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# 5.3 Using the price indices

The RPI and CPI are intended to help measure price changes, so we shall start this section by describing how to use them for this purpose.

## Example 23 A news report on inflation

The BBC News website reported (20 March 2012) ‘UK inflation rate falls to 3.4% in February’. What does that actually mean?

The rest of the BBC article makes it clear that this ‘inflation’ figure was based on the CPI rather than the RPI, but its meaning is still not obvious. What is usually meant in situations like this is the following.

### The annual rate of inflation

In the UK, the (annual) rate of inflation is the percentage increase in the value of the CPI (or the RPI) compared to one year earlier.

(In this course, it will always be made clear whether you should use the CPI or the RPI in contexts like this.)

The annual rate of inflation is sometimes called the year-on-year rate of inflation.

In February 2012, the CPI was 121.8. Exactly a year earlier, in February 2011, the CPI was 117.8. The ratio of these two values is

So the value of the CPI in February 2012 was 3.4% higher than in the previous February. That is the source of the number in the BBC headline.

## Activity 23 The annual inflation rate in February 2012

In February 2012, the RPI was 239.9. Exactly a year earlier, in February 2011, the RPI was 231.3. Calculate the annual inflation rate for February 2012, based on the RPI.

### Discussion

The ratio of the two RPI values is

or 103.7%. Therefore the annual inflation rate, based on the RPI was 3.7%. (Note that this is slightly higher than the annual inflation rate measured using the CPI.)

The fact that the inflation rates that are generally reported in the media relate to price increases (as measured in a price index) over a whole year means that one has to be careful in interpreting the figures, in several ways.

• Media reports might say that ‘inflation is falling’, but this does not mean that prices are falling. It simply means that the annual inflation rate is less than it was the previous month. So when the BBC headline said that the (annual) inflation rate had fallen to 3.4% in February 2012, it meant that the February 2012 rate was smaller than the January 2012 rate (which was 3.6%). Prices were still rising, but not quite so quickly.

• The change in price levels over one month may be, and indeed usually is, considerably different from the annual inflation rate. For instance, prices actually fell between December 2011 and January 2012: the CPI was 121.7 in December 2011 and 121.1 in January 2012. (Prices in the UK usually fall between December and January in the UK, as Christmas shopping ends and the January sales begin.) But the annual inflation rate for January 2012, measured by the CPI, was 3.6%.

• The effect of a single major cause of increased prices can persist in the annual inflation rates long after the prices originally increased. For instance, the standard rate of value added tax (VAT) in the UK went up from 17.5% to 20% at the start of January 2011, causing a one-off increase in the price (to consumers) of many goods and services. This showed up in the annual inflation rate for January 2011, where prices were 4.0% higher than a year earlier. Moreover, the annual inflation rate for every other month in 2011 was also affected by the VAT increase, because in each case the CPI was being compared to the CPI in the corresponding month in 2010, before the VAT increase.

Another important use of price indices like the RPI and CPI is for index-linking. This is used for such things as savings and pensions, as a means of safeguarding the value of money held or received in these forms.

## Index-linking an amount

To index-link any amount of money, the amount in question is multiplied by the same ratio as the change in the value of the price index. Another term for this process is indexation.

It is important to stress the notion of ratio in index-linking, because it is only by calculating the ratio of two indices that you can get an accurate measure of how prices have increased. For example, an increase in the RPI from 100 to 200 represents a 100% increase in price, whereas a further RPI increase from 200 to 300 represents only a further 50% increase in price.

## Example 24 Index-linking a pension

The value of the RPI for February 2012 was 239.9 whereas the corresponding figure for February 2011 was 231.3. So an index-linked pension that was, say, £450 per month in February 2011, would be increased to

for February 2012. The reason for index-linking the pension in this way is that the increased pension would buy the same amount of goods or services in February 2012 as the original pension bought in February 2011 – that is, it should have the same purchasing power.

Pensions can be, and indeed increasingly are, index-linked using the CPI rather than the RPI.

## Activity 24 Index-linking a pension using the CPI

An index-linked pension was £120 per week in November 2010. It is index-linked using the CPI. How much should the pension be per week in November 2011? The value of the CPI was 115.6 in November 2010 and 121.2 in November 2011.

### Discussion

The weekly amount in November 2011 should be

This principle leads to another much-quoted figure which can be calculated directly from the RPI: the purchasing power of the pound. (This is the purchasing power of the pound within this country, not its purchasing power abroad; the latter is a distinct and far more complicated concept.) The purchasing power of the pound measures how much a consumer can buy with a fixed amount of money at one point of time compared with another point of time.

The word compared here is again important; it makes sense only to talk about the purchasing power of the pound at one time compared with another. For example, if £1 worth of goods would have cost only 60p four years ago, then we say that the purchasing power of the pound is only 60p compared with four years earlier.

