12.3 The Government Purchases (Spending) Multiplier

Recall from Chapter 8 that government spending on goods and services, [latex]G[/latex], is an autonomous expenditure. This increase in autonomous spending is directly added to the Aggregate demand ([latex]AD[/latex]) equation and increases real GDP. Such increases in autonomous spending bring increases in induced expenditure because government investment spending is spent and re-spent. Therefore, spending in successive rounds will result in further increases in real GDP through additional induced expenditure, and the overall effect on GDP will likely be much greater than the initial Government spending. This is the multiplier effect.

The multiplier effect is a series of increases in induced consumption expenditure from an initial increase in autonomous spending. This increase in consumption spending comes from an increase in [latex]G[/latex].

The increase in real GDP over successive rounds is determined using the following multiplier formula:

[latex]\begin{align*}\text{Multiplier}=\frac{1}{(1-MPC)}\end{align*}[/latex]

Suppose the [latex]MPC=75\%[/latex], therefore, the multiplier is:

[latex]\begin{align*}\frac{1}{(1 - 0.75)}=\frac{1}{0.25}=4\end{align*}[/latex]

This implies a dollar increase in [latex]G[/latex] increases GDP by [latex]\$4[/latex].

The multiplier can also be calculated as:

[latex]\begin{align*}\frac{\text{Change in real GDP}}{\text{Change in}\;G}\end{align*}[/latex]

Suppose a government increase in [latex]G[/latex] by [latex]\$100\;\text{billion}[/latex] (expansionary fiscal policy) increases real GDP by [latex]\$400\;\text{billion}[/latex], the multiplier is:

[latex]\begin{align*}\frac{\$400\;\text{billion}}{$100\;\text{billion}}=4\end{align*}[/latex]

which implies a dollar increase in [latex]G[/latex] increases real GDP by [latex]\$4[/latex].