The marginal propensity to consume (MPC) is equal to ΔC / ΔY, where ΔC is change in consumption, and ΔY is change in income. If consumption increases by eighty cents for each additional dollar of income, then MPC is equal to 0.8 / 1 = 0.8.

The expenditure multiplier is the ratio of the change in total output induced by an autonomous expenditure change.

Look Out!
In the Keynesian model, government and private investment spending are considered to be autonomous while consumption is not because it is a function of income.

Some consumption is considered to be autonomous. Even with no income, some consumption will occur (savings will need to be used). So the consumption function could be expressed as C = α + (β × Y), where α represents consumption that occurs regardless of income, β is the marginal propensity to consume and Y is income.

Why is there a multiplier effect?
Suppose a large corporation decides to build a factory in a small town and that spending on the factory for the first year is $5 million. That $5 million will go to electricians, engineers and other various people building the factory. If MPC is equal to 0.8, those people will spend $4 million on various goods and services. The various business and individual receiving that $4 million will in turn spend $3.2 million and so on.

If the marginal propensity to consume is equal to 0.8 (4 / 5), then the multiplier can be calculated as:

Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.8) = 1 / 0.2 = 5

As a result of the multiplier effect, small changes in investment or government spending can create much larger changes in total output. A positive aspect of the multiplier effect is that macroeconomic policy can effect substantial improvements with relatively small amounts of autonomous expenditures. A negative aspect is that a small decline in business investment can trigger a larger decline in business activity and, thereby, create instability.

The previously mentioned formula for calculating the multiplier is a simplified one. Leakages (money spent, but not on domestic goods or domestic services) reduce the size of the multiplier. Examples of leakages include taxes and imports.

Another important point is that the multiplier effect takes time to work; months must pass before even half of the total multiplier effect is felt. Also, keep in mind that the multiplier effect can cause idle resources to be moved into production. If unemployment is widespread, then there should be little impact on resource prices.

Discretionary Fiscal Policy and Automatic Stabilizers

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