Inflation is measured in percentage which is obtained by calculating the change in percentage of current price index over the previous one. The price index is developed by carrying out a survey on costs of a number of goods and services that comprise the economy. These goods and services are put together into what is known as ‘market basket’. The cost of identical market basket today is compared to the cost of identical basket in the previous year or a base year in order to determine the rate of inflation.

### Consumer Price Index (CPI)

Consumer Price Index or CPI is an internationally comparable measure of inflation which measures changes in price from the purchasers’ perspective. It is a measure of price changes in consumer goods and services such as food, clothing, gasoline and automobiles but excludes housing costs and mortgage interest payments. It reflects changes in the prices of a market basket of goods and services purchased by consumers (individuals and households). CPI helps in the measurement of cost of living of urban consumers.

As defined by the U.S. Bureau of labor statistics, ‘CPI is a measure of the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services.’

CPI is a statistical estimate constructed with the help of prices of items that represent the economy, whose prices are collected periodically. The annual percentage change in CPI is taken as a measure of inflation.

Thus,

Where,

CPI_{1 }= CPI in previous year

CPI_{2} = CPI in current year

#### Calculating CPI

Calculation of CPI and inflation requires data on prices of goods and services in large scale. But, for the simple understanding, let us consider a simple economy in which consumer goods include bread and egg.

A step-wise calculation on CPI and inflation is explained below:

##### Step 1: Determination of basket of goods and services

Suppose, the market basket of a typical consumer contains 4 breads and 2 eggs.

##### Step 2: Determination of prices

Year |
Per unit price of Bread ($) |
Per unit price of Egg ($) |

2005 | 1 | 2 |

2006 | 2 | 3 |

2007 | 3 | 4 |

##### Step 3: Computation of cost of basket of goods in each year

The costs of market basket is calculated with the help of individual prices and relative quantity of goods.

Year 2005: ($1 per bread x 4 breads) + ($2 per egg x 2 eggs) = $8 per basket.

Year 2006: ($2 per bread x 4 breads) + ($3 per egg x 2 eggs) = $14 per basket.

Year 2007: ($3 per bread x 4 breads) + ($4 per egg x 2 eggs) = $20 per basket.

##### Step 4: Selection of base year (year 2005 in this case) and computation of CPI

Taking 2005 as the base year, and using the formula of CPI, we compute CPI for each given year as

Year 2005: ($8 / $8) x 100 = 100

Year 2006: ($14 / $8) x 100 = 175

Year 2007: ($20 / $8) x 100 = 250

##### Step 5: Computation of inflation rate using CPI

Using CPI from the above calculation and the formula of inflation, we derive inflation rate for each year

Inflation in 2006: (175 – 100) / 100 x 100 = 75%

Inflation in 2007: (250 – 175) / 175 x 100 = 43%

#### Product Price Index (PPI)

Product Price Index (PPI), also referred to as Wholesale Price Index (WPI), measures the average price changes of goods and services over time at wholesale level. In other words, PPI measures price change from the viewpoint of domestic producers.

PPI or WPI is an index of prices paid by retailers for the products that they would resale to the final consumers. It monitors the price changes made by manufacturers and wholesalers before the products reach the final consumers.

#### GDP Deflator

GDP deflator measures the changes in the overall prices of newly produced goods and services that are ready for consumption. It is an important economic metric that helps to determine the rate of inflation by converting output measured at current market prices into constant base year prices.

In other words, GDP deflator measures the relationship between nominal GDP (total output measured at current prices) and real GDP (total output measured at constant base year prices). It measures the current level of prices relative to the level of prices in the base year.

Since the GDP deflator is not based on a fixed market basket of products, it takes into account the change in consumption patterns of consumers as a result of newly manufactured products and services.

The GDP deflator is simply nominal GDP in a year divided by real GDP in that year, multiplied by 100.

Thus,

#### Calculating GDP Deflator

A step-wise explanation of the GDP deflator is given below:

##### Step 1: Determination of basket of goods and services

Suppose, the market basket of a typical consumer contains bread and egg.

##### Step 2: Determination of prices

Year |
Per unit price of Bread ($) |
Quantity of Bread |
Per unit price of Egg ($) |
Quantity of Egg |

2005 | 1 | 100 | 2 | 50 |

2006 | 2 | 150 | 3 | 100 |

2007 | 3 | 200 | 4 | 150 |

##### Step 3: Computation of Nominal GDP

Year 2005: ($1 per bread x 100 breads) + ($2 per egg x 50 eggs) = $200

Year 2006: ($2 per bread x 150 breads) + ($3 per egg x 100 eggs) = $600

Year 2007: ($3 per bread x 200 breads) + ($4 per egg x 150 eggs) = $1200

##### Step 4: Computation of Real GDP

Taking 2005 as the base year, we calculate real GDP as

Year 2005: ($1 per bread x 100 breads) + ($2 per egg x 50 eggs) = $200

Year 2006: ($2 per bread x 150 breads) + ($2 per egg x 100 eggs) = $350

Year 2007: ($3 per bread x 200 breads) + ($2 per egg x 150 eggs) = $500

##### Step 5: Computation of the GDP Deflator

Using the above mentioned formula of GDP Deflator, we derive

Rate of Inflation in 2006: (171 – 100) / 100 x 100 = 71%

Rate of Inflation in 2007: (240 – 171) / 171 x 100 = 40.35%

After computation of various price indices, rate of inflation is calculated using the following formula:

Where,

P_{t} = Price index in current (t) period

P_{t – 1} = Price index of previous (t – 1) period