Worksheet on Index Numbers (Tutor Version)

Step 1 - What Are Index Numbers?

It is important that students appreciate that a change in an index is taken from the previous value. This can be illustrated well by considering changes in the FTSE where it hasn't been rebased at all.

STEP 2 - Calculating Index Numbers

Let us now try an example of calculating an index number. Say we want to calculate inflation (a Retail Price Index) for four particular goods. We set the index for each good for the first year to 100 and then work out the percentage price change in each good. The first one is filled in in the table below - try the others:-

* We divide by the number of products to get the average change
@ The price has gone up by 50% and so the index goes from 100 to 150

The change in the overall index is the AVERAGE rate of inflation. What was the rate of inflation for these four products?

Inflation between year 1 and 2 ____13.75%___ ?

STEP 3 - Weighted Index Numbers

This section is to introduce students to the notion of weighting, and so initially gets them to try to appreciate that different items have a different level of importance in the average family's spending. The answers to the table can therefore vary significantly, but could perhaps form the basis for a discussion leading to how weighting in the RPI is actually done via the Family Expenditure Survey.

What should probably be clear from this is that the average family spend far less on toothbrushes than the other products. If this is the case then we should make the price change for toothbrushes have a much smaller overall effect on our price index. To do this we WEIGHT each price change to give it more or less importance in the overall index.

Here students need to multiply the index figure they worked out previously by the weight to get the weighted index in the last column, and then add those four figures up and divide by the sum of the weights (10) to get the overall index number.

* We divide the total of the weighted index by the total of the weights to get the average figure.
@ Each weighted index figure is worked out by multiplying the basic index by the weight.

Inflation between year 1 and 2 ___24.5%___ ?

This figure is very different from the original inflation figure and so can be used to illustrate how weighting changes can produce very different results.

Step 4 - Further Work on Index Numbers

Go to Penn World Data tables (http://www.bized.co.uk/dataserv/penndata/pennhome.htm) and scan through the variables available. How many of these are in index form. List them below:-

GDP relative to the US
Standard of Living Index

Now go to the ONS data (http://www.bized.co.uk/dataserv/ons/data/data.htm) and see how many of these are indices. Again, list them below:-

Retail Price Index - various different measures
GDP indices - various different measures
Purchasing power of the £
Retail sales - value and volume indices
All share index
Effective exchange rate