Formulae to establish the Multiplier

In a closed economy, all monies spent are received by fellow citizens, therefore there is no "leakage" of funds from the economy to other economies.


The formula for calculating the Multiplier in a closed economy is

1 ÷ MPS

where MPS is the Marginal Propensity to Save.

Likewise, if the MPC is 0.5, so also is the MPS

The formula for calculating the Multiplier in an open economy is

1 ÷ (MPS + MPM)

Once again, assume MPC = 0.8 (therefore MPS = 0.2).   The national norm in Ireland has been to spend approximately 40% of all extra income on imports.  This would give us, historically, an MPM of 40% or 0.4

Applying these figures, the formula becomes

1 ÷ (.2 + .4) = 1 ÷ .6 = 1.666...

Multiplier = 1.666...

Payment for Imports have an even more dramatic diminishing effect on the multiplier if we have a lesser Marginal Propensity to Consume.

If we have an MPC of 50%, then we also have an MPS of 50%, so our Multiplier Formula for an Open Economy would now be

1 ÷ (.5 + .4) = 1 ÷ .9 = 1.1111 ...

Multiplier = 1.111 ...

An injection now of 1,000 Euro would only yield 1,111 Euro by the time it works its way through the economy.


The Paradox of Thrift is still evident.  The more we save the less well off the economy is, while the more we spend the wealthier it is.


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