MPS is the marginal propensity to save. The multiplier is the ratio of change in real GDP to initial change in spending.
The fractions of an increase in income consumed and saved determine the cumulative spending effects of any initial change in spending and therefore determine the size of the multiplier. The MPC and the multiplier are directly related and the MPS and the multiplier are inversely related. The precise formulas are as shown in the next two equations:
a. When MPS is 0, 0.4, 0.6 and 1, the corresponding multipliers are calculated below:
When MPS is 0.4
When MPS is 0.6
When MPS iS1
When MPC iS1, 0.9, 0.67, 0.5, multiplier is calculated as follows:
When MPC is 0.9, multiplier is calculated as follows:
When MPC is 0.67, multiplier is calculated as follows:
When MPC is 0.5, multiplier is calculated as follows:
When MPC is 0, multiplier is calculated as follows:
Multiplier determines how much GDP will change in accordance with the change in spending, which depends on MPC.
If the MPC is 0.67, the change in GDP is calculated as follows:
During expansion, the investment demand curve shifts to the right, as from ID to ID' in the figure below. This outward shift overwhelmed any investment-decreasing effects of the increase of real interest rates. The net result turned out to be more investment (I to I''), not less (I to I').
The rightward shift of the investment demand reflected an increase in the expected returns from investment. Firms were facing an under-stock of existing capital relative to their current sales. Also firms were optimistic about the economy.
The actual multiplier in the is less than that in the example because income is spent on import and tax payment other than on savings. In the formula for multiplier, the multiplier and MPS are negatively related.
In reality, part of income is spent on import and tax payment, thus the multiplier formula overstates the multiplier. The formula should be restated aS1 over consumption other than domestic expenditure on goods and services.
Besides, spending may be partly dissipated as inflation rather than realized fully as an increase in real GDP.