# Construction of Simple and Weighed Price

There are different ways of construction of index numbers. In general, construction of index number is further available for the division in two parts: Simple and Weighted. Furthermore, the simple method is classified into simple aggregative and simple relative. Similarly, the weighted method is classified into weighted aggregative and weighted average or relative.

### Types of Methods of Construction

**Simple Method:**Aggregative and Relative**Weighted Method:**Aggregative and Relative

### Simple Aggregative Method

We use this method of construction for computation of index price. As a result, the total cost of any commodity in any given year to the total cost of any commodity in the base year is in percentage form.

**Simple Aggregative Price Index – (∑ P _{n}/ ∑ P_{0}) * 100**

Where

**∑P _{n} **= Sum of the price of all the respective commodity in the current time period.

**∑P**= Sum of the price of all the respective commodity in the base period.

_{o }The simple aggregative index is very simple to understand. However, there is a serious defect in this method. The first commodity, here, has more influence than the rest two. This is so because the first commodity has a high price than the rest.

Furthermore, if we anyhow change the units, the index number will also go through a change. This is one of the biggest flaws of this methods. Use of absolute quantities turn the tables around. Therefore, considering independent values for the three years would be a better option.

#### Simple Average of Relatives

In order to remove the errors and flaws coming from a simple aggregative index, a replacement would be a better choice. Hence, we can use a simple average of relatives method for construction of Index.

Using this method, we can invert the real values for any individual variable into percentage form of the base period. We term these percentages as *relatives. *One of the biggest reason to opt for relatives is that they are full numbers and have no absolute values like Rs. 35.60, Rs. 10.01, and so on. Hence, the index numbers that we get as a result is likely to stay as it is.

### Weighted Method

It is quite important to meet the needs of any sort of simple or unweighted methods. So, in such a case, we weigh the value of any commodity using any factor that deems fit. This factor is usually the quantity we sell it for during the base year. The categories of these indices are:

- Weighted Aggregative Index
- Weighted Average of Relatives

Let’s have a close look at the following two indices.

**Weighted Aggregative Index Method**

We generally use this method to weigh out the price of any commodity. The weighing is done using a very approximate factor. These factors are likely to vary and can be anything. It can be a quantity or it can be the volume that it is selling off for during the base year.

The year not necessarily needs to be the base year but can also be an average of other years or any year in general. Well, the choice of it will totally depend on the importance of the specific year. So, besides the quantity, it is on us about terming the importance of a specific year.

Weighted Aggregative Index generally comes off in the form of percentages. As a result, there are different formulas that we use for the same. Some of them are:

**Laspeyres Index**

Under this type of index, the quantities in the base year are the values of *weights.*

**Formula –** (**∑P _{n}Q_{o}/∑P_{o}Q_{o})*100**

**Passche’s Index**

Under this type of Index, the quantities in the current year are the values of *weights.*

**Formula – (∑P _{n}Q_{n}/∑P_{o}Q_{n})*100**

#### 3. Some of the methods that depend on a typical time period:

Index (∑P_{n}Q_{t}/∑P_{o}Q_{n}) * 100, here, the subscript “*t” *symbolizes the typical period of time in years. The quantities of these years are the values of weight.

**Note: **Using the following formulas, the indices are subject to return the values in the form of percentages.

**Marshall-Edgeworth Index**

Under this type of index, we take both i.e. the current year as well as the base year into consideration for specifying the methods.

**Marshall-Edgeworth Index – [∑P _{n}(Q_{n}+ Q_{n})/∑P_{o}(Q_{o}+ Q_{n})] * 100**

**Fisher’s Ideal Price Index**

The geometric mean of Laspeyres’ and Paasche’s is the Fisher’s Ideal Price Index.

**Formula – √[(∑P _{n}Q_{o}/∑P_{o}Q_{o})*(∑P_{n}Q_{n}/∑P_{o}Q_{n})]* 100**

**Weighted Average of Relatives**

We use the weighted average of relatives to avoid the disadvantage that comes along with the simple average method. Furthermore, the preference is weighted geometric mean but weighted arithmetic mean is used otherwise. Therefore, the representation of the weighted AM using the values of base year weights is:

**Formula – (∑P _{n}Q_{o}/∑P_{o}Q_{o}) * 100**

## Solved Examples for You

Example: For the given data find-

a) Simple Aggregative Index for the year 1999 over the year 1998.

b) Simple Aggregative Index for the year 2000 over the year 1998.

Commodity |
1998 |
1999 |
2000 |

Cheese (100 gm) | 12 | 15 | 15.60 |

Egg (per piece) | 3 | 3.60 | 3.30 |

Potato (per kg) | 5 | 6 | 5.70 |

Aggregate |
20 | 24.60 | 24.60 |

Index |
100 | 123 | 123 |

Solution:

Simple Aggregative Index for the year 1999 over the year 1998

**(∑ P _{n}/ ∑ P_{0}) = **( 24.60/20.00 ) * 100 = 123

Simple Aggregative Index for the year 2000 over the year 1998

**(∑ P _{n}/ ∑ P_{0}) = **( 24.60/20.00 ) * 100 = 123

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