# Cost of Living Index Number

18/04/2020

#### Uses of cost of living index number:

(i) It is used in wage negotiations, dearness allowance, bonus etc., to the workers.

(ii) The cost of living index number measures the change in the retail prices of a specified quantity of goods and services.

(iii) It is also useful to the government in framing policies relating to wages.

(iv) It is used as measures of change in the purchasing power of money and real income.

The cost-of-living index, or general index, shows the difference in living costs between cities. The cost of living in the base city is always expressed as 100. The cost of living in the destination is then indexed against this number. So to take a simple example, if London is the base (100) and New York is the destination, and the New York index is 120, then New York is 20% more expensive than London. Similarly, if London is the base and Budapest is the destination, and the Budapest index is 80, than the cost of living in Budapest is 80% of London’s.

What’s the methodology behind the index?

The cost-of-living index expresses the difference in the cost of living between any two cities in the survey. How is this index calculated?

Using exactly the same price data, but different methods of calculation, a number of different people could come up with a number of markedly different indices. The challenge, therefore, when seeking to construct an index is to know which method is best for the problem at hand and to represent equitably (in one figure) the general trend of price differences in separate locations. To illustrate this point, let us take a simple price survey comparing two fictional cities, “Mumbai” and “Delhi.”

 Mumbai Delhi Bread (1kg) 1.00 1.25 Potatoes (1kg) 3.00 2.00 Coffee (1kg) 2.50 1.75 Sugar (1kg) 1.00 1.75 TOTAL 7.50 6.75

Assuming we give equal weight to each of the products, which of the two towns deserves the higher cost of living index number? The answer is: it all depends on how the calculation is made.

1) Mumbai is more expensive if we simply add up the prices of the four items in the index and compare the two cities on that basis.

2) Delhi, however, is more expensive when we use Mumbai as a base city and calculate an index based on the average of relative prices in the two cities:

 Mumbai Delhi Bread 100 125 Potatoes 100 67 Coffee 100 70 Sugar 100 175 Index 100 109

However, if the same calculation is done with Delhi serving as a base city, Mumbai becomes the more expensive city:

 Delhi Mumbai Bread 100 80 Potatoes 100 150 Coffee 100 143 Sugar 100 57 Index 100 107.50

Thus with the standard price-relatives calculation we can end up in the paradoxical situation where each city is more expensive than the other.

3) Using a different method, both Delhi and Mumbai would have the same index number, ie 100, and neither would be considered more expensive than the other. Such a calculation would be made according to a well-established statistical formula that takes prices in both cities, makes an average of them, and uses this average as the basis for the index comparison. This formula, adopted by the Economist Intelligence Unit for its indices, has some distinct advantages over the standard price-relatives calculation described in Step 2 above. With the EIU formula, for example, the paradoxical situation of the two cities being more expensive than each other cannot arise: if city A = 100 and city B = 110, then this relationship is maintained, even if city B is used as a base (when B = 100 then A = 91). In other words, the EIU indices are reversible. This property ensures that the cost of living allowances established with the aid of the indices are consistent in that executives transferred from city A to B can be dealt with on the same footing as those transferred from city B to A. In addition, the indices are nearly circular. This means that the relationship between any three cities is maintained regardless of which of the cities is used as a base with which to compare the other two. This logical inter-relationship is important in assuring equitable cost of living compensation as executives are transferred from location to location.

The index formula. The index is based on the arithmetic mean of price levels in the two selected cities. In order to calculate the index for the two hypothetical cities examined on the previous page, we must first calculate the average price of each item:

 Mumbai Delhi Average price Bread 1.00 1.25 1.125 Potatoes 3.00 2.00 2.500 Coffee 2.50 1.75 2.125 Sugar 1.00 1.75 1.375

Next we compare prices in each town to these average prices:

 Average Mumbai Delhi Bread 100 89 111 Potatoes 100 120 80 Coffee 100 118 82 Sugar 100 73 127 General Index 100 100 100

As we can see the relationship between Mumbai and Delhi prices remains intact: bread is still 25% more expensive in Delhi, potatoes are still 50% more expensive in Mumbai. If we want to compare Mumbai as a base city to Delhi, we must divide Delhi’s index by that of Mumbai and multiply by 100. The result is 100. If we reverse the operation and use Delhi as base, the result is also 100. The two cities are equally expensive.