## Purchasing power of the pound

The purchasing power (in pence) of the pound at date compared with date is

The purchasing power of the pound could be calculated using the CPI instead, though the figures published by the Office for National Statistics do happen to use the RPI.

## Example 25 Calculating the purchasing power of the pound

(a)

The purchasing power of the pound in February 2012 compared with February 2011 was

(231.3 and 239.9 are the two RPI values given in Activity 23.)

We round this to give 96p.

(b)

The purchasing power of the pound in February 2012 compared with the base date, January 1987, was

(At the base date, the value of the RPI is 100 by definition.)

This is, after rounding, 42p.

## Activity 25 Annual inflation and the purchasing power of the pound

Table 15 Values of the RPI from January 2009 to December 2011
Month 2009 2010 2011

January

210.1

217.9

229.0

February

211.4

219.2

231.3

March

211.3

220.7

232.5

April

211.5

222.8

234.4

May

212.8

223.6

235.2

June

213.4

224.1

235.2

July

213.4

223.6

234.7

August

214.4

224.5

236.1

September

215.3

225.3

237.9

October

216.0

225.8

238.0

November

216.6

226.8

238.5

December

218.0

228.4

239.4

(Source: Office for National Statistics)

For each of the following months, use the values of the RPI in Table 15 to calculate the annual inflation rate (based on the RPI) and to calculate the purchasing power of the pound (in pence) compared to one year previously.

(a) May 2010

### Discussion

For May 2010, the ratio of the value of the RPI to its value one year earlier is

so the annual inflation rate is 5.1%.

The purchasing power of the pound compared to one year previously is

(b) October 2011

### Discussion

For October 2011, the ratio of the value of the RPI to its value one year earlier is

so the annual inflation rate is 5.4%.

The purchasing power of the pound compared to one year previously is

(c) March 2011

### Discussion

For March 2011, the ratio of the value of the RPI to its value one year earlier is

so the annual inflation rate is 5.3%.

The purchasing power of the pound compared to one year previously is

You have seen that the RPI can be used as a way of updating the value of a pension to take account of general increases in prices (index-linking). The RPI is used in other similar ways, for instance to update the levels of some other state benefits and investments. But the CPI could be used for these purposes.

Why are there two different indices? Let’s look at how this arose. As well as its use for index-linking, which is basically to compensate for price changes, the RPI previously played an important role in the management of the UK economy generally. The government sets targets for the rate of inflation, and the Bank of England Monetary Policy Committee adjusts interest rates to try to achieve these targets. Until the end of 2003, these inflation targets were based on the RPI, or to be precise, on another price index called RPIX which is similar to the RPI but omits owner-occupiers’ mortgage interest payments from the calculations. (There are good economic reasons for this omission, to do with the fact that in many ways the purchase of a house has the character of a long-term investment, unlike the purchase of, say, a bag of potatoes.) From 2004, the inflation targets have instead been set in terms of the CPI. The CPI is calculated in a way that matches similar inflation measures in other countries of the European Union. (So it can be used for international comparisons.)

In terms of general principles, though, and also in terms of most of the details of how the indices are calculated, the differences between the RPI and CPI are not actually very great. As mentioned in Subsection 5.1, the CPI reflects the spending of a wider population than the RPI. Partly because of this, there are certain items (e.g. university accommodation fees) that are included in the CPI but not the RPI. There are also certain items that are included in the RPI but not the CPI, notably some owner-occupiers’ housing costs such as mortgage interest payments and house-building insurance. Finally, the CPI uses a different method to the RPI for combining individual price measurements.

Because of these differences, inflation as measured by the CPI tends usually to be rather lower than that measured by the RPI. In Example 23, you saw that the annual inflation rate in February 2012 as measured by the CPI was 3.4%. The annual inflation rate in the same month, as measured by the RPI, was 3.7%, as you saw in Activity 23. The RPI continues to be calculated and published, and to be used to index-link payments such as savings rates and some pensions. (Arguably it is rather strange to use the RPI to index pensions, given that (as was said at the beginning of Subsection 5.1) the RPI omits the expenditure of pensioner households.) However, there are reasons why the RPI is more appropriate than the CPI for some such purposes, and it seems likely to continue in use for a long time. Furthermore, changes in how index-linking is done can be politically very controversial. For instance, in 2010, the UK government announced that in future, public sector pensions would be index-linked to the CPI rather than the RPI, which caused major complaints from those affected (because inflation as measured by the CPI is usually lower than that measured using the RPI, so pensions will not increase so much in money terms).

You might be asking yourself which is the ‘correct’ measure of inflation – RPI, CPI, or something else entirely. There is no such thing as a single ‘correct’ measure. Different measures are appropriate for different purposes. That’s why it is important to understand just what is being measured and how.