The Multiplier:

Determining the Size of the Multiplier:

Presume something happens to change the level of planned expenditure at every possible level of total income. Something that affects the level of autonomous spending will do. What would take place to the equilibrium level of total income and real GDP?

An upward shift in the planned spending line would increase the equilibrium level of total income. At the prevailing stage of national income, planned spending would be larger than real GDP. Businesses would discover themselves selling more than they were making and their inventories would drop. In response businesses would increase production to try to keep inventories from being exhausted and production would expand. How much production would increase depends on the magnitude of the change in autonomous spending and the value of the multiplier.

To compute the multiplier recall the simplified equation for planned expenditure:

E = A + MPE x Y

And the equilibrium condition:

Y = E
     
Substitute the second into the first as well as solve for Y:

Y = A/(1 - MPE)
     
Therefore if autonomous spending changes by an amount ΔA equilibrium real GDP changes by:

ΔY = 1/(1 - MPE) x ΔA
     
And if we feel like to express the denominator of this fraction in terms of the basic parameters of the model it is:

This factor 1/(1-MPE) = 1/(1-(Cy(1-t)-IM_y)) is the multiplier- it multiplies the upward shift in the planned spending line as a result of the raise in autonomous spending into a change in the equilibrium level of total income real, GDP and aggregate demand.

Why the factor 1/(1-MPE)? Imagine of it this way. The MPE -- the marginal tendency to expend -- is the slope of the planned expenditure line. A $1 raise in national income raises the equilibrium level of planned expenditure by $1 for the reason that expenditure has to go $1 higher to balance income and production. Above figure shows that it as well raises the level of planned expenditure by $MPE. Therefore a $1 increase in the level of total income closes $(1-MPE) of the gap between planned expenditure and total income. To close a complete initial gap of $ΔA between planned expenditure and national income the equilibrium level of national income must increase by ΔA/(1-MPE).

For the reason that autonomous spending is influenced by a great many factors:

Almost every change in economic policy or the economic environment will set the multiplier process in motion.

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