Measuring Price Change - Percentage Change

Percentage Change > Explanation

The change in an index number time series from one period to another is expressed as a percentage of its value in the first period (percentage change).

[EXPAND]

Working with Percentage Change

\textsf{Percent change} = \frac{\textsf{Change in }X}{\textsf{Original value of } X} \times 100

Can be written as:

\%\textsf{change} = \frac{\textsf{Final} - \textsf{Initial}}{\textsf{Initial}} \times 100

The changes measured by the Consumers Price Index are usually expressed as percentages. The percentage changes most frequently calculated and published are:

The change between the current period and previous period
The change between the current period and the same period of the previous year.

If there has been an increase from one period to the next then the percentage change will be positive. If there has been a decrease from one period to the next then the percentage change will be negative.

In the examples and exercises below the final answers are always to one decimal place.

EXAMPLES

a) If the CPI for the September 1998 quarter was 1009 and that for the June 1998 quarter is 1004 then the quarterly percentage change in the index between the June and September 1998 quarters is calculated as follows:

- 1004

× = 0.498 percent

An increase of 0.5%

b) If the CPI for the December 1997 quarter is 997 and that for the December 1998 quarter is 1001 then the annual percentage change for the year from the December 1997 to December 1998 quarter is:

× = 0.4 percent

An increase of 0.4%

c) If the CPI for the December 2012 quarter is 1439 and that for the December 2013 quarter is 1260 then the annual percentage change for the year from the December 2012 to December 2013 quarter is:

× = -12.4 percent

A decrease of 12.4%

EXERCISES

Tonga

The button below reveals a section of a table from the Tongan Statistics Office (view the full table here). Use this data to answer the questions below.
The Consumer Price Index for the Reference Period: October 2010 = 100.

View Table

All Items
Mar 13	106.3
Apr 13	107.1
May 13	107.0
Jun 13	106.9
Jul 13	106.4
Aug 13	106.6
Sep 13	106.8
Oct 13	106.9
Nov 13	105.9
Dec 13	107.1
Jan 14	109.5
Feb 14	110.1
Mar 14	111.4
Food
Mar 13	108.4
Apr 13	109.5
May 13	109.1
Jun 13	110.1
Jul 13	108.8
Aug 13	108.0
Sep 13	108.1
Oct 13	108.5
Nov 13	106.6
Dec 13	109.3
Jan 14	112.8
Feb 14	114.0
Mar 14	116.5
Housing
Mar 13	100.0
Apr 13	100.6
May 13	100.6
Jun 13	100.6
Jul 13	101.3
Aug 13	101.2
Sep 13	101.2
Oct 13	101.2
Nov 13	101.4
Dec 13	101.4
Jan 14	101.4
Feb 14	101.6
Mar 14	101.6

EXERCISE A

Fill in the blank for the percentage change between the September and October months for all items.

- 106.8

106.8

× 100 = 0.09 percent

The missing value is 106.9. An increase of 0.1%

Check

EXERCISE B

The annual percentage change for the year from March 2013 to March 2014 for all items.

114 - 106.3

× 100 = 4.79 percent

The missing value is 106.3. An increase of 4.8%

Check

EXERCISE C

Calculate the percentage change between the February 2014 and March 2014 months for the Food Group and select whether this is an increase or decrease.

The answer is %

Check

EXERCISE D

Calculate the percentage change between the October 2013 and November 2013 months for the Food Group and select whether this is an increase or decrease.

The answer is %

Check

EXERCISE E

Calculate the annual percentage change for the year from March 2013 to March 2014 for the Housing Group and select whether this is an increase or decrease.

The answer is %

Check

NOTE

1. If we are given a percentage change and the initial value then the final value can be calculated using the formula:

\textsf{Final} = \textsf{Initial} + \textsf{Change} = (1 + \%\textsf{change}/100) \times \textsf{Initial}

EXAMPLE

The CPI for a group of items was 1171 in the December 2013 quarter. The price had increased by 0.6% by the March 2014 quarter. The CPI for the March 2014 quarter was

\textsf{Final} = (1 + 0.6/100) \times 1171 = 1.006 \times 1171 = 1178

2. If we are given a percentage change and the final value then the initial value can be calculated using the formula:

\frac{\textsf{Final}}{100\% + \%\textsf{change}/100}

EXAMPLE

The CPI for a group of items was 1253 in the March 2014 quarter. The price had decreased by -0.56% from the December 2013 quarter. The CPI for the December 2013 quarter was

\begin{aligned} &= \frac{1253}{(1-0.56/100)} \\ &= \frac{1253}{0.9944} \\ &= 1260 \\ \end{aligned}

In the following exercises the final answer should be to one decimal place.

EXERCISE F

The index number for one month is 112 and there is an increase of 4% the next month. What is the index number for this month?

112 × (1 + 0.04) = 112 × 1.04 =

The correct answer is

Check

EXERCISE G

There is an increase in the index number from one month to the next of 2.8%. The index number in the second month is 102.7. What is the index number in the first month?

= \frac{102.7}{(1 + 0.028)} = \frac{102.7}{1.028}

The correct answer is

Check

EXERCISE H

The index number for one month is 114.7 and there is a decrease of -3.7% the next month. What is the index number for this month?

= 114.7 \times (1 - 0.037) = 114.7 \times 0.963

The correct answer is

Check

END PERCENTAGE CHANGE

[COLLAPSE]