 # GDP Deflator

Let’s imagine once again we are in the scenario from Consumer Price Index (CPI) with the pencils and notebooks for your upcoming school year.

Every year you buy the same number of pencils and the same number of notebooks, but this year it seemed to be more expensive than when you had bought the same supplies previously. How can we calculate these price increases?

GDP Deflator is another method to calculate an increase in prices, similar to CPI.

The difference between the CPI and the GDP deflator is that the GDP deflator measures the prices of all goods and services consumed and produced by the entire nation, not just the prices of consumer goods and services like the CPI.

In simplified terms...

The GDP Deflator combines both the CPI (Consumer Price Index) and the PPI (Producer Price Index) to arrive at an overall increase in prices for the entire economy.

The GDP Deflator is measured quarterly, at the same time GDP is calculated.

Before digging into the GDP Deflator, it's important to understand Nominal GDP vs. Real GDP.

## Nominal vs. Real GDP

### Nominal GDP explained

Nominal GDP is the total goods and services (expressed in dollars) produced this year using today’s prices.

Nominal GDP shows you how much economic activity there was in the economy, but there is one problem...

The nominal GDP does not account for inflation.

This means that if you see the nominal GDP going up, it could be for two very different reasons: 1) Output is going up or 2) Prices are going up. In an inflationary environment, nominal GDP is not a great measure of economic growth, because it is affected by price increases.

### Real GDP explained

Real GDP is the total goods and services (expressed in dollars) produced this year using base-year prices.

Real GDP shows you how much actual output you have, with inflation considered. Seeing a value for total output that is already adjusted for inflation gives a much better gauge of whether an economy is actually growing or not.

Now that we've learned about Nominal vs. Real GDP, let's move onto calculating the GDP Deflator!

## How to calculate GDP Deflator

The formula for calculating GDP Deflator is very simple…

GDP Deflator = [(Nominal GDP) / (Real GDP)] * 100

...but calculating the values to use in the equation can be more challenging.

To understand this, first, we need to learn how to calculate the Nominal GDP.

### Calculating Nominal GDP

Recall the definition of Nominal GDP:

Nominal GDP is the total goods and services (expressed in dollars) produced this year using today’s prices.

To state this mathematically in regards to two goods (X and Y), we could state the following:

Nominal GDP = (Qx{this year} * Px{this year}) + (Qy{this year} * Py{this year})

The most important thing to note here is that we're focusing on "this year" prices! Quantities will always be from "this year".

### Calculating Real GDP

Recall the definition of Real GDP:

Real GDP is the total goods and services (expressed in dollars) produced this year using base-year prices.

To state this mathematically in regards to two goods (X and Y), we could state the following:

Real GDP = (Qx{this year} * Px{base year}) + (Qy{this year} * Py{base year})

The most important thing to note here is that now, we're focusing on "base year" prices!

And...

Real GDP = (Qx{this year} * Px{base year}) + (Qy{this year} * Py{base year})

...we're still dealing with "this year" quantities!

Real GDP deals with "this year" quantities but "base year" prices because it's essentially taking inflation out of consideration, which deals with price (not quantity!).

### Applying to GDP Deflator

Now that we've learned how to calculate Nominal and Real GDP, let's apply it to an example:

A country produces only X and Y; their outputs last year and this year are given in the table below. Calculate the GDP deflator.

In order to calculate the GDP Deflator, we need to calculate Nominal GDP and Real GDP.

GDP Deflator = [(Nominal GDP) / (Real GDP)] * 100

Nominal GDP = (Qx{this year} * Px{this year}) + (Qy{this year} * Py{this year})

Remember: Nominal GDP deals with prices and quantities from "this year". We can apply the prices from "this year" like so...

Nominal GDP = (Qx{this year} * \$30) + (Qy{this year} * \$20)

...and the quantities from "this year" like so.

Nominal GDP = (120 * \$30) + (80 * \$20)

This results in a Nominal GDP of \$5200!

Nominal GDP = (120 * \$30) + (80 * \$20)
Nominal GDP = (\$3600) + (\$1600)
Nominal GDP = \$5200

Let's go ahead and plug that into our GDP Deflator equation like so:

GDP Deflator = [\$5200 / (Real GDP)] * 100

Next, let's calculate Real GDP.

Real GDP = (Qx{this year} * Px{base year}) + (Qy{this year} * Py{base year})

Remember: that deals with prices from "base year"...

Real GDP = (Qx{this year} * \$20) + (Qy{this year} * \$15)

...and quantities from "this year".

Real GDP = (120 * \$20) + (80 * \$15)

When we solve this out, we get a Real GDP of \$3600!

Real GDP = (120 * \$20) + (80 * \$15)
Real GDP = (\$2400) + (\$1200)
Real GDP = \$3600

Let's go ahead and plug that into our GDP Deflator equation like so:

GDP Deflator = [\$5200 / \$3600] * 100

Now, let's solve this out to arrive at our final GDP Deflator value of 144.4!

GDP Deflator = [\$5200 / \$3600] * 100
GDP Deflator = [1.444] * 100
GDP Deflator = 144.4

## Interpreting the GDP Deflator

Now that we’ve calculated and found the GDP Deflator, we can then use this value to determine the cumulative inflation percentage since the base year with the following simple formula:

Cumulative inflation% = (GDP Deflator  - 100)

Remember, the GDP Deflator is based on an index of 100, that’s why we’re subtracting 100 in our Cumulative Inflation equation; we are subtracting off the base year.

The GDP Deflator in the base year is always 100.

It is incredibly important to memorize the above point because without it you won’t be able to interpret GDP Deflator!

In essence, finding the difference allows us to calculate how much inflation we have experienced from the base year until today.

Using the data from our previous example and this formula…

Cumulative inflation% = (144.4  - 100)
Cumulative inflation% = 44.4

...this shows us that since the base year, the prices of Px and Py (all of the goods in this economy) have increased by 44.4% due to inflation!

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