Formulas to Calculate Consumer Price Index

Consumer price index is a measure to know the change in the price of goods or/and services in some particular category, area and period. It helps you to find out the cost of living as well as 'ideal cost of living' of people of that area. There are many advantages to work it out. A few are:

1-It is helpful in measuring inflation rate in an economy.

2-In many countries including the USA, the social security benefits are tied to consumer price index.

3-It helps the business to find out profitable business and investment opportunities.

More on Consumer Price Index

Variety of Formulas

There are a number of formulas to calculate consumer price index. A few of them are as under:

Laspeyres Index:

Paasche Index:

Carli:

Jevons:

Harmonic Mean of Price Relatives:

Carruthers, Sellwood, Ward, Dalen Index:

Dutor:

Ration of Harmonic Means:

Fisher:

Tornqvist:

Walsh:

You can go through summaries of these formulas at Wikipedia. Two of these formulas, Laspeyres, and Paasche, are most popular.

Laspeyres Index Formula

The Laspeyres consumer price index was developed by a German economist Etienne Laspeyres. It is also called “fixed-weighted” or “base weighted” because whatever increase in the price of a bundle of goods or services is weighed with the bundle of ‘fixed quantities’ of goods or services in the base year. Robert S. Pindyck and Daniel L. Rubinfeld say that Laspeyres Index formula replies this question:

“What is the amount of money of current-year prices that an individual requires to purchase the bundle of goods and services that were chosen in the base year divided by the cost of purchasing the same bundle at base-year prices?”

Calculations of Laspeyres Index are straight, but different economists write the formula in different ways.

According to this formula, the j0 refers to the base year value for good/service j. The t refers to the current year value of the j. We have to calculate the Lt for every year. For the base year, it is 1 and value of index would become 100.

Robert S. Pindyck and Daniel L. Rubinfeld give this formula:

They refer different factors like:

PFt and PCt are current year prices

PFb and PCb are base year prices

Ft and Ct are current year quantities

Fb and Cb are the base year quantities.

Wikipedia mentions this formula under the heading of Laspeyres Index:

In this formula:

The P refers to the relative index of the price levels in two periods’

The t0 denotes the base year,

And tn is the period for which this index is computed.

You can use any formula, but the main crux is that you have to compare the current price of goods and services in the current year with the price of fixed weight goods and services in the base year.

Paasche Index Formula

Paasche Index is another favorite way to calculate consumer price index. It was developed by another German economist Herman Paasche. He wanted to measure current level of price or quantity with a selected base period without fixing amount or quantity in the base year.

In this index, current period weighting is used. In other words, you can calculate the price of the current period goods or services with a base period prices of the same goods and services. The prices are weighed against current period quantities of services and goods. It means the weights will change with the change of years in the base period.

While developing this formula, it was kept in mind that ‘expenditure patterns’ of the consumers change in every year following changes in their preferences, tastes, and prices. So, it was considered unfair to keep the bundle of goods constant from base year to the current year.

Robert S. Pindyck and Daniel L. Rubinfeld give this formula:

They say that this index answers this question:

“What is the amount of money at current year prices that an individual requires to purchase the current bundle of goods and services divided by the cost of purchasing the same bundle in the base year?”

On first reading, this question may seem a bit confusing. However, we can clarify this confusion by comparing the both popular indexes

Comparison of Laspeyres and Paasche Indexes

When we compare both indexes we find out the following major points:

1-Laspeyres index focuses upon the price of the bundle of goods and services in the base year. However, Paasche Index focuses upon the price of goods and services in the current year.

2-In Laspeyres index the base year weights are kept constant while in Paasche Index the base year weights change on every calculation.

3-The Laspeyres index overstates the living cost (shows higher inflation), and Paasche Index understates (shows lower inflation) it.