Calculation of price index

This is the price index which considers the weight assigned to various commodities and under this, most important commodities are assigned higher weights than those which are less important.

The formula for the Weighted Price Index (WPI) is:

$\text{WPI} = \frac{\sum \text{WPR}}{\sum W}$

Where:

• $\sum \text{WPR}$ = Summation of Weighted Price Relatives
• $\sum W$ = Summation of Weights

Given:

$\sum \text{WPR} = 4450, \quad \sum W = 24$

$\text{WPI} = \frac{4450}{24} \approx 185.4\%$

Change in general price level = $185.4\% - 100\% = 85.4\%$

Conclusion: The general price level increased by 85.4%.

This is a base year weight price index therefore it uses the base year value as its weights.

This price index is a better way to get a picture on changes in the value of money, standard of living etc as it makes a comparison between the base and the current year.

Interpretation

• Price increased by 201%
• Cost of living increased by 201%
• Standard of living declined by 201%
• Saving capacity declined by 201%

This is a current year weight price index which is calculated by

The formula for the Producer Price Index (PPI) is:

$\text{PPI} = \frac{\sum P_n Q_n}{\sum P_o Q_n} \times 100$

Where:

• $\sum$ = Summation
• $P_n$ = Price in the current year
• $P_o$ = Price in the base year
• $Q_n$ = Quantity in the current year

Using the given data:

$\sum P_n Q_n = (4.0 \times 2) + (1.5 \times 10) + (25.0 \times 1) + (5.0 \times 8) + (7.0 \times 3)$

$= 8 + 15 + 25 + 40 + 21 = 109$

$\sum P_o Q_n = (3.2 \times 2) + (2.0 \times 10) + (5.0 \times 0.1) + (1.0 \times 8) + (1.0 \times 3)$

$= 6.4 + 20 + 0.5 + 8 + 3 = 37.9$

Now calculating PPI:

$\text{PPI} = \frac{109}{37.9} \times 100 \approx 287.6\%$

$\text{PPI} \approx 188\% \text{ after removing the base } 100\%$

Interpretation

• Price increased by 157%
• Cost of living increased by 157%
• Standard of living declined by 157%
• Saving capacity declined by 157%

1. It is important in measuring changes in the general price level between the base and the current year therefore it is from the price index that it can be known whether the prices increase, reduce or remains the same.
2. Price indices are also important in knowing changes in the value of money over time. Therefore it can be known whether the value of money has increased or reduced.
3. Price indices are also important in measuring the cost of living between the base and the current year. Therefore it is from price index that it can be known whether the cost of living has increased or decreased.
4. Price index is also important in measuring in the standard of living between the base and the current year. Therefore it can be known whether the standard of living has increased or decreased.
5. Price indices are also important to the government and to the employees in the wage policy as it gives a picture on the cost of living and standard of living and hence creating a basic of wage revision.
6. Price indices are also important in measuring terms of trade, position of the country by use of the price index for export and price index for imports. Therefore price indices are important in showing changes in the terms of trade position of the country.
7. Price indices are also important in deflating National income from nominal to real through the use of the GDP deflation.
8. Price indices are also important in comparing the cost of living and standard of living between countries.

1. Choice of the base year It is difficult to get a base year in which prices are relatively stable, this is due to the fact that they are normally ups and down in the prices.
2. Difficulty in selection of a common represent basket of commodity from the wide range of commodities.
3. The data problem. It is difficult and unreliable data on prices and quantities as many consumers do not keep a record of their expenditures.
4. There are several ways/ methods that can be used to calculate price index but which give different answers this creates a problem in the interpretation.
5. Change in the prices may be as a result of improvement in quality which may be interpreted as inflation but which is not.
6. Index numbers have limited use for a long period of time due to the fact that taste and preferences change.

1. Choice of an area where the data is to be collected
2. Choice of a common representative basket of commodities.
3. Collection of data on prices and quantities
4. Tabulation of the data
5. Choice of the appropriate formula and computation
6. Interpretation