2.4.4 - The multiplier

The Multiplier Process

The multiplier process begins when an injection such as government spending, investment, or exports enters the economy. The people and firms receiving that spending then pass on part of it through their own spending, so the effect spreads through several rounds.

Suppose the government spends GBP100 million on rebuilding schools in England. If the recipients of that extra income spend 80% of every additional pound they receive, the chain reaction looks like this:

1. Initial injection: the government pays construction firms GBP100 million.
2. Round 1: workers, suppliers, and subcontractors receive that income and spend GBP80 million.
3. Round 2: the people receiving the GBP80 million spend GBP64 million.
4. Round 3: the recipients of the GBP64 million spend GBP51.2 million.
5. The process continues, but each round gets smaller because some income leaks out of the circular flow.

So the total increase in national income is:

The original GBP100 million injection has therefore created a GBP500 million rise in national income. In this example, the multiplier is 5.

Marginal Propensities and Withdrawals

The size of the multiplier depends on what happens to each extra pound of income. Some of it is spent on consumption, but some of it is withdrawn from the circular flow.

The other important marginal propensities are the leakages. MPS is the proportion of extra income that is saved, MPT is the proportion taken in taxation, and MPM is the proportion spent on imports. Together they make up the marginal propensity to withdraw, MPW. In these formulas, MPC means the share of extra income spent on domestically produced goods and services, the part that stays in the circular flow; extra spending on imports is counted in MPM instead.

These relationships matter because every extra pound must go somewhere. If more of it stays in domestic spending, the multiplier is larger. If more of it leaks out through saving, tax, or imports, later rounds of spending shrink more quickly.

This also explains why the multiplier equals 1/MPW. The rounds of spending continue until the whole injection has leaked out: national income stops rising once the extra withdrawals, MPW times the rise in income, equal the original injection. In the schools example, MPW = 0.2, so national income must rise by GBP500 million before the full GBP100 million has leaked out ($0.2 \times 500 = 100$).

Worked Calculations

In exam questions, you may be given the multiplier directly, or you may have to calculate it from MPC or MPW. The key is to move carefully from the initial change in spending to the final change in national income.

If an initial injection of GBP50,000 leads to a final increase in national income of GBP500,000, the multiplier ratio is 10 because:

You can also calculate it from leakages. If MPS = 0.1, MPT = 0.2, and MPM = 0.1, then:

The other formula gives the same answer. In this economy MPC = 1 - 0.4 = 0.6, so:

The two formulas always agree, because MPC + MPW = 1.

The multiplier then tells you the total effect of an injection: final change in national income = multiplier $\times$ initial injection. If the multiplier is 4 and government spending rises by GBP20 million, national income rises by GBP80 million ($4 \times 20 = 80$).