:<math>C_{t} = \alpha Y_{t-1} </math>;

Thenthen an equation that makes firms' investment intentions react to the pace of change of economic activity:

:<math>I_{t} = \beta \mid [ C_{t} - C_{t-1} ] \mid </math>;

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 |___location=New York |publisher=John Wiley & Sons |year=1958 |pages=153–56 }}</ref><ref>{{cite book |first=Giancarlo |last=Gandolfo |authorlink=Giancarlo Gandolfo |title=Economic Dynamics |___location=Berlin |publisher=Springer |edition=Third |year=1996 |chapter=Second-order Difference Equations in Economic Models |pages=71–81 |chapterurl=https://books.google.com/books?id=ZMwXi67nhHQC&pg=PA71 }}</ref>