The Multiplier Effect

Examples of the Multiplier Effect

When the government buys $20 billion of goods from Boeing, that purchase has repercussions. The immediate impact of the higher demand from the government is to raise employment and profits at Boeing.

Then, as the workers see higher earnings and the firm owners see higher profits, they respond to this increase in income by raising their own spending on consumer goods. As a result, the government purchase from Boeing raises the demand for the products of many other firms in the economy.

This multiplier effect continues even after this first round. When consumer spending rises, the firms that produce these consumer goods hire more people and experience higher profits. Higher earnings and profits stimulate consumer spending once again and so on.

Thus, there is positive feedback as higher demand leads to higher income, which in turn leads to even higher demand. Once all these effects are added together, the total impact on the quantity of goods and services demanded can be much larger than the initial impulse from higher government spending.

Figure IV illustrates the multiplier effect. The increase in government purchases of $20 billion initially shifts the aggregate-demand curve to the right from AD₁ to AD₂ by exactly $20 billion. But when consumers respond by increasing their spending, the aggregate-demand curve shifts still further to AD₃.

Figure IV, The Multiplier Effect | Source: Slideshare Opens in new window

This multiplier effect arising from the response of consumer spending can be strengthened by the response of investment to higher levels of demand. For instance, Boeing might respond to the higher demand for planes by deciding to buy more equipment or build another plant.

In this case, higher government demand spurs higher demand for investment goods. This positive feedback from demand to investment is sometimes called the investment accelerator.

A Formula for the Spending Multiplier

Some simple algebra permits us to derive a formula for the size of the multiplier effect that arises when an increase in government purchases induces increases in consumer spending.

An important number in this formula is the marginal propensity to consume (MPC) — the fraction of extra income that a household consumers rather than saves. For example, suppose that the marginal propensity to consume is ³/₄.

This means that for every extra dollar that a household earns, the household spends $0.75 (³/₄ of the dollar) and saves $0.25.

With an MPC of ³/₄, when the workers and owners of Boeing earn $20 billion from the government contract, they increase their consumer spending by ³/₄ x $20 billion, or $15 billion.

To gauge the impact on aggregate demand of a change in government purchases, we follow the effects step-by-step. The process begins when the government spends $20 billion, which implies that national income (earnings and profits) also rises by this amount.

This increase in income in turn raises consumer spending by MPC x $20 billion, which raises the income for the workers and owners of the firms that produce the consumption goods. This second increase in income again raises consumer spending, this time by MPC x $20 billion). These feedback effects go on and on.

To find the total impact on the demand for goods and services, we add up all these effects:

Here “. . .” represents an infinite number of similar terms. Thus, we can write the multiplier as follows:

Multiplier = 1 + MPC + MPC² + MPC³ + …

This multiplier tells us the demand for goods and services that each dollar of government purchases generates. To simplify this equation for the multiplier, recall from math class that this expression is an infinite geometric series. For 𝑥 between – 1 and + 1,

1 + 𝑥 + 𝑥² + 𝑥³ + . . . = 1/(1 – 𝑥).

In our case, 𝑥 = MPC. Thus,

Multiplier = 1/(1 – MPC).

For example, if MPC is ³/₄, the multiplier is 1/(1 - ³/₄), which is 4. In this case, the $20 billion of government spending generates $80 billion of demand for goods and services.

This formula for the multiplier shows that the size of the multiplier depends on the marginal propensity to consume. While an MPC of ³/₄ leads to a multiplier of 4, and MPC of ¹/₂ leads to a multiplier of only 2. Thus, a larger MPC means a larger multiplier.

To see why this is true, remember that the multiplier arises because higher income induces greater spending on consumption. With a larger MPC, consumption responds more to a change in income, and so the multiplier is larger.

Other Applications of the Multiplier Effect

Because of the multiplier effect, a dollar of government purchases can generate more than a dollar of aggregate demand. The logic of the multiplier effect, however, is not restricted to changes in government purchases. Instead, it applies to any event that alters spending on any component of GDP – consumption, investment, government purchases, or net exports.

For example, suppose that a recession overseas reduces the demand for U.S. net exports by $10 billion. This reduced spending on U.S. goods and services depresses U.S. national income, which reduces spending by U.S. consumers. If the marginal propensity to consume is ³/₄ and the multiplier is 4, then the $10 billion fall in net exports leads to a $40 billion contraction in aggregate demand.

As another example, suppose that a stock market boom increases households’ wealth and stimulates their spending on goods and services by $20 billion. This extra consumer spending increases national income, which in turn generates even more consumer spending. If the marginal propensity to consume is ³/₄ and the multiplier is 4, then the initial impulse of $20 billion in consumer spending translates into an $80 billion increase in aggregate demand.

The multiplier is an important concept in macroeconomics because it shows how the economy can amplify the impact of changes in spending.

A small initial change in consumption, investment, government purchases, or net exports can end up having a large effect on aggregate demand and, therefore, the economy’s production of goods and services.