# The Multiplier Effect

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## Multiplier Effect Definition

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 Model)

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 Graph

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.

k = 1/MPS

= 1/(1-MPC)

### Calculating the Multiplier Effect for a complex economy

k = 1/MRL

= 1/(MPS + MRT + MPM)

= 1/(1-MPC)

## Multiplier Effect Example

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 the Marginal Rate of Taxation (MRT), Marginal Propensity to Import (MPM) and Marginal Propensity to Save (MPS) to calculate “k.” Prateek Agarwal
Member since June 20, 2011
Prateek Agarwal’s passion for economics began during his undergrad career at USC, where he studied economics and business. He started Intelligent Economist in 2011 as a way of teaching current and fellow students about the intricacies of the subject. Since then he has researched the field extensively and has published over 200 articles.

### 3 thoughts on “The Multiplier Effect”

1. Assuming that the GDP contracts by a given amount, how can the government use the Keynesian multiplier to determine the necessary government spending to correct for that contraction?

2. Hello Prateek,
I’m working on an analysis to measure the effect of tourism visitor spending in my state (Arizona) as part of the leisure/hospitality industry. All academic examples I see of the multiplier effect use government spending as the baseline. In this case it’s not. There’s visitor spending, operating expenses (which is also local spending), tax revenues (lodging + visitor spending sales taxes). Of course, not all spending stays in the state (I estimate 75% stays).

How would you calculate a defensible multiplier to show GDP contribution or economic impact in this case?
-Mark Beauvais
Phoenix, AZ

3. 