Prices, location and spread
Prices, location and spread

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Prices, location and spread

Exercises on Section 5

The following exercises provide extra practice on the topics covered in Section 5.

Exercise 10 Calculating the RPI for February 2012

Find the value of the RPI in February 2012, using the data in the table below. The value of the RPI in January 2012 was 238.0.

Table 16 Calculating the RPI for February 2012

GroupPrice ratio for February 2012 relative to January 2012: r2012 weights: wPrice ratio times weight: r w

Food and catering

1.009

161

Alcohol and tobacco

1.005

85

Housing and household expenditure

1.003

412

Personal expenditure

1.040

84

Travel and leisure

1.005

258

Total

(Source: Office for National Statistics)

Discussion

sum w =1000 comma sum r w=1007.760 comma
all minus item price ratio = fraction sum r w over sum w end = fraction 1007 .760 over 1000 end =1.007760 comma
value of RPI in February 2012 =238.0 times 1.007760 =239.84688 simeq 239.8.

(The published index was 239.9. Again, the difference between this and your calculated value is because the ONS statisticians used more accuracy in their intermediate calculations.)

Exercise 11 Annual inflation rates and the purchasing power of the pound

For each of the following months, use Table 15 (in Subsection 5.3) to calculate the annual inflation rate given by the RPI and to calculate the purchasing power of the pound (in pence) compared to one year previously.

(a) October 2010

Discussion

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

fraction 225 .8 over 216 .0 end simeq 1.045 comma

so the annual inflation rate is 4.5%.

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

fraction 216 .0 over 225 .8 end times 100 p simeq 96 p .

(b) January 2011

Discussion

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

fraction 229 .0 over 217 .9 end simeq 1.051 comma

so the annual inflation rate is 5.1%.

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

fraction 217 .9 over 229 .0 end times 100 p simeq 95 p .

Exercise 12 Index-linking another pension

An index-linked pension (linked to the RPI) was £800 per month in April 2010. How much should it be in April 2011? (Again, use the RPI values in Table 15.)

Discussion

The RPI for April 2011 was 234.4 and the RPI for April 2010 was 222.8. So in April 2011, the pension should be

pounds 800 times fraction 234 .4 over 222 .8 end simeq pounds 842 per month .
M140_1

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