The Multiplier Effect

Idea

An injection into the economy raises national income by more than the injection itself, because the income it creates is partly re-spent, creating further income in turn. The multiplier k measures the total expansion relative to the initial injection.

Mechanism

Suppose an injection of government spending or investment ( $\Delta J$ ) enters an economy with excess capacity. The chain runs:

The injection generates income for the firms whose output is first demanded, which raise output and so employ more factors of production.
This creates disposable income for households. They spend a fraction of it on induced consumption — the fraction given by the marginal propensity to consume — and withdraw the rest as saving, taxation and imports, the fraction given by the marginal propensity to withdraw.
That induced consumption is income for firms in other sectors, who again employ resources and pay out income, a fraction of which is spent again.

The rounds of spending and re-spending continue, each smaller than the last, until the increment becomes negligible — formally, until the induced withdrawals have cumulatively risen to match the initial injection ( $\Delta W = \Delta J$ ). Summing the rounds gives the final change in national income:

$\Delta Y = k \times \Delta J, \qquad k = \frac{1}{1 - MPC} = \frac{1}{MPW}$

A larger marginal propensity to consume (a smaller marginal propensity to withdraw) means more is re-spent at each round, so the multiplier is larger.

Diagram

The multiplier effect on the AD–AS diagram. An autonomous injection shifts AD from AD0 to AD1 (the initial impulse); the induced rounds of re-spending carry it on to AD2, a final shift larger than the first, raising real national output from Y0 to Y2.

Considerations

The size of the multiplier turns on the marginal propensity to withdraw, which in turn depends on the marginal propensities to save, to tax and to import. An economy like Singapore has a high MPW — mandatory saving through the Central Provident Fund raises the MPS, and heavy reliance on imports raises the MPM — so its multiplier is small, and a given injection produces a smaller final expansion than in a more closed economy. The effect is also strongest when there is spare capacity; near full employment, the extra demand raises the general price level rather than real output.