The expenditure multiplier and national income (QCE Economics Unit 2)

What this dot point is asking

QCAA wants you to explain why an initial change in spending (an injection) produces a larger eventual change in national income, define the marginal propensities to consume and save, derive and apply the multiplier formula, and connect the size of the multiplier to the leakages in the economy. Expect a calculation plus an explanation in IA1 or the EA.

The answer

The idea behind the multiplier

The circular flow shows that one person's spending becomes another person's income. The expenditure multiplier captures the consequence: an initial injection of new spending does not stop at the first round. The recipients of that spending pass part of it on as further spending, and so on, so the final increase in national income is a multiple of the original injection.

Marginal propensities

The size of each successive round depends on how much of any extra income households spend rather than withdraw.

Marginal propensity to consume (MPC) is the fraction of an extra dollar of income that households spend on consumption.

Marginal propensity to save (MPS) is the fraction saved.

In the simplest model with saving as the only leakage, $MPC + MPS = 1$. Every extra dollar of income is either spent or saved.

Leakages and the marginal propensity to withdraw

In a realistic open economy with government, income also leaks into taxation and imports. The total fraction of extra income that leaks out is the marginal propensity to withdraw (MPW):

where MPT is the marginal propensity to tax and MPM the marginal propensity to import. The remaining fraction is re-spent on domestic output.

The multiplier formula

The multiplier (k) is the reciprocal of the marginal propensity to withdraw:

In the simplest closed economy with no government, this reduces to:

The final change in national income is the multiplier times the initial change in injections:

Why the multiplier works: the rounds

Suppose the government raises infrastructure spending by $1 billion and the MPC is 0.8 (in a simple model with saving the only leakage, so MPS is 0.2).

• Round 1. $1 billion is paid to construction workers and firms. Income rises by $1 billion.
• Round 2. They spend 0.8 of it ($800 million) on goods and services. That becomes income for other firms and workers.
• Round 3. Those recipients spend 0.8 of $800 million ($640 million).
• The rounds continue, each smaller than the last.

The sum of the rounds is a geometric series: $1 + 0.8 + 0.64 + \ldots = \frac{1}{1 - 0.8} = 5$. The multiplier is 5, so the $1 billion injection eventually raises national income by $5 billion.

Bigger leakages mean a smaller multiplier

The more income that leaks out at each round (into saving, tax or imports), the less is re-spent, so the multiplier is smaller. This is why the Australian multiplier is modest: Australia has a relatively high marginal propensity to import (a large share of manufactured goods are imported), so a good deal of each extra dollar leaks overseas rather than re-circulating domestically.

For example, if MPS is 0.1, MPT is 0.2 and MPM is 0.2, then MPW is 0.5 and the multiplier is only 2. The same $1 billion injection raises income by $2 billion, not $5 billion.

Application to policy

The multiplier explains why discretionary fiscal policy can have an amplified effect on AD and why the composition of spending matters.

• Spending directed at low-income households (who have a high MPC) re-circulates more than tax cuts for high-income households (who have a higher MPS).
• Spending on domestically produced goods and services leaks less overseas than spending on imports.

This is why, during the 2008 GFC, the Rudd government's stimulus included cash payments and school-building programs: the design aimed to maximise the domestic multiplier by directing spending where the marginal propensity to consume domestic output was high.

Examples in context

Example 1. Calculating a stimulus effect. Suppose the government funds a $4 billion regional infrastructure program. The economy has MPS of 0.15, MPT of 0.25 and MPM of 0.10, so MPW is 0.50 and the multiplier is $1 / 0.50 = 2$. The eventual increase in national income is$\Delta Y = 2 \times $4\text{ billion} = $8\text{ billion}$, provided spare capacity exists. If the marginal propensity to import were higher, the multiplier and the income effect would both be smaller.

Example 2. Why design matters. Two stimulus options each cost $2 billion. Option A is a cash payment to low-income households with an MPC of 0.9 on domestic goods. Option B is a tax cut to high-income households who save more and buy more imported luxury goods, with an effective domestic re-spending fraction of 0.4. Option A re-circulates far more, so its multiplier and its effect on domestic income and employment are larger. This is a standard QCE evaluation point about the effectiveness of fiscal policy.

Try this

Q1. Define the marginal propensity to consume and the marginal propensity to save, and state the relationship between them when saving is the only leakage. [3 marks]

• Cue. MPC is the fraction of extra income spent on consumption; MPS is the fraction saved; when saving is the only leakage, MPC + MPS = 1.

Q2. An economy has MPS of 0.2, MPT of 0.2 and MPM of 0.1. Calculate the multiplier and the change in national income from a $5 billion increase in government spending. [3 marks]

• Cue. MPW = 0.2 + 0.2 + 0.1 = 0.5; multiplier $k = 1 / 0.5 = 2$; $\Delta Y = 2 \times \$5\text{ billion} = \$10\text{ billion}$.

Q3. Explain why the Australian expenditure multiplier is relatively modest, and why the composition of fiscal stimulus affects its size. [5 marks]

• Cue. Australia has high leakages, especially a high marginal propensity to import, so much of each extra dollar leaks overseas and the multiplier is smaller; spending targeted at high-MPC households and at domestically produced goods leaks less and re-circulates more, raising the effective multiplier; near full capacity, extra spending adds to inflation rather than real income.