Using Index Numbers (AQA A Level Economics)

Revision Note

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Written by: Lorraine

Reviewed by: Steve Vorster

An Introduction to Index Numbers

An index number is a tool economists use to track changes in prices, quantities, or economic activity over time
- Index numbers are a way of standardising economic data so as to make easier comparisons between countries

How to create an index

Step 1: Select the items

Determine what items or variables you want to measure such as prices or other economic indicators

Step 2: Select the base period

Choose a base period against which all future observations will be compared
This period typically serves as the reference point with an index value of 100

Step 3: Data collection

Gather data for the selected items or variables over time, including during the base period

Step 4: Weighting (if applicable)

Assign weights to each item based on their relative importance
This step is common when constructing composite indices like the Consumer Price Index (CPI)

Step 5: Index calculation

Multiply each item's value by its weight (if applicable) and sum them up to obtain the index value for the current period

Step 6: Interpretation

Analyse the index values to understand trends or changes in the measured variables over time

Worked Example

An economy's GDP increased from $500 billion in 2017 to $540 billion in 2019. Using 2016 as the base year, establish the value of the index for GDP in 2018 and comment on its significance

Step 1: Calculate the Index for 2019 using the formula

$Index for 2019 = \frac{Real GDP 2019}{Real GDP base year} x 100 Index for 2019 = \frac{$ 540 billion}{$ 500 billion} x 100 Index for 2019 = 108$ [1 Mark]

Step 2: Comment on the value

The value of the GDP has increased by 8 percent in this period

Calculating Inflation

Inflation is the sustained increase in the general price level in an economy
The UK uses two inflation indices and each is calculated slightly differently
- The consumer price index (CPI)
- The retail price index (RPI)

Consumer Price Index (CPI)

The Consumer Price Index (CPI) measures changes in the average level of prices paid by households for goods and services during a specific time period

The Construction of the CPI

Steps	Explanation
Step 1: Selection of goods and services	A selection of 700 goods and services are selected as a typical ‘household basket’ each month. This is determined through household expenditure survey Each year, some goods and services exit the basket and new ones are added
Step 2: Collection of price data	Usually, on a monthly basis, prices for each item in the basket are collected from a 150 locations across the country The number of goods in the basket varies from country to country, e.g. the UK has 700 'goods' in their basket and Singapore has 4,800
Step 3: Weighting	Goods and services in the basket are weighted based on the proportion of household spending E.g. More money is spent on food than shoes, so shoes have a lower weight in the basket The price x weighting determines the final value of the good or service in the basket

Using the CPI to calculate inflation

The formula used to calculate the CPI is

$CPI = \frac{Cost of basket in current year}{Cost of basket in base year} \times 100$

Once the index number has been calculated, the percentage difference between two index numbers represents the rate of inflation

$Inflation rate = \frac{New CPI - Previous CPI}{Previous CPI} x 100$

Worked Example

Using the information in the table, calculate the inflation rate for 2021, if the price of the basket in the base year (2019) was $400 [3]

Household Item	Price 2020	Price 2021	Basket Weight	Cost of Basket in 2020 (Price xWeight)	Cost of Basket in 2021 (Price xWeight)
Housing, water, electricity, gas	950	1200	34%	323.00	408.00
Transport	250	325	11%	27.50	35.75
Food	500	620	9%	45.00	55.80
Recreation & culture	300	340	10%	30.00	34.00
Clothing & footwear	190	210	5%	9.50	10.50
				$435.00	$544.05

Step 1: Calculate the CPI for 2020

$CPI = \frac{Cost of basket 2020}{Cost of basket in base year} \times 100 CPI = \frac{435}{400} \times 100 CPI = 108.75$

Step 2: Calculate the CPI for 2021

$CPI = \frac{Cost of basket 2021}{Cost of basket in base year} \times 100 CPI = \frac{544.05}{400} \times 100 CPI = 136.01$

Step 3: Calculate the CPI for 2020

$Inflation rate = \frac{New CPI - Old CPI}{Old CPI} \times 100 Inflation rate = \frac{136.01 - 108.75}{108.75} \times 100 Inflation rate = 25.07 %$

3 marks for the correct answer or 1 mark for any correct working. The final answer should be rounded to 2 decimal places

The Retail Prices Index (RPI)

The retail price index (RPI) is calculated in exactly the same way as the CPI
- Certain goods and services that are excluded from the CPI are included with the RPI
  - These include council tax, mortgage interest payments, house depreciation, and other house purchasing costs such as estate agents fees
Due to the extra inclusions, inflation measured using the RPI is usually higher than the CPI
- This is mainly due to its sensitivity to interest rate changes, which affect mortgage interest
- It is argued that the RPI is a more accurate indication of a households inflation

Last updated: 14 October 2024

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Previous:Macroeconomic IndicatorsNext:Using National Income Data

Using Index Numbers (AQA A Level Economics)

Revision Note

An Introduction to Index Numbers

How to create an index

Step 1: Select the items

Step 2: Select the base period

Step 3: Data collection

Step 4: Weighting (if applicable)

Step 5: Index calculation

Step 6: Interpretation

Worked Example

Calculating Inflation

Consumer Price Index (CPI)

Using the CPI to calculate inflation

Worked Example

The Retail Prices Index (RPI)

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Author: Lorraine

Author: Steve Vorster