3.4 Adding up or weighting indices

The calculation of an index always involves a large number of different kinds of commodities, which may have very different meanings to different consumers or producers. For example, according to consumption data in the 2000=100 index, 1.8 per cent of total consumer spending goes on electricity and 0.04 per cent on carrots. The weight of electricity in the consumer price index is 45 times greater than that of carrots. In other words, price hikes in electricity have a much greater impact on household consumption expenditure than does an increase in the price of carrots. It is important that this is reflected in the way the index is calculated.

Commodities are usually weighted together in proportion to their base period weights. The weight of an individual commodity Vi₀ is calculated as follows:

The price of commodity i at base period ₀ (Pi₀) is multiplied by the quantity of commodity i consumed/produced at base period ₀ (Qi₀),

or Pi_{0 *} Qi₀ = Vi₀

For example,the weights of three commodities, coffee, petrol and a toothbrush, are obtained by multiplying the quantities of consumption of these commodities at base period by their prices at base period:

Once the weights have been computed, they can be used to establish the total index for these three commodities, or I_Y. In order to obtain this value, we need to know the price index and value weight for each commodity. The Table below lists the weights and indices for the three examples just mentioned. As we can see the weight for petrol is clearly higher than for other commodities. This means that price trends for petrol are of much greater consequence to the total index than those for toothbrushes.

The index is usually calculated by multiplying the index of each commodity by its weight and by adding together the values of all commodities (12 444). The sum is then divided by the sum of the commodities' weights (130):

I _Y =

I _Y =

     = 95.7

The price of our "shopping basket" in this example has dropped by 4.3 per cent from base period (95.7-100 = - 4.3).