Inflation, CPI & RPI (AQA Level 3 Mathematical Studies (Core Maths))

Revision Note

Jamie Wood

Expertise

Maths

Inflation

What is inflation?

  • Inflation is the increase in prices of goods and services over time

    • Deflation is when prices decrease over time

  • As inflation occurs, money is worth less than it was in the past

    • The same amount of money will now buy less, or has less "purchasing power"

  • For example:

    • In 1980 the average UK house price was £23 500

      • By 2000 it was £81 600

      • By 2020 it was £229 800

    • In 1980 the average price for a loaf of bread was 35 pence

      • By 2000 it was 52 pence

      • By 2020 it was 104 pence

  • The rate of inflation will be different for different products and services

    • This is partly due to different levels of supply and demand over time

  • Economists tend to agree that moderate, predictable inflation is a positive for an economy overall

    • Potential positives and negatives of inflation are summarised in the table below

Potential positives of Inflation

Potential negatives of Inflation

Reducing debt

As money is worth less, debt is reduced in real terms.

Reduced purchasing power

Less can be bought with the same amount of money, so quality of life may decrease if incomes do not increase.

Stimulating the economy

If inflation is predictable, there is incentive to make purchases sooner rather than later.
If people feel they have less money, they may strive to find ways of making more money.

Uncertainty and risk

High and/or unpredictable inflation can create uncertainty for businesses and consumers.
Businesses can struggle to plan and forecast for future costs.
Consumers may lack confidence to make purchases due to increasing prices.

Economic growth

Moderate inflation can be a sign of a growing economy. If consumer spending increases then businesses may raise prices.

Lower value from savings

Interest rates will often not keep up with inflation, so money in savings loses value over time.
This makes saving for long term goals harder, and may mean less money is invested.

What does "in real terms" mean?

  • The phrase "in real terms" is often used to take inflation into account

  • Consider a sum of money put into a savings account for 1 year with a 3% interest rate per year

    • If inflation is equal to 3% for that year, the money is worth the same in real terms

    • If inflation is more than 3% for that year, the money is worth less in real terms

    • If inflation is less than 3% for that year, the money is worth more in real terms

Worked Example

Laurinda has been given a pay rise for her work in the past year.
Her salary has changed from £28 000 to £28 840.
The rate of inflation nationally for the year was 3.9%.

Decide if Laurinda has been given a "real terms" pay rise, relative to inflation.

Calculate how much Laurinda's new salary should be, if it were to increase in-line with inflation

A multiplier of 1.039 can be used to find an increase of 3.9%

£28 000 × 1.039 = £29 092

This is greater than Laurinda's new salary

An alternate method is to calculate the percentage increase Laurinda has received

£28 840 ÷ £28 000 = 1.03

This is equivalent to a 3% increase, which is smaller than the 3.9% inflation

Laurinda has not been given a "real terms" pay rise

CPI & RPI

What is CPI?

  • CPI is the Consumer Price Index

  • CPI quantifies how prices are changing over time

  • The index considers the total cost of a "basket" of over 700 goods and services including:

    • Food and drink

    • Clothing and shoes

    • Electricity and gas

    • Furniture and household goods

    • Recreational activities

  • The items in the basket are reviewed regularly, as well as their weightings

    • The weightings consider how much an item should affect the index

      • This is informed by the proportion of money consumers spend on these items

    • E.g. Petrol has a higher weighting than tea

  • CPI is measured relative to a base year which is given an index of 100

    • For the table below, 2015 is the base year (CPI=100)

    • The table shows CPI each month during 2023

Month

CPI

Jan 2023

126.4

Feb 2023

127.9

Mar 2023

128.9

Apr 2023

130.4

May 2023

131.3

Jun 2023

131.5

Jul 2023

130.9

Aug 2023

131.3

Sep 2023

132.0

Oct 2023

132.0

Nov 2023

131.7

Dec 2023

132.2

  • The figure of 130.9 in July 2023 means that prices are 30.9% higher than in 2015 (the base year)

  • Values can also be compared to each other, rather than just the base year

    • This is how inflation is calculated between two points in time

    • Comparing CPI in January 2023 (126.4) to December 2023 (132.2)

      • 132.2 ÷ 126.4 = 1.045886076...

      • This means there was a 4.59% (3.s.f.) increase in CPI between January and December in 2023

  • CPI is also tracked over the long term

    • The graph below shows how the value of CPI has changed between 1989 and 2024, using 2015 as a base year

Graph of CPI from 1989 to 2024

What is RPI?

  • RPI is the Retail Price Index

  • RPI works in a very similar way to CPI, but is an older version and has now been replaced by CPI for most purposes

    • RPI is still used by the government for some purposes for historic reasons

    • E.g. There are pension structures that are linked with RPI

  • It also uses a basket of goods and services, but these are slightly different to those included for CPI

    • RPI includes several measures relating to housing costs

      • E.g. Mortgage interest payments, house depreciation, and buildings insurance

    • CPI includes university accommodation fees, stockbrokers' charges, and tuition fees for foreign students

      • None of these are included in RPI

  • RPI is usually expressed relative to January 1987 (the base year)

  • When both use the same base year, RPI is generally higher than CPI

  • There are other indexes which are also used to measure inflation

    • CPIH is similar to CPI but includes the costs of housing too

    • HPI is the House Price Index

Worked Example

The table below shows CPI (2015 = 100) and RPI (1987 = 100) for January 2021 and January 2022.

CPI (2015 = 100)

RPI (1987 = 100)

Jan 2021

109.0

294.6

Jan 2022

114.9

317.7

(a) Calculate the percentage change between January 2021 and January 2022 for each price index.

Find the 2022 value as a percentage of the 2021 value
Then write this as a percentage change

For CPI first

114.9 ÷ 109.0 = 1.05412844...
This is an increase of 5.412844...%

For RPI next

317.7 ÷ 294.6 = 1.078411405...
This is an increase of 7.8411405...%

CPI has increased by 5.41% (3.s.f)
RPI has increased by 7.84% (3.s.f)

(b) Explain why these two indexes do not show the same percentage change.

CPI and RPI use a different selection of goods and services to track
For example, RPI also includes housing costs

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Jamie Wood

Author: Jamie Wood

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.