# The Multiplier Effect

The Multiplier Effect is defined as the change in income to the permanent change in the flow of expenditure that caused it. In other words, the multiplier effect refers to the increase in final income arising from any new injections.

Injections are additions to the economy through government spending, money from exports, and investments made by firms. Injections increase the flow of income. Here are some examples of injections:

- Investment (I). Money invested by firms in purchasing capital stock.
- Exports (X). Money coming from abroad to buy domestically produced goods.
- Government spending (G). Government welfare benefits, spending on infrastructure.

An injection of extra income leads to more spending, which creates more income, and so on. It emphasizes the effect of an expansionary fiscal policy. The Multiplier Effect continues until savings = amount injected. (See the Circular Flow of Income)

According to a study published on VoxEU, “Many researchers and policymakers alike have argued that multipliers could be higher during times when unemployment rates are high or when interest rates are at the zero lower bound. Indeed, recent theoretical research has suggested that government spending multipliers can be much larger when the interest rates are at the zero lower bound.”

## The Multiplier Effect Diagram

From the diagram below we can see, that an increase in government spending would shift the Aggregate Demand (AD) curve from AD1 to AD2. However, the multiplier effect shifts the AD curve to AD3 instead of AD2.

The reason for this is because one person’s spending is another’s income, so there’s this constant exchange of money that gets spent.

## The Multiplier Effect Formula (‘k’)

### Important Terms:

1. MRL – Marginal Rate of Leakages

2. MPS – Marginal Propensity to Save

3. MRT – Marginal Rate of Taxation

4. MPM – Marginal Propensity to Import

5. MPC – Marginal Propensity to Consume – The marginal propensity to consume (MPC) is the increase in consumer spending due to an increase in income. This can be expressed as ∆C/∆Y, which is a change in consumption over the change in income.

### Calculating the Multiplier Effect for a simple economy

k = 1/MPS

= 1/(1-MPC)

### Calculating the Multiplier Effect for a complex economy

k = 1/MRL

= 1/(MPS + MRT + MPM)

= 1/(1-MPC)

## Example of the Multiplier Effect

If the government increases expenditure by $100,000, then the national income or real GDP increases by $100,000. We assume that this money is going towards constructing a new freeway.

However, the $100,000 is only the income for the people who the government pays. In our example, we assume the government hires a firm to construct the road. The company, in turn, pays workers wages. These workers then spend the money.

If the Marginal Propensity to Consume (MPC) is 0.8, which means that the consumer spends 80% of the income. Therefore 0.2 (20%) is saved Marginal Propensity to Save (MPS), it follows that the Multiplier (k) = 5 (since k = 1/(1-0.8)

Therefore, the cumulative effect of the $100,000 added to the economy is $500,000.

Similarly, for a sophisticated economy, we can plug in values for Marginal Rate of Taxation (MRT), Marginal Propensity to Import (MPM) and Marginal Propensity to Save (MPS) to calculate “k.”