Multiplier-accelerator model: Difference between revisions

Revision as of 09:59, 11 June 2015

Revision as of 12:49, 11 June 2015

Line 10:

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" />

:<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" /> 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}^2</math>.<ref name="Mullineux 1984" />

== References ==