3.6.4 Keynesian multiplier (HL only) Notes

1. Imagine that an initial increase in C, I, G or (X-M), lead to an increase in Aggregate Demand, and hence an increase in real output (GDP).
2. Even though it is easy to assume that the increase in real output will be proportional to the increase in the initial injection, in reality, the total increase in real output will be higher (The reasoning is discussed further below).
3. The reason behind this is the Keynesian Multiplier, which is calculated by:
   1. $\text{Multiplier} =\frac{\text{Change in Real GDP}}{\text{Initial Change in Expenditure}}$
   2. $\text{Change in Real GDP} = \text{Multiplier} \times \text{Initial Change in Expenditure}$

Marginal Propensities

1. The Keynesian multiplier is influenced by the consumer spending, in specifics, the marginal propensities in the economy. We can use these marginal propensities to calculate the multiplier as well.
2. Marginal Propensities are the tendencies for consumers to allocate additional income for a certain purpose.
   1. Marginal Propensity to Consume (MPC): The fraction of additional income that is spent on consumption.
   2. Marginal Propensity to Save (MPS): The fraction of additional income that is saved.
   3. Marginal Propensity to Tax (MPT): The fraction of additional income that is paid in taxes.
   4. Marginal Propensity to Import (MPM): The fraction of additional income that is spent on imports.
3. The propensities are all related such that: $\text{MPC}+\text{MPS}+\text{MPT}+\text{MPM}=1$

Calculating the Keynesian Multiplier

1. Therefore, the Keynesian multiplier can be calculated using these formulas:
   1. $\text{Multiplier} = \frac{1}{\text{MPC}}$
   2. $\text{Multiplier}= \frac{1}{(\text{MPS}+\text{MPT}+\text{MPM})}$

The Effects of Multiplier on Aggregate Demand

Discussed before, the total change in real output will be higher than the initial investments.

The diagram below illustrates the Keynesian multiplier effect:

1. The initial injection shifts the aggregate demand curve from $AD_1$ to $AD_2$.
   1. This is called autonomous spending, which is equal to the initial spending.
   2. The multiplier effect causes further shifts in the aggregate demand curve, eventually reaching $AD_3$.
      1. This is called induced spending.
   3. Therefore, the final increase in real GDP is greater than the initial injection.
      1. $\text{Total Effect} = \text{Autonomous spending} + \text{Induced Spending}$
2. Further, in order to enjoy the effects of the multiplier effect to its full extent, the price level needs to stay constant.
3. This can be analysed by observing at Keynesian model.

1. In the diagram above, the following can be observed:
   1. The horizontal distances between each AD curves are equivalent.
   2. The shift from $AD_1 to AD_2$, occurs without a price increase, hence indicating the multiplier effect is at its fullest.
   3. This results in the change in real output to be equal to the change in AD.
   4. However, the shift from $AD_2$ to $AD_3$, causes a price increase ($PL_1→PL_2$), and the increase in real output is smaller ($Y_3-Y_2<Y_2-Y_1$)
   5. The shift from $AD_3$ to $AD_4$ happens in the vertical part of the AS curve, where there is no increase in real output, but the price level increases to $PL_3$.
   6. At this point, the multiplier effect is fully absorbed by the price increase.