The multiplier effect, the cornerstone of Keynesian fiscal policy, states that an increase in autonomous spending (on consumption expenditures, gross private domestic investment, government spending, or net foreign investment) will cause a multiple growth of aggregate demand. Keynesian economists believe that this increase in aggregate demand will cause an equal increase in gross national product, whereas classical economists believe that this increase will only lead to an increase in the price level (inflation).
The multiplier is dependent on the marginal propensity to consume. It is best explained by example. Assuming the marginal propensity to consume (MPC) is 0.8; the marginal propensity to save (MPS) will be 0.2 because MPC+MPS=1. If Bob finds $100 buried in the ground and spends it at the local computer store, the gross national product will have increased by $100 through the new spending. The owner of the computer store will decide to save $20 (0.2*$100) and spend $80 (0.8*$100). The owner spends the $80 at a tailor for a suit. The increase in disposable income by finding $100 has yielded an increase in $180 in gross national product. He will save $16 (0.2*$80) and spend $64 (0.8*$80). Expanding this a few more rounds:
1: $100 ,-> $80 ,-> $64 ,-> $51.2 ,-> $40.96
2: x .8 | x.8 | x.8 | x .8 | x .8
---- | --- | --- | ----- | ------
3: $80 -' $64 -' $51.2 -' $40.96 -' $32.768
1: The input money
2: The MPC
3: The ouput money
This continues ad infinitum. If you add the original $100 to all the outputs, you will get $500:
$100
80
64
51.2
40.96
32.768
26.2144
20.97152
16.777216
13.4217728
10.73741824
+ 42.94967296 == all other rounds
-------------
$500
This $500 is also equal to $100 * (1/0.2) because 0.2 is the MPS and some mathematical stuff I won't explain here. It has to do with the fact that it is the sum of the infinite series $100 * 0.8^x, where x is the set of integers from 0 to positive infinity.