### Price index (PI)

A price index (PI) is a measure of how prices change over a period of time, or in other words it is a way to measure inflation. There are multiple methods on how to calculate the inflation (or deflation), in this guide we will take a look at a couple of methods on how to do so. Inflation is one of the core metrics monitored by the FED in order to set interest rates.

The general formula for the price index is the following:

#### PI_{1,2} = f(P_{1},P_{2},X)

Where:

- PI
_{1,2}: Some PI that measures the change in price from period 1 to period 2 - P
_{1}: Price of goods in period 1 - P
_{2}: Price of goods in period 2 - X: Weights (the weights are used in conjunction with the prices)

**Quantity index numbers**

Quantity index numbers measure the change in the quantity or volume of goods sold, consumed or produced during a given time period. Hence it is a measure of relative changes over a period of time in the quantities of a particular set of goods.

Just like price index numbers and value index numbers, there are also two types of quantity index numbers, namely

- Unweighted Quantity Indices
- Weighted Quantity Indices

Let us take a look at the various methods, formulas, and examples of both these types of quantity index numbers.

**Value Index Number**

The value index number compares the value of a commodity in the current year, with its value in the base year. What is the value of a commodity? It is nothing but the product of the price of the commodity and the quantity. So the value index number is the sum of the value of the commodity of the current year divided by the sum of its value in the chosen base year. The formula is as follows,

**v _{01} = (**∑p1q1/∑p0q0)

**× 100**

or alternatively, **v _{01} = (**∑V1/∑V0

**)× 100**

In this case of a value index number, we do not apply any weights. Since these are considered to be inherent in the value of a commodity. Thus we can say that a value index number is an aggregate of values.

The value index number is not a very popular statistical tool. Price and quantity index numbers give a clearer picture of the economy for study and analysis. They even help in the formulation and implementation of economic policies.

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