Monetary Policy - Inflation - Causes
Worksheet 4 - Measuring inflation - how inflated are prices?
The purpose of this worksheet is to look at the different measures of inflation and see what they mean. It also looks at how index numbers are calculated.
The main measure of inflation is now the Consumer Price Index (CPI). This became the official measure in December 2003. Prior to that, the government used the Retail Price Index (RPI). As the names suggest, they are both examples of an index, so the first stage of this worksheet is to look at index numbers.
What are index numbers?
Index numbers are used when it is necessary to show the AVERAGE change in a large number of variables. There are a number of particularly well known ones, some of which are announced on the news on a regular basis.
1. Fill in any examples of an index that you know of in the table below:
| Index | Shows changes in? |
|---|---|
An index number is usually started in a base year at a value of 100. It will usually say something like '1990=100' to indicate when the base year was. The number itself has no meaning and has no units. It is the changes in the number that are important. These changes are expressed in percentage terms around the base. For example:
| Year | Index |
|---|---|
| Year 1 | 100 |
| Year 2 | 120 |
| Year 3 | 150 |
Between year 1 and year 2, the index has increased by 20 from a base of 100. It has therefore increased by 20%. From year 2 to year 3, it has increased by 30, but this time it started from 120. It has therefore increased by a further 25% (divide the change of 30 by 150 and multiply by 100).
2. Try the following examples for yourself (remember Windows has a calculator in 'accessories'):
| Year | Consumer Price Index | Percentage change (inflation) |
|---|---|---|
| 1 | 100 | |
| 2 | 115 | |
| 3 | 140 | |
| 4 | 175 | |
| 5 | 190 |
Calculating index numbers
Let us now try an example of calculating an index number. Say we want to calculate inflation (a retail or consumer 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 change in each good.
3. The first one is filled in the table below - try the others:
| Product | Price - year 1 | Index - year 1 | Price - year 2 | Index - year 2 |
|---|---|---|---|---|
| Bread | 40p | 100 | 60p | 150* |
| Beer | 200p | 100 | 220p | |
| Toothbrushes | 100p | 100 | 75p | |
| Newspapers | 50p | 100 | 60p | |
| TOTAL | 400/4** | |||
| Overall index | 100 |
* The price has gone up by 50% and so the index goes from 100 to 150.
** We divide by the number of products to get the average change.
The change in the overall index is the average rate of inflation.
4. What was the rate of inflation between year 1 and 2 for these four products?
Weighted index numbers
The problem with the index we have calculated above, is that it treats each price change as being EQUALLY important. However, the products in the price index are clearly not equally important.
5. Fill in below roughly how much you think the average family would normally spend on each of the products over a year (at the prices given). In the last column work out what percentage of their total spending (on these four products) that represents:
| Product | Price | Total spending per year (£) | Proportion of total spending (%) |
|---|---|---|---|
| Bread | 40p | ||
| Beer | 200p | ||
| Toothbrushes | 100p | ||
| Newspapers | 50p | ||
| TOTAL | 100% |
What should probably be clear from this is that the average family spends 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.
6. In the table below, we have done this - see if you can finish off filling in the last column:
| Product | Weights | Price - year 1 | Index - year 1 | Weighted index - year 1 | Price - year 2 | Index - year 2 | Weighted index - year 2 |
|---|---|---|---|---|---|---|---|
| Bread | 4 | 40p | 100 | 400* | 60p | 150 | 600 |
| Beer | 3 | 200p | 100 | 300 | 220p | 110 | |
| Toothbrushes | 1 | 100p | 100 | 100 | 75p | 75 | |
| Newspapers | 50p | 100 | 200 | 60p | 120 | ||
| TOTAL | 10 | 1000/10** | |||||
| Overall weighted index | 100 |
* Each weighted index figure is worked out by multiplying the basic index by the weight.
** We divide the total of the weighted index by the total of the weights to get the average figure.
7. What is the rate of inflation according to the weighted index between years 1 and 2?
The figure should be very different from the original inflation figure. It should be considerably higher. This is because the most important products (the ones with the highest weights) went up in price the most. The effect of the price of toothbrushes falling on the overall index was reduced because they had a very small weight.
A weighted index gives a much better figure for inflation. After all, we wouldn't want changes in the prices of shoelaces, matches and soap to have the same effect on the Consumer Price Index as changes in the price of food, fuel and housing!
Retail Price Index
8. The RPI was the measure used to represent inflation prior to 2003. The government still calculates the RPI. There are also two other measures of the RPI, called RPIX and RPIY. Use the glossary to investigate what each of these measures is. Fill in the details below:
RPI
RPIX
RPIY
9. Which one of these measures is usually called the 'headline rate of inflation'?
10. Which one of these measures is usually called the 'underlying rate of inflation'?
11. If the underlying rate of inflation is below the headline figure, what may have happened?
12. Use the data section to find out the retail price index figures for inflation for the last 20 years. You will need to use the following variable:
- CZBH UK Retail prices all goods and services
| Year | Inflation (RPI) |
|---|---|
| 1984 | |
| 1985 | |
| 1986 | |
| 1987 | |
| 1988 | |
| 1989 | |
| 1990 | |
| 1991 | |
| 1992 | |
| 1993 | |
| 1994 | |
| 1995 | |
| 1996 | |
| 1997 | |
| 1998 | |
| 1999 | |
| 2000 | |
| 2001 | |
| 2002 | |
| 2003 |
13. Which periods saw the most rapid inflation over the last 20 years?
14. Go to this In the News article and identify the main differences between the CPI and the RPI
