# Multiplier Effect

Multiplier effect is a macro-economic phenomenon in which an initial change in spending results in a greater ultimate change in real GDP. The initial change is usually a change in investment but other components of GDP such as government spending, net exports and a change in consumption which is not caused by change in income can also have multiplier effect on the GDP.

The ratio of ultimate change in GDP to initial change in spending is called the multiplier and it is represented using the following formula:

$$\text{Multiplier} = \frac{\text{Change in Real GDP}}{\text{Initial Change in Spending}}$$

Reordering the above formula, we get,

$$\text{Change in Real GDP} = \text{Multiplier} \times \text{Change in Initial Spending}$$

So if an increase of $50 billion in investment increases real GDP by a multiplier of 5, the real GDP will increase by$250 billion [= 50×5]. In this example, the multiplier effect is positive but it can also occur in other direction as well i.e. decrease in initial spending reducing real GDP by multiple times of initial decrease in spending.

Multiplier effect occurs under the assumption that the economy has room to expand so that increase in spending does not result solely in inflation.

Since the money spent in an economy is received by others as income and assuming that an average person is likely to change their spending in direct proportion to their income, therefore an initial increase or decrease in spending will start a chain of increased or decreased spending by a number of people. The ultimate change in GDP will be the total of the incremental changes in spending of multiple people caused by the initial change in spending.

## Example

Consider the example given above where the initial change in investment is $50 billion. This initial investment increases GDP by$50 billion is first stage. The initial investment is received in the form of income by a number people. Provided that they consume 80% of their income and save the rest, $40 billion [=$50×0.8] of the initial investment will be spent in second stage. The amount spent in second stage is also received by other people as income. In third stage, $32 billion [=$40×0.8] will be spent. In forth stage, $25.6 billion [=$32×0.8] will be spent. If we continue this process long enough and add all the amounts together or, we can simply use the following formula to calculate the total of this convergent geometric series:

$$\text{Change in Real GDP} = \frac{\text{Initial Change in Spending}}{\text{1} - \text{MPC}}$$

$$\text{Change in Real GDP} = \frac{\text{\50 billion}}{\text{1} - \text{0.8}} = \text{\250 billion}$$

As you may have noted, the multiplier is related to percentage of total income spent by people who directly or indirectly derive income from initial spending. This percentage is known as marginal propensity to consume.