Measuring Price Change

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).

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:

1. The change between the current period and previous period
2. 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.

 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%

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%

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.

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.

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.

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 =

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}
=