**Formula of Multiplier (Table of Contents)**

## What is the Multiplier Formula in Economics?

Multiplier formula denotes an effect which initiates because of increase in the investments (from the government or corporate levels) causing the proportional increase in the overall income of the economy, and it is also observed that this phenomenon works in the opposite direction too (the decrease in income effects a decrease in the overall spending). Following is the formula for the calculation of the multiplier effect.

**Multiplier (k) = Change in Real GDP (Y) / Change in Injections**

For the calculation of the multiplier formula in economics, the formula used is

**Multiplier (k) = 1 / MPS**

Or

**k = 1 / (1 – MPC)**

Where,

- MPS = (1- MPC)

This formula shows the relation between the increase in the earning of the nation due to the investments by the respective government or the corporates, if, there is a fixed pattern of expenditure from the additional income.

This formula works on a premise that the expenditure of one person is the income for another person apart from that portion which is being saved by the earning person. There is an assumption that the expenditure of one person is another person’s income in the form of profit, wages, salaries, etc and that person, in turn, spend it again majorly on the consumption front. This circle keeps on rolling on an on till the saving gets equal to the amount injected in the economy.

### Important Definitions

**GDP:**GDP or Gross Domestic Product of the country denotes the production of finished goods or services of the country for a specific period of time in market value terms. It indicates the commercial well-being of the economy of a nation. It helps to gauge the economic condition of the nation and used heavily for national policymaking.**Real GDP:**GDP could be of two types; Real GDP, and Nominal GDP. Inflation is the difference between the real GDP and nominal GDP. The Real GDP accounts for the value of all goods and services produced at a constant price and doesn’t consider the effects of inflation. On the contrary, the nominal GDP does take into account the actual prices of all the produced goods and services, and the full effect of inflation in its calculation. So, if the primary consideration is to evaluate the comparative production levels of the nation, Real GDP turns out to be a winner, because it does not take into account the inflationary prices and keeps the focus fixed on the actual production.**Injections:**Injections are nothing, but an addition to the total expenditures already happening in the economy. These expenditures could come from any direction; be it from corporates, government, export contributions, etc. A few examples to understand it clearly would be the corporates investing in the capital goods of the company or taking up expansion plans, the government taking up the infrastructure activities and or spending on welfare schemes, or, international companies purchasing goods from domestic producers. All these would fall under the injections criteria.**MPC:**Marginal Propensity to Consume is an essential tenet of the multiplier formula. It indicates the basic idea of consumption pattern which would remain constant over the series of consumption. For instance, let’s assume the MPC is 0.8 or 80% of the earning, and in simple terminology, it reflects the spending behavior of the person. If a person earns $100, around 80% or $80 would be spending on consumer goods. And the remaining amount would be saved. Again, the spending of one person would become the earning of another party and that too would spend 80% of it on consumer spending. This circle keeps on happening over a period of time unless it reaches a negligible amount. The formula of MPC is changed in the spending over the change in the earning. ( Change in Consumption / Change in the Earning )**Marginal Propensity to Save:**It speaks about the saving which a person would do when there is a change in the earning. In other words, it is arrived by deducting the earning by marginal propensity to spend. So, The formula for MPS would be: Earning – Marginal Propensity to Spend.

### Examples of Multiplier Formula in Economics

Given below are the examples of multiplier formula.

#### Example #1

**Let’s assume that the govt. has come up with an investment of $2,00,000 in the infrastructure project in the country. This additional income would follow the pattern of marginal propensity to save and consume. If the marginal propensity to consume is 0.8 or 80% then calculate the multiplier in this case. **

**Solution:**

We got the following data for the calculation of multiplier.

Calculation of multiplier formula is as follows –

- Multiplier Or (k) = 1 / (1 – MPC)
- = 1/( 1 – 0.8)
- = 1/( 0.2)

**Value of multiplier is**

**= 5. 0**

Now we will calculate the change in Real GDP

- Change in Real GDP = Investment * Multiplier
- = $ 1,00,000 * 5
- = $ 5,00,000

In the above-mentioned example, the government has invested $ 100,000 in the economy for infrastructure development and after the application of Multiplier effect ( k ) which resulted in multiples of 5, the real GDP would increase to $ 5,00,000.

This increase in GDP is based on the assumption that there is a constant expenditure pattern to the tune of 0.8 or 80% of the change in differential income.

#### Example #2

**In the year 2019, there was an investment of $600,000 in the private sector of the country. The marginal propensity to consume is 0.9 which will remain constant over the period of time. Calculate the multiplier effect and also find out the change in the Real GDP. **

**Solution:**

We got the following data for the calculation of the multiplier effect.

Calculation of multiplier effect formula is as follows –

- Multiplier Or (k) = 1 / (1 – MPC)
- = 1 / ( 1 – 0.9)
- = 1 / ( 0.1)

**Value of multiplier effect is**

**= 10. 0**

Now we will calculate the change in Real GDP

- Change in Real GDP = Investment * Multiplier
- = $ 6,00,000 * 10
- = $ 60,00,000

Here again, the investment of $ 6,00,000 would bring a change in the real GDP by $ 60,00,000. And the multiplier is calculated as 10.

#### Example #3

**The government is trying to boost the economy and one of the measures suggested by the committees to invest $200,000 into the economy and let it roll for a while. Calculate the Multiplier Effect and also find out the change in the Real GDP, if the multiple propensities to consume is 0.7**

**Solution:**

We got the following data for the calculation of the multiplier effect.

Calculation of multiplier effect formula is as follows –

- Multiplier Or (K) = 1 / (1 – MPC)
- = 1 / ( 1 – 0.70)
- = 1 / ( 0.30)

**Value of multiplier effect is**

- = 3.33

Now we will calculate the change in Real GDP

- Change in Real GDP = Investment * Multiplier
- = $ 2,00,000 * 3.33
- = $ 6,66,667

Here again, the investment of $ 2,00,000 would bring a change in the real GDP by $ 6,66,667. And the multiplier is calculated 3.33. This indicates that if the pattern of the consumption would remain at 70% throughout the time of investments, it will help change in GDP by $6,66,667.

### Importance and Uses of Multiplier Formula** in Economics**

Even though the multiplier formula in economics has various limitations, it has a far-reaching impact on economic decisions and policymaking of the nation. Following are some noted uses and importance of the Multiplier formula:

- This formula has established a straight connection with investments in economy and job creation. The Multiplier theory also states that pumping funds in the economy would create a ripple-like effect in the cash flow of the economy, even a percentage of amount is being saved at every level.
- Multiplier provides that even if the small investment has been put in the system, eventually, after a span of time, the invested figure would grow manifolds. It encourages the ruling government, and public or private investors to remain invested and increasing investments in the market.
- Sound knowledge of this concept helps to judge and understand various cycles of business as it entails an understanding which is fairly accurate.

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